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Andrey Vyacheslavovich Yakovlev
Andrey Sergeevich Istomin
Dmitry Alexandrovich Zatuchny
Yury Grigorievich Shatrakov
Conditional
Function Control
of Aircraft
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Andrey Vyacheslavovich Yakovlev ·
Andrey Sergeevich Istomin ·
Dmitry Alexandrovich Zatuchny ·
Yury Grigorievich Shatrakov
Conditional Function Control
of Aircraft
Translated by Kudriashova Anna
Andrey Vyacheslavovich Yakovlev
Lipetsk, Russia
Andrey Sergeevich Istomin
Lipetsk, Russia
Dmitry Alexandrovich Zatuchny
Moscow, Russia
Yury Grigorievich Shatrakov
Saint Petersburg, Russia
ISSN 1869-1730
ISSN 1869-1749 (electronic)
Springer Aerospace Technology
ISBN 978-981-16-1058-5
ISBN 978-981-16-1059-2 (eBook)
https://doi.org/10.1007/978-981-16-1059-2
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
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Introduction
The problem of the safe transport of people and valuable goods is the main challenge
facing civil aviation. In current conditions, this problem has to be solved in conditions
of steadily increasing air traffic, when dangerous aircraft rapprochements began to
be recorded quite often in almost all regions of the world.
As a result, under such conditions, increased demands are placed on air traffic
control systems. Moreover, the probability of the risk of the dangerous approach
of aircraft or even their collision varies greatly depending on the stage and flight
conditions. It is necessary to take into account such possible specific types of aircraft
flights as flights under special conditions and exceptional cases in flight.
The purpose of this book is to describe the various built models, as well as modern
approaches to modeling various processes related to air traffic control based on the
correct use of an available information resource and following existing national and
international guidelines on air traffic management.
The book presents various models of the functioning of ATC information systems
and the construction of the best aircraft trajectories in terms of the absence of conflicts
between them.
Theoretical studies of air traffic control processes, presented in this book and
carried out using methods of probability theory and mathematical statistics, as well
as graph theory, are supported by statistical data for the analysis of some aircraft
accidents that have occurred.
The book presents the results obtained on the formation of a conflict-free flight
sequence of aircraft and the calculation of the parameters of the trajectory of the
aircraft maneuver in the event of a potential conflict, which can be used to make
recommendations to those responsible for air traffic services.
v
Contents
1 Analysis of the Problem Functioning Modeling Ergatic Air
Traffic Management Information System . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 State of the Security Problem and Traffic Management
Aircraft in the Area of the Aerodrome . . . . . . . . . . . . . . . . . . . . . . . .
1.2 A Modern Approach to the System-Dynamic Description
of an Ergatic System Functioning . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Theoretical-Multiple Model of Information Interaction
of Air Traffic Control Ergatic Information System Elements . . . . .
1.4 Presentation of Informational Interaction Ergatic Elements
in an Ergatic Information System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Logical–Linguistic Model for Choosing an Analytical
Model Parry Adverse Effects for Ergatic Elements . . . . . . . . . . . . .
1.6 Synthesis of a Procedural Model for Decision-Making
by an Ergatic Element in the Formation of an Aircraft Stream . . . .
1.7 The Method of Models for the Representation Synthesis
of Ergatic Elements in an Ergatic Information System . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 The Methodology of Functional Control of the Aircraft
and Parrying Special Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Analysis of Aircraft Failures and Malfunctions by Aviation
Systems and Groups of Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Decision-Making Model for Parrying Special Situations
Onboard an Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Methods of Functional Monitoring of the State
of the Aircraft and the Organization of Information Support
for Decision-Making in Special Situations . . . . . . . . . . . . . . . . . . . .
2.4 A Model of the Functioning of the Information Support
System for Decision-Making of the Aircraft Crew
in a Particular Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
7
13
20
25
30
36
41
43
43
45
51
54
56
vii
viii
Contents
3 The Architecture of Safety Flights System in the Airspace
of the Russian Federation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 The Role and Place of the Decision Support Information
System in the Structure of the Ergatic System “Aircraft–
Crew,” “Aircraft–Operator of an Unmanned Aerial Vehicle” . . . . .
3.2 Development of the Russian Federation Safety System
Architecture in the Airspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 A Model for the Optimal Placement of Critical Information
Entities in a Unified Safety System . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 The Concept of the Creation and Development of the Air
Navigation System of Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
57
59
62
70
75
4 A Mathematical Model for Constructing a Conflict-Free Flow
of Aircraft in the Zone of the Near Zone Officer Responsibility
(Circle Dispatcher) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1 Features of Information Support During the Formation
of the Flow of Aircraft During Approach . . . . . . . . . . . . . . . . . . . . . 77
4.2 Justification of the Need to Develop a Method and Models
for Organizing Information Support for the Near Zone
Officer (Circle Dispatcher) in the Detection and Resolution
of Potential Conflict Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Determination of the Space and Trajectories of the Aircraft
During Approach Conflict-Free Flow Formation . . . . . . . . . . . . . . . 84
4.4 A Model for Constructing an Aircraft Delay Maneuver
for a Given Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5 The Method of Organizing Information Support for the Near
Zone Officer (Circle Dispatcher) in the Detection
and Resolution of Potential Conflict Situations . . . . . . . . . . . . . . . . . 93
4.5.1 Description of the Method of Organizing Information
Support for the Officer of the Near Zone (Circle
Dispatcher) When Detecting and Resolving Potential
Conflict Situations Between Aircraft Landing . . . . . . . . . . . 93
4.5.2 Organization of Information Support for the Officer
of the Near Zone (Circle Dispatcher) When Forming
the Aircraft Queue Without Priority . . . . . . . . . . . . . . . . . . . . 97
4.5.3 Organization of Information Support for the Near
Zone Officer (Circle Dispatcher) in the Formation
of the Queue of Aircraft with a Priority of Service
at the Incoming Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Contents
ix
4.5.4 Organization of Information Support for the Officer
of the Near Zone (Circle Dispatcher) When Forming
a Queue of Aircraft with a Priority of Service
and Taking into Account Fuel Residues Onboard
Each Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Formation of Solutions for Optimizing the Activities
of the Landing Zone Officer (Landing Dispatcher) . . . . . . . . . . . . . . . .
5.1 Building a Model of a Guaranteed Aircraft Landing
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Defining a Set of Safe Approach Paths . . . . . . . . . . . . . . . . . . . . . . .
5.3 Determining the Optimal Safe Approach Path . . . . . . . . . . . . . . . . .
5.4 A Mathematical Model for Constructing an Optimal
Approach Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 The Principle of Maximum Performance in Solving
the Problem of Parrying Deviations from the Landing
Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Aircraft Movement Model During Approach
for Landing with a Decrease in Speed and Two Turns . . . .
5.4.3 Aircraft Double Turn Modeling . . . . . . . . . . . . . . . . . . . . . . .
5.5 Development of a Set of Problem-Oriented Programs
and Simulation Confidence Assessment . . . . . . . . . . . . . . . . . . . . . . .
5.6 Assessment of the Complexity of the Algorithmic Ensure
of the System Decision-Making Support for the Workstation
of the Landing Zone Officer (Landing Dispatcher) . . . . . . . . . . . . .
5.7 Construction of a Landing Approach Zone
and Recommendations to the Officer of the Landing
Zone (Landing Dispatcher) on Aircraft Control Using
the Decision Support System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 Software Development of a Decision Support System
for an Automated Workstation of a Landing Zone Officer
(Landing Dispatcher) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Reliability Assessment of the Model for Constructing
an Optimal Approach Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Development Of The Technology For The Operation Of Air
Traffic Control (Flight Control) Service Dispatchers During
Flights In Special Conditions And Individual Cases In Flight . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
105
105
107
108
112
112
117
121
123
128
129
130
133
137
143
Abbreviations
ACCID
ACFT
ACP
ADAS
ADF
AE
AE
AFCS
ANS
AT
AT
ATC
ATCS
ATIS
ATM IS
ATM
ATS
ATZ
AWS
BL
CA
CAS
CIS
CNS/ATM
CO
CPTY
CR
DB
DCN
DCS
DLRB
DMS FS
Aircraft accident
Aircraft
Aerodrome control point
Airborne data acquisition system
Automatic direction-finding equipment
Aircraft engine
Aviation Equipment
Aircraft flight control system
Air navigation system
Air traffic
Aviation technology
Air traffic control
Air traffic control system
Automatic terminal information service
Air traffic management information system
Air traffic management
Air traffic services
Aerodrome traffic zone
Automatized working station
Base leg
Civil aviation
Condition assessment system
The Commonwealth of Independent States
Communication, navigation, surveillance/Air Traffic Management
Control object
Capacity
Control radar
Database
Distributed computing network
Data collection system
Distant location radio beacon
Database management system of flight safety
xi
xii
DMS
DPS
DS
DS
DSIS
ECS
EE
EE
EEF
EIS
EP
ES
EU ATM
FAA
FD
FHS
FMT
FOA
FOO
FSRCA
GPI
HI
IAC
ICAO
ILS
IPS
KB
LH
LR
LRVA
MC
NID
NZO
PPI
RA
RBS
RDS
RF
RILS
RNL
RP
RS
RSA
RTS
SCHPS
Abbreviations
Decision-making system
Data processing system
Dangerous situation
Dynamic system
Decision support information system
Ergatic control system
Electronic equipment
Ergatic element
External environment functioning
Ergatic information system
Ergatic part
Ergatic system
Unified Air Traffic Management System
Federal Aviation Administration for Airspace Control
The final destination
Fuel and hydraulic systems
Flight management team
Flight operations assistant
Flight operations officer
Federal System of Reconnaissance and Control Over Airspace
Glide Path Indicator
Heading indicator
Interstate Aviation Committee
International Civil Aviation Organization
Instrument landing system
Information presentation system
Knowledge base
Landing heading
Landing radar
Landing radar visibility area
Means of communication
Navigation information display
Near zone officer
Plan position indicator
Regional airlines
Radar beacon system
Recommendation development system for a decision-making system
Russian Federation
Remote indicator of the landing system
Radio navigation landing system
Roll-in point
A radar system
Aircraft responder
Radio-technical support
State change prediction system
Abbreviations
SHORAN
SR
SR
SW
TC
TP
TWY
UAV
USW RS
WR
xiii
Short-range air navigation system
Secondary radar
Surveillance radar
Software
Transmission controls
Technical part
Taxiway
Unmanned aerial vehicle
Ultra-short wave radio stations
Weather radar
Chapter 1
Analysis of the Problem Functioning
Modeling Ergatic Air Traffic
Management Information System
1.1 State of the Security Problem and Traffic Management
Aircraft in the Area of the Aerodrome
The high accident rate in state aviation is one of the crucial factors affecting the
readiness of aviation to fulfill its mission and constituting a threat to the national
security of Russia. Over the past ten years, the total losses of all state aviation in
Russia amounted to more than 300 aircraft. The relative indicator (the number of
accidents per 100 thousand flight hours), which characterizes the accident rate for
30 years, is at the level of 4–5 accidents per 100 thousand flight hours. At that time,
as in the leading aviation powers, this figure is two or more times lower.
The solution to the problem of high accident rate in Russian aviation will ensure
reducing the risks of accidents, loss of human, natural, economic, and defense potentials; creation of conditions for sustainable development of state aviation; achievement of safety performance indicators corresponding to the level of advanced aviation
powers.
In the medium term, aviation accidents remain one of the most critical challenges
to the stable development and functioning of state aviation. Their manifestation will
inevitably lead to a further decrease in the motivation of Russian citizens for aviation
activities, including flight work, to a reduction in the combat readiness and combat
effectiveness of state aviation, as well as to a decrease in the export potential of
domestic aviation equipment.
The following disadvantages of the existing flight safety system contribute to this
state of affairs [1–4]:
• imperfect regulatory laws and regulations (incomplete, outdated, insufficiently
harmonized with each other and the regulatory framework in related fields);
• making decisions on the formation of ACFT in the absence of complete and
reliable information about the state of the elements of ATC, the features of their
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. V. Yakovlev et al., Conditional Function Control of Aircraft,
Springer Aerospace Technology,
https://doi.org/10.1007/978-981-16-1059-2_1
1
2
•
•
•
•
1 Analysis of the Problem Functioning Modeling Ergatic Air …
interaction in the process of organizing, preparing, and operating flights, and the
impact of negative influences;
potential interest conflict in the event of an accident (operating organizations—
suppliers of aviation equipment and supplies; regulatory and supervisory bodies—
operating organizations; federal executive bodies—regulatory and supervisory
bodies, etc.);
mismatch of allocated resources (material, technical, financial, administrative,
organizational, personnel, information) of the scale and complexity of the tasks
of ensuring flight safety;
«fuzziness» of the official effective state policy in ensuring field the safety of civil
aviation (CA);
outdated views on flight safety issues, the low culture of aviation personnel in the
field of flight safety, reluctance, or inability to adopt best practice experience that
has justified itself.
The reduction in accident rate requires different approaches and other program
activities that should be carried out ahead of the implementation of aviation
development programs [5–7].
With the beginning of the restructuring of economic relations, the volume of
CA production activity in all CIS member states has significantly decreased. The
financial situation of CA enterprises has become more complicated, which entailed
a reduction in its development and improvement. However, its importance as one
of the main modes of transport in the new conditions not only did not decrease but
also increased due to the increasingly developing trends of the globalization of the
economy and the expansion of interstate connections. The reduction in the volume
of work on the development and improvement of CA led not only to a slowdown
in scientific and technological progress but also to a deterioration in its technical
condition. A significant increase in tariffs for air transportation of passengers and
cargo has become one of the significant reasons for the reduction in the volume of
these flights in the last decade of the twentieth century. These negative consequences
manifested themselves to varying degrees in all CIS member states [2].
The necessary, to ensure flight safety and formation of aircraft (ACFT) flow, the
transmission of additional data on the secondary channel of aerodrome radar systems,
along with the determination of the aircraft coordinates with the required accuracy
and resolution, determines the trend of the widespread introduction of single-pulse
secondary radars soon, creating a basis for switching to the mode with an address
request.
What is important is the gradual cessation of the use of secondary radars using air
traffic control (ATC) (ATC-M) codes and a request frequency of 837.5 MHz and a
response of 740 MHz, and the transition to radar facilities that meet the requirements
of the International Civil Aviation Organization (ICAO) in parts of the RBS mode
with frequencies of 1030/1090 MHz. The transition to these frequencies, caused by
a conflict between mobile operators and ATC services, will lead to a decrease in the
resolution of radars and, as a result, to a decrease in the reliability of the information
used in the formation of aircraft flows in the aerodrome zone.
1.1 State of the Security Problem and Traffic Management Aircraft …
3
In general, the global trend of improving ATC equipment in the aerodrome zone
is associated with the transition to CNS/ATM technologies by introducing tools and
systems based on automatic-dependent monitoring and modern air-ground data lines.
The technical condition of equipping airborne centers and control points is characterized by insufficient, in modern conditions, implementation of data processing
tools, decision support, and can improve by automating the information processes
of the formation of aircraft flows in the airfield.
An additional factor that makes the problem more acute is the fact that the training
system for aviation personnel does not fully meet the needs of airlines. Work on
improving training programs for flight personnel, including the development of
actions in special flight conditions, is carried out at unacceptably low rates [6, 8, 9].
The relevance of solving the problem of improving the aviation safety of the
Russian Federation is due to factors presented in Fig. 1.1.
In recent years, along with economic growth in the Russian Federation, there
has been a significant increase in the number of aviation flights, at the same time a
significant increase in accident rate due to the obsolescence of the aircraft fleet, the
loss of skills in managing ACFT, flight personnel, and ATC specialists [1, 5].
Therefore, the main direction of improvement in this area is the introduction of
air traffic control ergatic information system (EIS) at aerodromes, providing for the
collection, processing, and display of airborne radar, radio direction finding, cartographic, meteorological, planning and other information, automation of planning
Non-decreasing aircraft accident amount
High relative accident rates
15-19 ACCID
per year
0,6 ACCID per 100
thousand flight
hours
Significant material damage
from accidents
More than 8 billion
rubles a year
High percentage of accidents
with a manifestation
«Human factor»
up to 60-65%
Fig. 1.1 Aviation safety level factors
4
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.2 Absolute aviation safety indicators for commercial aviation operators
processes, situation forecasting and support decision-making to prevent conflicts
due to the influence of negative factors and lack of time for adoption addressing ATC
specialists [10].
General characteristics of aircraft flight safety indicators in Russian airlines, their
absolute and relative indicators for the number of accidents are presented in Figs. 1.2
and 1.3.
Compared to 2017, in 2018, the number of accidents, disasters, and people killed
in them has increased, while the average values of these indicators of past years
exceeded. The increase in the number of accidents occurred with both aircraft and
commercial helicopters. The tendency in the number of accidents with aircraft of
operators that meet the requirements of the FAA (“N ACCID—Commercial air transportation operators”) and the requirements of only the FAA (“N ACCID—operators
of the aerial work”), as well as information on the number of accidents and disasters
(fatalities people) with commercial, civil aircraft in 2012–2018 are shown in Fig. 1.2
[5].
This state of flight safety requires urgent measures to prevent accidents.
Information on the relative safety indicators for commercial aircraft (the total
number of accidents and disasters per 100 thousand flying hours) for 2018, 2017,
and the ten years preceding it from 2007 to 2016 shown in Fig. 1.3. Comparison of the
relative indicators of aviation accident rate allows us to conclude that the measures
1.1 State of the Security Problem and Traffic Management Aircraft …
5
Fig. 1.3 Relative safety indicators of commercial aviation
taken to reduce the accident rate in the aviation industry of the Russian Federation
and the availability of reserves and opportunities for changing this situation based on
the experience of other countries and modern research in the field of ergatic systems
[2, 5, 8].
The distribution of the leading causes of accidents by specific gravity (G%) is
shown in Fig. 1.4.
Fig. 1.4 Distribution of causes aviation accidents by specific gravity in the period 2007–2018
6
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.5 Erroneous actions cause the distribution of crews in the period 2007–2018
Underlying the largest group of ACCID, causes with human victims (disasters) are
not only the errors of the aircraft crews related to shortcomings in their professional
activities and personal characteristics but also the negative influence of other reasons
related to the universal human factor that reduces the reliability and safety [2, 5, 8]
(Fig. 1.5).
Studies of a broad array of ACCID and incidents conducted at the Academy of
Civil Aviation showed that the failure rate of ACFT in flight is four times the error
rate of aircraft crews. The transition of special situations into catastrophic ones when
parrying aviation technology (AT) failures occurs three times more often due to errors
of aircraft crews.
The central role in the strategy for the prevention of aircraft accidents (ACCID)
should be played by the crews of the aircraft in collaboration with ATC specialists. It
is necessary to switch to a system for managing the quality of operational procedures
and personnel in aviation based on selected strategies, which for the most part, require
the improvement of everyday functions and management technology.
Analyzing the distribution of ACCID in groups, we can identify the primary
methods for managing the processes of ensuring flight safety, which include
methodological tools for influencing the following elements:
• optimization of the professional activities of aviation personnel (flight personnel,
air traffic control specialists, engineering and other personnel) according to the
criteria of reliability of their activities;
• optimization of systems (processes) management for ensuring safe operations
by the aviation administration (aviation management personnel) according to the
selected criteria for management quality systems;
1.1 State of the Security Problem and Traffic Management Aircraft …
7
• specialized professional training of aviation personnel, forming professionally
essential qualities of aviation specialists according to the criteria of reliability of
their activities.
Inquiries of ACCID by investigators of the International Aviation Committee
(IAC) showed that 48.5% of cases are directly related to deliberate violation by the
aircrew of flight rules, production, and flight discipline. Erroneous actions of the
aircraft crews during the piloting process at various stages of the flight occurred in
51.5% of cases, which were the cause of the development of ACCID [1, 2, 5, 11].
Errors in the professional activities of the crew members contributed to such factors
as:
• ergonomic imperfections in the layout of ACFT cabin equipment occurred in at
least 8.5% of cases;
• poor health and fatigue occurred in at least 8.5% of cases;
• little experience in flight operations took place in 6% of cases;
• low professional training took place at least in 11% of cases;
• violation of interaction of the aircrew with the experts of the ATM took place at
least 9.5% of cases;
• low psycho-emotional stability occurred in at least 31% of cases;
• disruption of the interaction between aircraft crew members occurred in at least
13.5% of cases;
• the imperfection of the regulatory documentation governing flight activity
occurred in at least 3.5% of cases [2, 11].
Therefore, the urgency of the problem is confirmed by a large number of accidents
occurring with ACFT from year to year. In almost all accident investigations, one of
the leading or related causes indicated:
• violations (errors) of ACFT crew members in the operation of aviation technology
(AT);
• insufficient level of training for ACFT crews related to actions in dangerous situations (DS), assessment of the degree of threat to the life of the crew and the use
of rescue equipment;
• untimely provision of qualified assistance to crews by air traffic controllers in the
event of a DS.
1.2 A Modern Approach to the System-Dynamic
Description of an Ergatic System Functioning
Based on the results of research on the theory of systems, it can be argued that any
system of general form S can be represented by a formal relation over the sets of
inputs U, outputs Y, and states X [9, 12–15]:
S ⊂ U × X × Y.
(1.1)
8
1 Analysis of the Problem Functioning Modeling Ergatic Air …
S
y
R
u
x
F
Fig. 1.6 Structural diagram of a dynamic system of a general form
If S is a dynamical system, then it is represented as [15, 16]:
= {R : U × X → Y };
(1.2)
= {F : U × X → X }.
(1.3)
where —system response (“input-state-output” display) [15, 16];
—state transition display (“input-state-state” display) [15, 16].
The structural diagram of a dynamic system of a general form shown in Fig. 1.6
[13–16].
The concepts of inputs and outputs of a dynamic system in the literature are
interpreted unambiguously [8, 9, 12–15].
Since these concepts are crucial in the synthesis of the EIS structure, their
definitions are given below.
Definition 1.1 Inputs U ∈ U refer to the totality of all impacts coming into the
system from its environment (external to the system of the environment in question)
[8, 9, 12–15].
Definition 1.2 The outputs Y ∈ Y are the totality of the effects that the system has
on the external environment [8, 9, 12–15].
Naturally, the interaction of the system with the environment can have the nature
of the exchange of matter, information, and (or) energy.
Different authors put different meanings into the concept of “the state of the
system.” The concept of a state is strictly defined in the work of Zadeh [8], where it
is considered as some (internal) characteristic of the system, the value of which at
the current moment determines the current value of the output quantity and affects its
future, and the state of the system, L. Zadeh, contains all the information about the
background of the system, which is necessary to find its future behavior. Therefore, it
is advisable to adopt the following definition of the concept of the state of a dynamic
system.
1.2 A Modern Approach to the System-Dynamic Description …
9
Definition 1.3 The state of a dynamic system is a set of its internal variables, the
values of which at the current moment contain the entire history of the system and
allow determining the current value of the output variables necessary to determine
its future behavior [8, 9, 12–15]. The “construction” of the state space should carried
out in compliance with four compatibility conditions imposed on the system’s functioning process: coverage, closure under truncation, uniqueness, and continuation
introduced in [8, 15] through bundles of components of the dynamic description,
which treated in it as actual trajectories in the space “input-state-output.”
If the compatibility conditions are met, the relations [8, 9, 12–15] can express
then the system dynamics described by the mappings (1.2) and (1.3):
Y (t) = (x(t0 ); U (t, t0 ));
(1.4)
x(t) = (x(t0 ); U (t, t0 ));
(1.5)
where Y (t)—is the value of the output variables at the current time;
x(t)—are the values of the state variables at the specified time;
U(t, t 0 )—is the interval of the input action on the time interval [t 0 , t];
t 0 , t—is the initial and current time instants, respectively.
Taking into account the continuation condition, relations (1.4), (1.5) can also be
written as:
x(t) = (x(t0 ); U (t, t0 ));
(1.6)
Y (t) = (x(t); U (t, t));
(1.7)
where U(t, t) − U(t)—the current input exposure value.
The dynamical system described by relations (1.6) and (1.7) is called a system,
according to L. Zadeh, who investigated its essential properties and conditions of
existence in [8, 15]. The structure of the system, according to L. Zadeh, is shown
in Fig. 1.6. Here, in contrast to the system shown in Fig. 1.7, the concept of a state
as a label of an “aggregate” representing the actual phase trajectory of a functioning
dynamic system is concretized.
x(t0)
u(t)
y(t)
x(t)
F
R
Fig. 1.7 Structure of a dynamical system according to L. Zadeh
10
1 Analysis of the Problem Functioning Modeling Ergatic Air …
x(t0)
u(t)
F
x(t)
y(t)
R
Fig. 1.8 Structure of a dynamical system according to R. Kalman
L. Zadeh, discussing systemic dynamics, emphasizes that when an input–output
pair determined by an input–output relation in the form of a differential or difference
equation, expressions of the form (1.4) are a general solution to this equation, and the
state x(t 0 ) is the initial condition for obtaining a single solution. In this case, when
constructing the state space, it is necessary to verify that the general solution has the
property of separation of the reaction.
R. Kalman argues that the values of the variables of the output of the system at
the current time do not depend on the values of the input variables at the same time
so that relations of the form describe the system dynamics:
x(t) = x(t0 ); U t, t Q ;
(1.8)
Y (t) = (x(t)).
(1.9)
Further refinement of the representation of dynamical systems by R. Kalman leads
to the structure shown in Fig. 1.8.
A characteristic feature of the system, according to R. Kalman, is the absence of
dependence of the values of the output variables at the current time on the values
of the input variables at a time. Therefore, the system, according to R. Kalman,
represents dynamical systems described by differential or difference equations, i.e.,
these systems are a particular case of systems, according to L. Zadeh.
Any “human–machine” system consists of parts interacting with each other and
the external environment—technical (TP) and ergatic (EP). The circuit shown in
Fig. 1.9 represents the functioning of such a system. The process of interaction
between TP and EP consists of the fact that the output of the EP is here the input of
the TP, and the output of the TP is the input to the EP.
Let us consider in more detail the decomposition of the “human–machine” system
into mechanical and ergatic parts.
At present, there are two approaches to the allocation of the “human–machine”
subsystems, forming it from the system. In the first case, the “human–machine”
system combines two fundamentally different subsystems—“purely human” and
“purely machine” subsystems. The structure of such a system is shown in Fig. 1.10,
where the following are indicated: CTS—control transfer bodies, CO—control
object; SPI—system of presenting information [8, 9, 12–15].
1.2 A Modern Approach to the System-Dynamic Description …
u
EP
u
y
u
11
y
ТP
yт
Fig. 1.9 General structure of the “human–machine” system
TP
CTS
y
u
CO
HO
SPI
Fig. 1.10 Structure of the human–machine system
In the second approach, it is considered appropriate to consider the human operator
together with the means of activity as a generalized system object “man—means of
activity” (Fig. 1.11).
In the future, the “human–technology” systems with the structure of Fig. 1.10
were called the “human–machine” system [8, 9, 12–15], and the “human–technology” systems with the structure (Fig. 1.11)—the ergatic system. Representation
of the “human–technology” system in the form of a “human–machine” system is
advisable when analyzing and identifying patterns of human–machine interaction,
in the implementation of professional functions. However, in conditions of practical
measurement of the studied parameters, the inputs available through the information acquisition systems and the outputs of the ergatic element are accessible to
measurement. Then the description of the human operator (the crew of the aircraft,
the operator of an unmanned aerial vehicle (UAV), air traffic control specialist), satisfying the system relations of the form (1.5), (1.6) or (1.7), (1.8), is possible only when
using the functional structure. The representation of the human–technology system
in the form of an ergatic system (Fig. 1.11) reflects the cybernetic approach to the
analysis of the functioning of such systems and is, in our opinion, more constructive
for practical use.
12
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.11 Ergatic system structure
The analysis of the subject area showed that almost all existing and promising
control systems for ACFT and ATC are built by analogy with the system shown in
Fig. 1.11. The structure of which does not highlight the information part is the basis
for decisions taken by specialists to parry the OS and create a conflict-free flow of
aircraft in the zone responsibility.
Thus, the analysis of the modeling problem of the ergatic air traffic control information system functioning is proved the actual practical problem—in ergatic information systems, with an increase in the intensity of information about aircraft, the
information load on the ergatic element increases, which leads to an increase in erroneous actions, especially in conditions negative impacts. The results of the analysis
allow us to draw the following main conclusions:
(1)
(2)
(3)
(4)
(5)
Any ergatic system at all periods of its life cycle can be considered as a component of the control system and is an object of control in it, and its effective
functioning can be ensured by a directed change in the values of the variables
of the state space of the ergatic system.
The existing systems to support the aircraft crew in the OS do not provide
sufficient information when developing failures of aircraft in the DS.
When uninformative failures develop onboard an aircraft, the crew is not notified or does not provide specific information on the necessary actions, which
significantly increases the time to identify the failure, including the loss of the
aircraft.
The central air traffic control systems are currently not information support
systems for air traffic control specialists, because they either do not adequately
assess the situation in the aerodrome area or do not have the means of such
assessment, which makes the development of ergatic air traffic information
systems in the aerodrome area urgent.
Improving the functioning efficiency of the ergatic systems “aircraft–crew”
(“aircraft–UAV operator”), “aircraft–crew-air traffic control specialist” can be
implemented based on the organization of an information support system.
1.2 A Modern Approach to the System-Dynamic Description …
(6)
(7)
(8)
13
The theory of system analysis and modeling of ergatic information systems
is in the development stage, manifested in the multiplicity of formulations of
the principles of the system approach, the ambiguity of interpretations of the
basic concepts, etc., which complicates their application and necessitates the
further development of the system theory of assessing the state and functioning
efficiency of ES.
The “natural” decomposition used in ES analysis does not have a rigorous
justification, leads to the ambiguity of structural representations of ergatic
systems as a combination of the ergatic, informational and technical parts and
complicates the analysis of ES, which necessitates the construction of rigorous
formal justifications of decomposition processes into components and analysis
procedures functional structures of ES.
The well-known models of operator activity are practically not applicable for
determining the parameters of the ergatic part of the ES due to the insecurity
in the process of the target functioning of the ES measuring and/or recording
the information used by these models with the necessary accuracy.
1.3 Theoretical-Multiple Model of Information Interaction
of Air Traffic Control Ergatic Information System
Elements
Imagine the process of information interaction of an ergatic information system in
the form of a set-theoretic model. For this, it is advisable to clarify this concept, to
determine its main differences from the information and ergatic system.
An information system is an organizational and technical set of means for
collecting, processing, and storing information necessary for presenting it in an
aggregated form for a decision-maker in the relevant subject field [10, 15, 17–19].
An ergatic system is a sophisticated control system, a component of which is a
human operator (a group of operators), a goal-oriented system that includes a person,
a technical device, an object of activity, and the environment in which a person is
located. It is a person who generates and transforms the goals of the functioning of
the ergatic system, reaches them with the help of a technical device [10, 15, 17–19].
An ergatic element is an object that represents an organic whole and acts
as a minimal unit with functional properties and the ability to manifest them
[10, 15, 17–19].
Ergatic information system is a class of ergatic systems that implement information functions in critical systems. Criticality lies in the potential danger of a violation
of their functional stability since a complete or partial failure of the system can lead
to significant economic, political, military, environmental, moral, or other damages
[10, 15, 17–19].
14
1 Analysis of the Problem Functioning Modeling Ergatic Air …
The functional stability of the EIS is a property of ergatic information systems,
which consists of the ability to implement specified information functions (information processing processes) in the context of adverse external and internal destabilizing
effects [10].
Ensuring the functional stability of the EIS is a problem whose solvability is
possible based on a systematic solution of a set of interconnected tasks for developing
theoretical foundations, methods, and models for representing dynamic systems. That
allows them to be decomposed, to build reliable models of the control object and
information processing processes, to make requirements for functional stability and
evaluate their implementation.
The principle of integrity requires considering the functioning of EIS as a single
whole. At the same time, the principle of hierarchy allows us to decompose it for
subsequent analysis of the resulting simpler systems compared to EIS.
Based on an analysis of the literature [10, 15, 17–19], which describes the Krohn–
Rhodes structural decomposition theorem and its application, the description of the
EIS is based on the fact that any finite state space can be represented so that the set of
phenomena observed on it triangulated. In addition, the coordinate actions must be
either (a) simple permutation groups closely related to the transformation semigroup
or (b) one of three possible transformation semigroups, the largest of which is of the
order of three.
In this case, the EIS is:
S = {U, X, Y, , },
(1.10)
where U—multiple EIS inputs; X—multiple states of EIS;
Y —multiple EIS outputs;
= {R: U × X → Y }—multiple EIS reactions (“input-state-output” display);
= {F: X × Y → Y }—multiple information functions of EIS (“input-state-state”
display).
The EIS described in the form (1.10) is presented as a plexus of simpler constructions. Denote by S, S E , S I , and S T description of the EIS as a whole, its ergatic,
technical, and informational parts, respectively. The connections between the parts
of the EIS and the external environment are presented in Fig. 1.12.
In Fig. 1.12, the set of inputs of the U E of the ergatic part contains two subsets:
U eiae —input actions coming from the external environment and U jia —and input
actions coming in S E from the information part of the EIS. The set of inputs U j of the
information part of the EIS also contains two subsets: U iia —the set of input actions
on S i and from the external environment and U ij —from the external environment
and S T from the ergatic part of the EIS [10, 20].
For a dynamical system with a description of the form (1.1)–(1.3), the conditions of
the Krohn–Rhodes theorem are satisfied, since in them, the family —characterizes
the internal behavior of the system, and the family of mappings —its external
behavior.
1.3 Theoretical-Multiple Model of Information Interaction …
15
Fig. 1.12 Structural model of EIS
Ergatic, technical, and informational parts of EIS have a different physical basis;
therefore, it is advisable to present it in the form:
X = X E × X I × XT .
(1.11)
To take into account the relations between the considered S i and S j systems with
each other and with the external environment (Fig. 2.1), we describe the structure of
the spaces of the inputs and outputs of the EIS and its parts.
The set of U E inputs of the ergatic part contains two subsets:
U Eia —input actions coming from the external environment and U jiia —input
actions coming to S j from the information part of the EIS. The set of inputs U j
of the information part of the EIS also contains two subsets: U iia —the set of input
actions on S i and from the external environment and U ij —the set of input actions
on S i from the ergatic part of the EIS. It follows that the sets of inputs of the ergatic
control system contain two subsets—U jia and U iia , and in the general case, these
subsets can be intersected. We partition the set U into the following disjoint subsets
U jo U io U jio U to U jto [8, 10, 20]:
U jio = U jBo ∩ Uiia ,
(1.12)
U jro = Uiia ∩ Utia ,
(1.13)
U js = U je / U je ∩ U jis ∩ U jts ,
(1.14)
Uio = Uiia / Uiia ∩ U jio ,
(1.15)
16
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Uto = Ute / Ute ∩ U jto .
(1.16)
It is clear that U js , U is, U ts are subsets of the set of inputs to the EIS, combining
the input effects from the external environment only on the ergatic, only on the
technical and only on the information parts, respectively, and U js —are the inputs
acting simultaneously on all parts of the EIS.
The set can now also be represented as the Cartesian product of the introduced
subsets [8, 10, 20]:
U = Ujs × Uis × Uts .
(1.17)
For the multiple inputs of the ergatic, technical, and information parts of the EIS,
you can write:
U E = U js × Uet × U jis ,
(1.18)
UI = Uis × Uie × U jis ,
(1.19)
UT = UTS × UTe × U jTS .
(1.20)
The set of outputs of the Y of the system S j can be represented as the Cartesian product of disjoint subsets of Y jv , Y jt , Y jtv characterizing the outputs of S j ,
which, respectively, come only to the output of the EIS, only to the input of S t ,
simultaneously to the output of the ECS and the input of S t :
Y j = Y je × Y jt × Y jte .
(1.21)
The set of outputs Y i of the system S i can also be represented as the Cartesian
product of three disjoint subsets of Y ie , Y ji, and Y jie characterizing the outputs of S i
that arrive only at the output of the EIS, only at the input S j , at the same time at the
output of the EIS and the input S j :
Yi = Yie × YiE × YiEe .
(1.22)
The following sets are also valid:
U jt = YiE × YiEe , UtE = Y ji × Y jie .
(1.23)
Then the space of the outputs of the EIS should be presented in the form of the
following Cartesian product:
Y = YEe × YEie × Yie × YiEe YEte × Yte × YtEe .
(1.24)
1.3 Theoretical-Multiple Model of Information Interaction …
17
An analysis of relations (1.11)–(1.24) shows that, when performing structural
decomposition of an EIS, its scheme along with the systems S j , S i and S t should
contain elements that ensure the formation of subsets according to the above
expressions, and these elements, as can be seen from (1.11)–(1.24), are triggers
[8, 10, 20].
Based on the analysis, the EIS structure intended for ATC in order to create a
conflict-free ACFT flow should include the following elements (Fig. 2.1):
• ergatic element (ergatic part—ATC specialist or a group of ATC specialists);
• technical element (technical part—radar, communication and radio-technical
support for aviation flights, means for displaying radar information);
• information element (the information part is the knowledge base about aircraft,
the subsystem for checking the accuracy of the information, the recognition of the
situation, the subsystem for creating a list of tasks and criteria for their solution, the
subsystem for substantiating decisions, the subsystem for ranking and choosing
alternatives).
The functioning of the ATC ergatic information system in the area of responsibility
of the flight management team depends directly on their actions, as well as on the
aircraft crews. In developing the model, we believe that the interaction between ATC
specialists and aircraft crews is ideally, and it represents external ATC systems in the
aerodrome impact zone [12, 16].
The tasks solved by the ATC EIS system can be divided into two classes: current
planning, i.e., programming the movement of ACFT, and control along the trajectories of the current plan, i.e., the formation of a stream of ACFT relative to program
trajectories. The tasks of the first-class relate to the deterministic tasks of constructing
optimal ACFT motion programs, complicated by restrictions on the phase coordinates, which are caused by the requirements for ensuring air traffic safety. In the
process of controlling the movement of ACFT relative to programmed trajectories,
it is necessary to evaluate the real trajectories and synthesize optimal control actions
on the ACFT. The equations describing the motion of a single ACFT, we write in the
following vector form [12]:
X C (t + 1) = F(X C (t), U (t)),
(1.25)
where X C = [x1C , x2C , . . . , x RC ]T , r = 1, . . . , R,—state vector of the model whose
elements are the parameters of the ACFT motion;
U C = [u 1C , . . . , u rC , . . . , u RC ]T , r = 1, . . . , R,—vector of control actions on
the ACFT;
F—in the general case, a nonlinear vector function that determines the dynamics
of the ATC system.
The linearized version of the model (1.25) has the form:
X C (t + 1) = B · X C (t) + U C (t),
(1.26)
18
1 Analysis of the Problem Functioning Modeling Ergatic Air …
where B—dimension matrix R × R.
It should be borne in mind that X C (t) ⊂ X (t). The vector of control actions U C (t)
is free, and its choice determines the solution of Eq. (1.25). Among the permissible
control actions U 1C (t) can always choose u 01C (t) in which a particular solution satisfies the boundary conditions and constraints. Such a particular solution is called
software, and if it provides an extremum by the criterion of optimality, then the
optimal programmed motion of the ACFT.
It should be noted that in many cases, some components of the vector X 0 are
known a priori, for example, schemes of standard approach and takeoff paths in
takeoff and landing zones, which significantly reduces the dimension of the problem
and simplifies its solution for a single ACFT. However, the task is complicated by
the fact that some restrictions on the coordinates are not constant, but are caused by
the movement of other ACFT located in the airfield:
xi − x j ≥ M1 ; i j = 1, N ; i = j,
(1.27)
where
—vector of spatial separation norms (separation standards)
in the longitudinal, lateral, and vertical directions.
(1.27) must be satisfied for intersecting time intervals [t0i , tki ] ∩
Constraints
t0 j , tk j = 0 all ACFT for which movement programs are being built. The domain of
definition of Eq. (1.25) imposes restrictions on the vector of control actions U BC (t)
by the flight performance of ACFT and the coordinates due to spatial restrictions in
the area [12]:
|u| ≤ u g ; |x| ≤ x g ,
(1.28)
where vector components u g and x g —given positive numbers or functions.
From the analysis of the literature [3, 10, 12], the most frequently used optimality
criterion is to minimize the time spent by ACFT in the airfield:
JT =
K
ti → min,
(1.29)
i=1
where ti —time determining delays in the formation of control actions in the aerodrome zone; K—the number of options for actions implemented in the formation of
control actions in the airfield.
The problem of minimizing functional (1.29) is called the optimal performance
problem. The problem of optimal performance concerning the ECS ATC in the area
of the aerodrome was considered in some works [12, 21]. With a constant flight
speed and the absence of wind, the optimal trajectory for planar motion consists of a
1.3 Theoretical-Multiple Model of Information Interaction …
19
combination of rectilinear sections and the arcs of circles of the minimum allowable
radius that are associated with them. The functioning of the ECS ATC concerning
the research objective is a composition of the effects on ACFT of various levels of
the system [12, 21].
In the process of forming the flow of ACFT, ATC specialists form “strategic” and
“operational” control actions on the ACFT flow. The “strategic” impact is aimed at
achieving the goal of the system’s functioning during long-term planning and is the
preparation and coordination of a planned flight table for a given time. “Operational”
control action contains a time-ordered sequence of ATC specialist’s actions, the result
of which ensures achievement of the set goal in the period [0; T ] and has the form
[12, 21]:
U (t) =
m
Y {u i (t)}, U (t) ∈ .
(1.30)
i=1
where U (t)—“operational” control action on the observed time interval [0; T ];
u i (t)—control action generated at the ith level of ATC system;
Y {u i (t)}—composition of control actions of various levels of ATC system;
—area describing the goal.
The task of creating a conflict-free aircraft flow, which is to achieve the extreme
value of the efficiency criterion Z, is a linear function of the controlled parameters
of the system, with limited resources [10, 12, 15, 17, 19, 21]. The task is aimed
at minimizing the time spent by the flow of aircraft in the area of responsibility of
the flight management team. In this case, the following rules for the functioning of
ergatic elements and restrictions for maintaining safety should be highlighted:
(1)
(2)
(3)
(4)
if the aircraft that appears in the zone of responsibility of the circle dispatcher
(at the point of entry to the route) has a longitudinal separation of ≥20 km to the
aircraft in front, then the movement model is: maneuver along the established
route before landing;
if the aircraft appearing in the zone of responsibility of the circle dispatcher
(at the entrance to the zone of responsibility of the landing dispatcher) has a
longitudinal separation interval ≥10 km to the aircraft in front, then there is a
movement model: maneuver along the established route to the landing;
if the value of the longitudinal separation interval does not satisfy rules 1 and
2, then there is a movement model: maneuver in the direction to increase the
time before landing;
if the value of the interval of the longitudinal separation on final straight:
(a)
(b)
(c)
between the same type of aircraft (with a probability of 0.95) is ≥8 km;
between different types of aircraft, moreover, if the front is a higher-speed
aircraft and the rear is a lower-speed aircraft, is ≥5 km;
between different types of aircraft, and, if the front less than the speed
of the aircraft, and behind more high-speed aircraft is ≥12 km;
20
1 Analysis of the Problem Functioning Modeling Ergatic Air …
(d)
(5)
then there is a motion model: a straight flight to the entrance to the glide
path;
if the value of the longitudinal separation interval on the pre-landing a straight
line does not satisfy rule 4, and then there is a motion model: maneuver in the
direction until the error is corrected.
Limitations due to the structure of the aerodrome zone and aircraft flight
performance:
• restrictions that determine the structure of the aerodrome zone and possible trajectories of ACFT approach, which are disjoint trajectories in the form of a convex
polygon with control points (determined by the instructions of the aerodrome);
• restrictions on the maneuverability of the aircraft (speed—at the entrance to the
aerodrome zone 550–600 km/h; at the entrance to the pre-seat line 270–320 km/h;
according to the roll—values 5◦ , 10◦ , 15◦ , 30◦ , 45◦ ).
Limitations due to the following factors [12, 21]:
•
•
•
•
limited fuel supply onboard ACFT;
limited maneuverability characteristics of ACFT (ACFT roll, speed, etc.);
height restrictions within the boundaries of many maneuvers for ACFT time delay;
restrictions on the angle of the lapel of ACFT from the original path.
When solving the problem for specific cases, we obtain impacts based on the
determination of the delay time and maneuver for ACFT, at which the total flight time
in the airfield is minimized by the criterion (1.29), which are the basis for organizing
information support for ATC specialists in the formation of a conflict-free ACFT
flow.
1.4 Presentation of Informational Interaction Ergatic
Elements in an Ergatic Information System
Let be Z a global problem solved by air traffic controllers, determining the purpose
of the system as a whole and being at the top level of the hierarchy, i.e., is the root
of the tree D z of tasks solved by the ergatic element in the EIS.
It is advisable to determine the place of an arbitrary task in the task tree by the
number of the hierarchy level (decomposition), the value of which varies in the range
[0, U z ], i.e., u z = 0, K z . The task Z is at the level of decomposition u z = 0. At the
next level of decomposition u z = 1, many individual tasks are placed, the solution
of which ensures the achievement of the goal of ATC specialists, etc. The global task
and tasks of the first level can be represented as follows:
Z = {Z i1 , i1 = 1, I 1};
(1.31)
1.4 Presentation of Informational Interaction Ergatic Elements …
21
Fig. 1.13 The tree of tasks solved by air traffic control specialists
Z i1 = {Z i1,i2i1 , i1 = 1, I 1, i2i1 = 1, I 2i1 }.
(1.32)
Figure 1.13 shows a general view of the task tree D z solved by ATC specialists.
An analysis of the task tree shows that it describes the subordination of functional
units that provide the solution to target tasks. To clarify the relationships of the
subordinate nodes of the tree is advisable to use the mathematical diagram of their
information interaction, i.e., morphology of the system (morphology of the solution
of the problem).
z
In describing the morphology of solving an arbitrary target problem Z i1,i2i1 ,...,iu ...i2
i1
z
the process of solving, it can be represented as an abstract system Ri1,i2
,
z
i1 ,...,iu
z
which is described by the relation (1.32) over the input spaces X i1,i2
z
i1 ,...,iu
output
z
Yi1,i2
z
i1 ,...,iu ...i2
i1
...i2i1
and
z
of task Z i1,i2i1 ,...,iu ...i2
:
i1
z
z
Z i1,i2i1 ,...,iu ...i2
⇒ Ri1,i2
z
i1 ,...,iu
i1
...i2i1
...i2i1
z
⊆ X i1,i2
z
i1 ,...,iu
...i2i1
z
× Yi1,i2
z
i1 ,...,iu
...i2i1
.
(1.33)
z
,
For the convenience of formalization, we omit the subscripts i1, i2i1 ,...,iu ...i2
i1
denoting it by Z k . Then expressions (1.32) and (1.33) can be written:
where
Z = {Z k , k = 1, K };
(1.34)
R z ⊂ X z × Y z ; Rkz ⊂ X kz × Ykz ,
(1.35)
z
X z = {xiz , i = 1, I }; X kz = {xk,i
, i k = 1, Ik };
k
z
Y z = {y zj , j = 1, J }; Ykz = {yk,
jk , jk = 1, Jk }.
22
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.14 Scheme of informational interaction of subtasks in the process of solving the problem
The scheme of information interaction of subordinate tasks is presented in
Fig. 1.14.
For a mathematical description of the relationships of subordinate tasks Z in
solving the target problem, we will sequentially consider the structures of the sets of
their inputs X kz and outputs Ykz , as well as the relations with the sets of inputs X z and
outputs of problem Z.
The set of inputs X kz can be represented as two disjoint subsets: a subset of “external
inputs” X kz_ex and a subset of “internal inputs” X kz_in . In general, we can write
X kz = {X kz_ex , X kz_in }; X kz_ex ⊆ X z ; X kz_in ⊂ X z ;
X kz_ex X kz_in = X kz ; X kz_ex X kz_in = ∅;
K
K
X kz_ex = X z ;
k=1
X kz_in = X kz_in ,
k=1
(1.36)
1.4 Presentation of Informational Interaction Ergatic Elements …
23
where
z_ex
z_ex
= 1, Ikz_ex ;
X kz_ex = xk,i
z_ex , k − 1, K , i k
(1.37)
k
z_in
z_in
X kz_in = {xk,i
= 1, Ikz_in }.
z_in , k − 1, K , i k
k
K
It should be noted that the intersection results
k=1
X kz_ex and
K
k=1
X kz_in not neces-
sarily empty sets, because individual elements of the sets of “external” and “internal”
inputs of subtasks may coincide.
Consider the structure of the set of outputs Ykz of the subtask Z k . It can be represented in the form of three pairwise disjoint subsets: Ykz_ex —subsets of “external
outputs,” whose elements are outputs of the task Z and are not inputs of other subtasks;
Ykz_in —subsets of “internal outputs,” whose elements are inputs of other subtasks and
are not outputs of task Z—subsets of “mixed outputs,” the elements of which are
simultaneously inputs of other subtasks and outputs of task Z. Then we can write:
Ykz_ex
Ykz_in = ∅; Ykz_ex
Ykz_ex
Ykz_mix
Ykz_mix = ∅; Ykz_mix
Ykz_in = ∅;
Ykz_in = {Ykz_ex , Ykz_mix , Ykz_in } = Ykz ;
K
K
(Ykz_in ×Ykz_mix ) = X kz_in ;
k=1
(Ykz_ex ×Ykz_mix ) = Y z ,
(1.38)
k=1
where
z_ex
, k = 1, K , jkz_ex = 1, Jkz_ex ⊆ Y z ;
Ykz_ex = yk,
j z_ex
k
Ykz_mix
=
z_mix
yk,
,k
jkz_mix
= 1, K , jkz_mix = 1, Jkz_mix ⊆ Y z ;
z_in
Ykz_in = yk,
, k = 1, K , jkz_in = 1, Jkz_in ⊂ Y z .
j z_in
(1.39)
k
the expression (1.39), it can be seen that the
subsets
of the “internal outputs”
From
z_in
z_mix
and the subsets of the “mixed outputs” Yk
give the subsets of the
Yk
“internal inputs” X kz_in .
The formation of the elements of a set X kz_ex can be represented as a selection
z_ex
z_ex
of the
from the set X z of its elements xizz , which are the input effects xk,i
z_ex ∈ X k
k
subtask Z k .
It should be noted that for Q kz_ex = qi z ,ikz_ex is a mapping of the formation of
z_ex
z_ex
“external inputs” of the k-th subproblem and for each pair xizz ∈ X z , xk,i
z_ex ∈ X k
k
is rightly the relation:
24
1 Analysis of the Problem Functioning Modeling Ergatic Air …
qi z ,iqz_ex =
z_ex
1, if xiz = xk,i
z_ex ;
(1.40)
k
z_ex
0, if xiz = xk,i
z_ex ,
k
z_ex
z_ex
where a write of the form xiz = xk,i
z_ex ; means that the ith input of the task Z is i k
k
z_ex
z
input of the subtask Z k , and the opposite case is described by the record xi = xk,i z_ex .
k
If the sets X kz_ex and X z are column vectors of dimension, respectively, Ikz_ex and
I z , then:
X kz_ex = Q kz_ex · X z ,
(1.41)
where Q kz_ex —dimension matrix Ikz_ex × I z .
Similarly, elements of the set X kz_in
From the sets Y z_in and Y z_mix are
are formed.
selected, using the family Q kz_in = qi z ,ikz_in of formation of “internal inputs,” such
z_in
z_in
elements of it y zj z_in and y zj z_mix which will be the input effects xk,i
of the
z_in ∈ X k
k
subtask Z k :
(1.42)
X kz_in = Q kz_in · (Y z_in × Y z_mix ).
(1.43)
An analysis of relations (1.36)–(1.39) shows that they describe the structures of
the sets of inputs X kz and outputs Ykz of the sub-tasks Z k that provide the solution
to the target task Z under consideration, and the expressions (1.40)–(1.43) describe
the rules for the formation of elements of the sets of inputs X kz and outputs Ykz ,
i.e., morphological description of the information interaction of subtasks Z k in the
process of solving the target task.
Expressions (1.36)–(1.43) describing the morphology of the solution of the target
problem can be represented as a composition:
K
R z = ◦ Rkz ,
(1.44)
k=1
where join operation «◦» determined by the relations (1.33)–(1.43).
Returning now to the original notation (1.33), for the case under consideration we
obtain:
z
Ri1,i2
z
i1 ,...,iu
...i2i1
=
I (u z +1)...i2i1
◦
i(u z +1)...i2i1 =1
z
Ri1,i2
.
z
i1 ,...,i(u +1)...i2
i1
(1.45)
1.4 Presentation of Informational Interaction Ergatic Elements …
25
The consistent application of expression (1.44) to all nodes of the task tree D z
allows us to obtain a generalized model R z for solving the entire set of tasks performed
by ATC specialists.
The decomposition tree D z and the morphology of problem solving form a
structural–morphological model of problems solved by a specialist in ATC:
M z =< D z , R z >,
(1.46)
where D z —mission management task structure, R z —their morphology.
The solution of general and (or) particular problems solved by ATC specialists is
carried out using software (SW) from the information support tools of ATC specialists, if available, they realize the information functions of the ergatic element in ATC
EIS.
1.5 Logical–Linguistic Model for Choosing an Analytical
Model Parry Adverse Effects for Ergatic Elements
Due to the high accident rate of ACFT, there is a need to develop methods and
analytical models for the presentation of the “Crew–ACFT–ATC Specialist–Operating Environment” system. Ergatic elements (crew, ATC specialist), during operation, use information from various technical and radar tools to make decisions and
subsequent issuance of commands. Information exchange in the ergatic ATC system,
which allows determining the interaction of the structural elements of the system, is
presented in Fig. 1.15.
Figure 1.15 presents external sources of information: control radar (CR), surveillance radar (SR), automatic direction-finding equipment (ADF), short-range air
navigation system (SHORAN), landing radar (LR), weather radar (WR), navigation information display equipment (NID); means of transmission (reception)
of commands: ultra-short wave radio stations (UWRS), short-wave radio stations
(SWRS); FOA—flight operations assistant [1].
An analysis of the subject area showed that the currently used methods and models,
which are part of the information exchange model and describe the functioning of
EE in EIS ATC, do not allow developing models that provide useful information
support for EE since each ATC specialist has a unique set of information functions
that together. They influence the achievement of a common goal—ensuring safety
and regularity of flights. In this regard, the transition to quality indicators of EE
functioning will significantly reduce computational costs.
To ensure such a transition, a logical–linguistic model has been developed for
choosing an analytical model for counteracting negative impacts for EE, which is a
set of fuzzy production rules that describe actions in unforeseen situations that look
like: If z i (k) is a rule that determines the unforeseen situation in ATC system EIS
in the area of responsibility of ATC specialist, and Fi1 are the values of linguistic
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.15 Information exchange model in EIS ATC
26
1.5 Logical–Linguistic Model for Choosing an Analytical Model …
27
variables characterizing the situation, where k—are discrete time intervals, then the
corresponding analytical model determining motion parameters of ACFT traffic in a
particular situation [12, 21].
The functioning of ergatic elements of the ATC does not allow to develop an
invariant model, as each specialist ATC has a unique set of features that together
contribute to the achievement of a common goal—ensuring the safety and regularity
of flight.
In connection with the need of the air situation in the form of binary relations safe
intervals between aircraft, their analysis is characterized by the use of high computational cost, so the shift to quality metrics allows to reduce them significantly. Saving
computing capacity for evaluation and forecast of development of emergencies based
on the two-stage handle situations where the first stage uses a qualitative approach
that does not require significant accuracy, but at the same time, allows us to classify the situation of the condition of ACFT (normal, abnormal, emergency). The
second step is the exact calculation of the indicators to exit a situation that defines a
deterministic set of values for the parameters of the aircraft traffic.
One of the stages of creating an information system is the design of its structural and algorithmic parts, including the development of the composition and structure of information processes and algorithms of their processing. In this regard, of
paramount importance, the issues related to the formalization of information systems
and the development of mathematical models of information processes occurring in
them. To solve these problems is advisable to use an approach based on the theories of stochastic processes or mathematical statistics. The use of this approach does
not allow us to obtain effective solutions in the absence of the necessary sets of
stochastic data, which leads to the impossibility of constructing the relevant distributions. The use of the deterministic approach that has proven its worth in solving
technical problems based on the machine differential equations is difficult due to the
lack of information theory itself, so it is unclear what information the processes
will described in the form of the corresponding equations. The most promising
approach for constructing mathematical models of EIS at present is the theory of
fuzzy sets; however, built logical–linguistic models lead to the necessary introduction of linguistic variables and use a large number of terms, which entails a high
computational cost. Auspicious and exciting is the method of Takagi and Sugeno,
which based on the fact that the result of the work of the rules of the logical–linguistic
model is not the term and functional dependence. The developed fuzzy rule selection
of an appropriate analytical model for countering the negative impacts specialist of
the Department of Internal Affairs is contained in the base rules and have the form:
Rule z1 (k):
If the ATC specialist = “flight officer” & aircraft speed = “high” & flight height
= “small” & wind direction = “passing lateral” & wind speed = “exceeding
permissible” then the movement model is going to the second circle:
ẋ1 (t) = A1 x(t) + B1 (t) + w1 (t)
,
y1 (t) = C1 x(t) + v1 (t), for i = 1 . . . I
(1.47)
28
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Rule zi (k):
If the ATC specialist = “landing zone officer” & landing speed = “high” &
aircraft location = “out of range” & aircraft height = “below the glide path” &
range to runway = “small” & wind direction = “lateral “& wind speed = “exceeding
permissible” v meteorological conditions = “difficult meteorological conditions” v
decision time = “small” then the movement model is horizon (direct flight to the
glide path):
ẋi (t) = Ai x(t) + Bi (t) + wi (t)
yi (t) = Ci x(t) + vi (t), for i = 1 . . . I
In expression (1.47): xi (t) = [x1 (t), x2 (t), . . . , xn (t)]T ∈ R n×1 —state vector
of dynamic objects of ATC system, t ∈ k—continuous-time within k i interval;
u i (t) = [u 1 (t), u 2 (t), . . . , u m (t)]T ∈ R m×1 —dynamic object control vector (engine
thrust, roll, pitch); wi (t) = [w1 (t), w2 (t), . . . , wn (t)]T ∈ R n×1 —environmental
influences (wind speed and direction, atmospheric characteristics, ornithological situation); yi (t)—system outputs (characteristics of the observation equation); vi (t)—
measurement error; Fig —values of linguistic variables about the air situation,
depending on the number and types of ACFT trajectories and parameters of their
movement, location of obstacles, closure zones, meteorological conditions, and
atmospheric phenomena; z 1 (k), z 2 (k), . . . , z g (k), Ai ∈ R n×m , Bi ∈ R n×m —rules
governing the classification of unforeseen situations in ATC system; L—the number
of rules in the considered logical–linguistic model on k interval of the function. To
achieve the goal of the functioning of the system qualitative information is used,
presented in a logical–linguistic model with the corresponding terms, to formalize
which membership functions used, which makes it possible to switch from model
(1.47) to a generalized model (1.48):
L
ẋ(t) =
=
i=1
L
μi (z(k))[Ai x(t) + Bi u(t)]
+ w(t)
L
i=1 μi (z(k))
h i (z(k))[Ai x(t) + Bi u(t)] + w(t),
(1.48)
i=1
L
y(t) =
μi (z(k))[Ci x(t)]
h i (z(k))[Ci x(t)] + v(t),
+ v(t) =
L
i=1 μi (z(k))
i=1
L
i=1
where
μi (z(k)) =
g
j=1
Fi j (z j (k)),
(1.49)
1.5 Logical–Linguistic Model for Choosing an Analytical Model …
29
μi (z(k))
h i (z(k)) = L
,
i=1 μi (z(k))
z(k) = [z 1 (k), z 2 (k), . . . , z g (k)]
(1.50)
where Fi j (z j (k))—membership function z j (k) in Fi j .
Accepting for everyone k:
μi (z(k)) ≥ 0 and
L
μi (z(k)) > 0, at i = 1, 2, . . . , L
i=1
We get:
h i (z(k)) ≥ 0, at i = 1, 2, . . . , L
and
L
h i (z(k)) = 1.
(1.51)
i=1
We assume that the reference model has the form:
ẋr (t) = Ar xr (t) + r (t),
(1.52)
where xr (t)—initial state of ATC system, Ar —asymptotically stable matrix, r (t)—
limited control input in ATC system.
The functioning of the EIS ATC is to perform the following actions:
1.
2.
3.
4.
5.
6.
A set of initial parameters determined to solve a specific problem in the EIS
ATC (corresponding specialist ATC by the task tree).
A classification of the unfavorable situation with ACFT in the EIS ATC is carried
out based on the use of a knowledge base (fuzzy rules (1.47)).
Areas of permissible values of ACFT parameters determined in the event of an
adverse situation (by ACFT parameters and instructions).
Fuzzy rules for describing the dependencies between variables in (1.47)–(1.49)
formed, types of membership functions are selected.
The uncertainty of the state of the aircraft in the air traffic control system reduced
by solving the problem of determining deterministic control parameters.
Repeat steps 2–5 until the optimal conditions for the EIS ATC found.
Thus, the developed model allows the selection of an analytical model of parrying
adverse effects for ergatic elements based on the use of appropriate term sets,
which are determined by functional dependencies and determines the basis for the
functioning of the modeling subsystem of the decision-support information system.
30
1 Analysis of the Problem Functioning Modeling Ergatic Air …
1.6 Synthesis of a Procedural Model for Decision-Making
by an Ergatic Element in the Formation of an Aircraft
Stream
The main activity of ATC specialists is the adoption of decisions on the formation
of a conflict-free flow of ACFT.
The behavior of ATC specialists is not strictly defined and has a clearly expressed
probabilistic nature, characterized by the following parameters:
• the time lag in the perception of information and the formation of control action;
• accuracy of the reproduction of dynamic air conditions;
• reliability of the perception of dynamic air conditions.
A generalized scheme of the work of ATC specialists in the air control mode
presented in Fig. 1.16. The complexity of modeling the professional activity of EE
lies in the fact that obtaining quantitative values for evaluating information is not
feasible, due to the imperfection of the methodology for assessing the meaning and
significance of the information.
The structure of ATC specialist functioning in the control mode of dynamic air
conditions shown using operators that convert the signal and noise:
(1)
(2)
(3)
(4)
(5)
(6)
r(t)—is the sensory perception of an ATC specialist;
x(t)—physical signal (marks from the aircraft performing flight under the
control of an air traffic control specialist);
s(t)—a signal in the form of a random function of judgments (actions);
β(t)—designation of noise in the model (marks from extraneous aircraft, flocks
of birds, local objects, etc.);
R1 —operator of signal mapping x(t) into the perception of ATC specialist—
r(t);
R2 —decision-making operator that converts the input signal into action.
The described activity of an ATC specialist characterized by the presence of
observations consisting of random processes, one of which is a useful signal (e.g., the
sudden appearance of an aircraft having damage in the area of responsibility), and the
other is an obstacle (a sharp change in the direction of the wind). Information about the
useful signal and interference presented in the form of the known probabilities of the
occurrence of the event P(x) and P(β). The observation results estimated by posterior
probabilities P(x/r ) and P(β/r ). In the process of forming the flow of aircraft from
Fig. 1.16 The structure of ATC specialist in the control functioning mode of dynamic air conditions
1.6 Synthesis of a Procedural Model for Decision-Making …
Table 1.1 Matrix of
efficiency of ATC specialist
decisions
Decisions
31
Situations
x
β
x
q11 , P11
q12 , P12
β
q21 , P21
q22 , P22
an ATC specialist, it required to give a deterministic answer in the conditions of
initial stochastic information, which can be represented as the following:
•
•
•
•
the presence of a signal when it is—P(x/x);
the presence of a signal when it is not—P(x/β);
lack of signal when it is—P(β/x);
no signal when it is not—P(β/β).
In this case, it is fair:
P(x/x) + P(β/x) = 1.
(1.53)
Similarly to the expression (1.53), we have [19–21]:
P(x/β) + P(β/β) = 1;
P(x) + P(β) = 1.
(1.54)
The coefficients used to assess the optimality of ATC specialist activities in the
air control mode qij (i, j = 1, 2) (Table 1.1).
The effectiveness of air traffic control by an ATC specialist is to minimize the
value that determines incorrect answers. Then, the analytical model in the form of a
general indicator of the effectiveness of ATC specialist decisions has the form:
2 2
qi j Pi j .
U = q11 P(x / x) + q22 P(β β) + q12 P(x β) + q21 P(β x) =
i=1 j=1
(1.55)
In the expression (1.55), the signs of the coefficients qij determine the direction of
optimization. The selection rule, which used to assess the average risk of a decision,
based on (1.55), has the form:
U(1) = q12 P(x/β) + q21 P(β/x).
(1.56)
Thus, the ATC specialist forms a threshold value commensurate with the ratio of
the probabilities of the onset of events. Introducing weights qij , we define:
lS =
P(β)q2
,
P(x)q1
(1.57)
32
1 Analysis of the Problem Functioning Modeling Ergatic Air …
where q2 = q21 − q11 ; q1 = q12 –q22 .
An analysis of the results of experiments on training operators (air traffic
controllers) showed that an untrained operator uses the criterion of an ideal observer
as an optimality criterion, according to which a detection rule selected that provides
the minimum signal skipping probability:
(2)
= P(β/x) → min,
U
(1.58)
at a given false alarm value P(x/β) ≤ k.
When increasing the number of training, the operator uses the criteria (1.55) or
(1.56), while developing a critical value of the likelihood ratio. If the values of P(x)
and P(β) are not defined, then it is advisable to use the minimum criterion, which
forms a solution from the condition of minimum–maximum risk of the form (1.56).
By a solution, we mean ui = (ui1 , …, uin ), where uij are the solutions to counter the
adverse effects of the ith situation. The set Gu can be represented as a set of disjoint
subsets of variants of the air situation G (S)
u (s is the number of variants of the air
situation), while the set of H performance indicators i :
H S (u is ) → H (1 , 2 , . . . , N ),
(1.59)
following the values of (1.59), the set of particular indicators is in the area G YS :
Yi ∈ G YS .
(1.60)
The exponent (1.59) allows us to determine the optimal solution uis = u*is if
H s (u*is ), which reaches its maximum value. The main task of ATC specialist is
to select a subset of the solutions in which the feasible G (S)
u solution will be the
maximum. The optimality assessment of the sequence of actions of an ATC specialist
determined as a function:
Fi [HuS (u is )],
(1.61)
where s = 1, . . . , m.
For each subset G su on which the score maximized (1.61), the range of performance
indicators (1.59) estimated, then the “best” of them is determined, taken as the locally
optimal u*is . After comparing all the solutions, one of the obtained locally optimal
solutions taken as optimal. A formalized description of the activities of an ATC
specialist in developing a control solution x presented in Fig. 1.17.
As an example of making the optimal decision, we consider the task of the
dispatcher, forming a circle of a conflict-free aircraft flow during the approach.
In the first step, the circle dispatcher detects a mark from the aircraft by flights,
makes an individual identification of the aircraft, and reports on the acceptance of
the aircraft under his control.
1.6 Synthesis of a Procedural Model for Decision-Making …
33
Fig. 1.17 A formalized description of the activities of an ATC specialist in developing an optimal
solution
In the second step, dispatcher evaluates the relative position of the aircraft
performing the approach, tells the crew the method of approach, etc. During the
flight, the circle dispatcher monitors the maintenance of a given flight altitude, as
well as the location of the aircraft relative to a given path and other ACFT. After the
crew report on the passage of the short-range navigation radio station (SHORAN),
the dispatcher gives him the command to perform the flight to the start point of the
turn for the landing heading. After checking the aircraft’s location after it appears
from the “dead” funnel of the radar control station (Rmv dpl = 3xH p ), he assigns
the flight altitude to the crew at the roll-in point for the landing heading, controls
the occupation of the indicated height, while observing the longitudinal and vertical
separation standards. When several aircraft simultaneously exit to RP, the circle
dispatcher determines the sequence of their turn to LH, giving commands to delay
the turn, forming a stream of aircraft at the landing heading so that after the turn to
LH, the longitudinal intervals between the aircraft are no less safe.
In the third step, based on the information received, using the assumptions put
forward earlier, a subset G su formed from which it is necessary to choose the optimal
34
1 Analysis of the Problem Functioning Modeling Ergatic Air …
one. If particular performance indicators are known, then the evaluation process is
determined by the matrix:
M = Yi(s) ,
(1.62)
where i = 1, …, ns —number of compared solutions uis .
In the fourth step, the range of feasible solutions is evaluated:
Yi(S) (u) ≥ 0,
(1.63)
with normalization 0 ≤ Yi(S) (u) ≤ 1.
A positive value of the performance indicator corresponds to the correct choice
of a private indicator:
f i(s) = F Yi(s) ≥ 0.
(1.64)
where f i(s) —lap dispatcher performance indicator; F Yi(s) —evaluation of the
decision of the circle dispatcher.
The probability distribution of the choice of each solution has the form:
pi(s)
Fi(s) Hu(s)
.
=
(s)
(s)
N
H
F
u
i=1 i
(1.65)
where Fi(s) Hu(s) —assessment of the admissibility of a locally optimal solution Hu(s) ;
N
(s)
Hu(s) —the sum of assessments of admissibility of all decisions made.
i=1 Fi
At the fifth step, the locally optimal solution u*is determined. The optimal solution
u*is one that has a maximum probability P(S) of choosing the right solution [18].
The described algorithm for the activities of the circle dispatcher can be used in
the formation of a conflict-free flow of aircraft in the area of the aerodrome. The
structure of the decision-support information system as part of the ergatic air traffic
information system is shown in Fig. 1.18.
The structure of the DSIS includes the following main elements:
• modeling subsystem (allows, based on the input information about the aircraft, to
create a conflict-free approach flow, to calculate the aircraft delay maneuver for
a given interval, to synthesize the optimal sequence of departing aircraft, to form
the optimal trajectory during the approach, etc.);
• knowledge base (contains structured information about the aircraft, the area of
the airfield, etc.);
• the subsystem of verification of information reliability, situation recognition;
1.6 Synthesis of a Procedural Model for Decision-Making …
35
Fig. 1.18 Place DSIS in the structure of the ergatic air traffic information system
• the subsystem of forming a list of tasks and criteria for their solution;
• decision justification subsystem;
• the subsystem of ranking and choice of alternatives.
Based on the analysis of the activities of ATC specialists, the developed decisionmaking model is necessary to include in their workplaces a decision-support information system. That allows organizing information support (assessing and classifying
the air situation, forming a forecast for its development, from the moment the aircraft
appears in the airfield to landing, while determining the optimal sequence of actions
to eliminate adverse external influences).
To improve the efficiency of the EIS, ATC is required to provide the professionals
ATC tool object-oriented of decision-support information system. DSIS professionals ATC, due to the heterogeneity of the processed information streams using
the following elements (Fig. 1.19):
•
•
•
•
•
•
subsystem recognition of the input information;
subsystem recognition of the situation;
subsystem the choice of solution method and justification of results;
generating subsystem alternatives;
knowledge base, data, and models of the domain description (ATC);
graphical user interface.
Thus, the design of DSIS professionals ATC will allow:
• to ensure the invariance of informational support of decision-making;
• to reallocate time ATC from routine operations on more critical and hazardous
phases of flight of the aircraft;
36
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.19 ATC decision-support information system
• to increase the capacity of the aerodrome, based on automation of decision-making
functions for the formation of the conflict-free flow of the aircraft;
• to reduce the service time of one sun in the stream, thereby relieving professionals
of the ATC during the flight change through the transfer of part of functions to
monitor the traffic situation on DSIS;
• to ensure the reduction of errors of the output VS the line landing course:
• to increase the efficiency and regularity of air traffic:
• to increase the efficiency of the organization of information support of crew during
emergencies, based on a structured knowledge base and database, implemented
in DSIS.
1.7 The Method of Models for the Representation Synthesis
of Ergatic Elements in an Ergatic Information System
The purpose of the development of the method is to increase the efficiency of EIS
functioning based on the synthesis of elementary structures, taking into account their
properties and the combination of EIS elements. The specified goal achieved by the
fact that the method examines complex systems from the perspective of a “gray”
box, assuming knowledge of the initial boundary conditions for the functioning of
the system and the objective function. According to the proposed method, EIS is
considered a set of elementary structures to identify new properties and improve
1.7 The Method of Models for the Representation …
37
its qualities that even the sum of disparate components that make up the system
complex does not possess. However, not always, an increase in quantity leads to the
desired quality. The result of integration can lead to the desired result if the physical
properties of the simple, i.e., elementary systems and changes in their properties, are
known when creating connections with other elements. Therefore, first, knowledge
is needed about the properties of the elements of EIS, namely:
(1)
(2)
(3)
Elements of EIS should have a physical essence, a specific difference between
each element, their stability. That means that each elementary system must
reflect the law of conservation of the physical property displayed by the
individual parameter;
The number of parameters characterizing the EIS element should be
unchanged, i.e., permanent;
The parameters must be invariant concerning some evolutions (changes, e.g.,
coordinate systems).
We will call the simple system the simplest one, which includes the smallest
number of components of objects that are a complex of sources or drains and channels
(lines) connecting them to realize material and information flows.
The following types of elementary systems intended to be used: tandem,
compound, circulation torus, and oscillatory (Figs. 1.20 and 1.21).
Each elementary system is analytically mapped to physical parameters, to conservation laws, and the corresponding invariants. Elementary systems (Fig. 1.20) may
consist of an arbitrary number of sources (•) and flows (°); each element performs
one of two functions of the system. Elementary systems (Fig. 1.21) contain elements
of the complex that have the properties of both a source and a drain, and the number
of such complex functional elements in these simplest systems is strictly defined:
in (1B)—3 (in E2) and 4 (in E3). In systems (Fig. 1.21), sources and sinks are
active material media, and in (Fig. 1.20) sources (•)—active, and flows (°)—reactive (passive). Therefore, there are two classes of simple systems: the first class (I)
includes simple systems of two types—sources and sinks, and at the same time—
they are autonomous but incomplete. The second class (II) includes simple systems in
Fig. 1.20 Topology of elementary structures (tandem and compound)
38
1 Analysis of the Problem Functioning Modeling Ergatic Air …
Fig. 1.21 Topology of elementary structures (ring and oscillatory)
which the components are strictly complementary, although they are also autonomous
not only in the aspect of geometry but also in the aspect of physical functioning
processes. However, they require an external activating effect for this, and it must be
above a critical value:
|γ| ≥ |γcrit |,
(1.66)
that means the class I contains classical (super quantum systems) and class II contains
simple quantum systems. In this case, the effect should be adequate to the properties
of the test object, which is reflected by the essence of γ crit .
So, each of the open elementary elements of the EIS has a classification feature
in the form of an independent parameter based on its specific conservation law, i.e.,
strictly physically and mathematically justified.
The systemic method contrasted with the classical method of studying a single
influence on the object under study “one impact–one response.” That is a oneparameter method, and it is challenging to implement, because it is required to
carry out a preliminary series of detuning methods from interfering factors, and at
the same time, this is not always possible. For example, in order for an AC circuit
in a complex system, where R ≡ 0 and Z ≡ 0R could be independently measured,
it is necessary to feed the circuit with an alternating voltage ωkp = ω (σ, μ, ) that
is strictly defined, respectively, electrical conductivity, magnetic permeability for a
given geometry of the test object.
However, the synthesis of EIS can occur not with any set of elementary structures,
but only selectively, if they have some commonality that they intend to combine.
Moreover, there is no such force that they can be combined in a forced manner, in
an arbitrary desired combination. For example, at the same time, it is impossible
to create such a system as an aggregate in the form of a sum: j + U + R, where,
respectively, j is the electric current density, U is the voltage drop, R is the active
resistance.
1.7 The Method of Models for the Representation …
39
Such a connection is possible in the EIS based on summation, only if the elementary structures would have the same dimension of the parameters of the quantities
characterizing them.
We can expand the scope of creating systems to more general cases in which we
can create or have ready-made ones when we can act on elementary structures in the
corresponding system by several other elementary structures with different physical
dimensions. This class of systems is vast, but it is still not it is infinite and has some,
in the general case, individual restrictions.
The first elementary system—the tandem, by definition, is conservative, has the
property of transmitting information (I n ) from one elementary structure to another,
or in the opposite direction, and at the same time, it is always strictly determined. One
break in the communication line leads to the destruction of information, including
the flow of matter:
J1 ⇔ J2 ∨ J2 ⇔ J1 ,
(1.67)
J1 (I )¬ ⇔ J2 (I ) ∨ J2 (I )¬ ⇔ J1 (I )
(1.68)
The second most straightforward system, the compound, includes three elementary structures interconnected. This simple system can be connected to a compound
(K), a network, or a star (Z), which is essentially the same as a torus ( 2 ). In the first
two and the fourth systems in E2 and the torus ( 3 ) in E3 (where En is the Euclidean
space), one break in the network localizes one element of the EIS, and the third
breaks one connection in the system and its quality does not violate, i.e., toroidal
communication has the property of reliable communication, despite the presence of
a network break. That means that the toroidal system even in elementary form, i.e.,
in two-dimensionality, has, as a specific invariant (along with other invariants), the
invariant, and the reliability of communication concerning a single discontinuity.
In addition to the four typically torus invariants in E3 , the two-dimensional torus
also has several invariants characteristic of the geometry of the triangle, which can
be useful for a more thorough knowledge of the properties of this connection system.
Elementary systems considered above, i.e., with a minimum number of connections with full functioning, as they are interesting not only for practice but also for
theory.
Therefore, it has been established that four types of elementary structures can be
at the heart of one or another arbitrarily complex EIS. That will allow us to determine
the physical laws to which all four of these elementary structures obey in isolated
conservative systems of arbitrary scales:
Td ⇒
Ko ⇒
(E − U )i ;
qk ;
40
1 Analysis of the Problem Functioning Modeling Ergatic Air …
⇒S≡
dϕ(qk ∨ E) ≡ const ∨
dt (T −
) ≡ const;
0
C ⇒ c2 ≡ ε : ρ ≡ const ∨ T (t) ≡ const,
(1.69)
where T d ⇒ law of energy conservation: E 0 = (E i − U) (also Kirchhoff’s circuit
laws);
Kn ⇒ charge conservation law: Q0 = qi ;
⇒ law of conservation of angular momentum: I 0 = I j , S—convolution;
C⇒ law of conservation of oscillations propagation velocity.
Minimal metrics can classify systems, for example, in Euclidean space (En ),
the compound can be in E1 —one-dimensional; the tandem system in E2 is twodimensional; toroidally flat in E2 is also two-dimensional; toroidal-volumetric in
E3 —three-dimensional, with the smallest number of elements in the system—4
(ring); vibrational in E2 is two-dimensional.
In the time aspect, EIS can be formed for functioning in processes differently [8,
12, 21]:
(a)
(b)
(c)
(d)
simultaneously acting, i.e., in the time compound (adiabatic time characterized
by a transition process in the system);
stretched in a quantum scale—a tandem in the time continuum;
in the circulation mode, which has both tandem and a compound with a
localized system;
kinetic behavior of the elementary structure, i.e., disclosure of influence.
The tandem in time of EIS provides an opportunity to remove the restriction on
the types of combinations of elementary structures in systems, i.e., the sequence of
systemic influences on one or another elementary structure can be removed in the
system, and therefore the system: j + u + R, j(t 1 ) + u(t 1 + t 2 ) + R(t 1 +
t 2 + t 3 )—it is quite acceptable, this system is one of the control systems for the
elementary structure.
In the three-dimensional Euclidean space (E3 ), an even more significant number
of invariants revealed. In particular, in E3 a system of four non-coplanar points
uniquely characterizes an invariant torus, i.e., twice circular, and it already allows
we to know a wide variety of topological properties of torus systems, which open the
way to the creation of very economical and very reliable communication systems.
For example, the plane of the geodesic tandem covers all sections of the invariant
torus, revealing the topological properties and physical properties of in the entire
initially homogeneous system of the torus.
The simplest and at the same time, very effective EIS is a double-compound and
double-tandem system—a computer model of an elementary technical (artificial)
neuron (Fig. 1.22).
It turned out that this model is an element of the system in the form of a torus with
one jumper, to which two different signals are applied simultaneously (compound),
and a signal vented away from one (three-compound) signal.
1.7 The Method of Models for the Representation …
41
Fig. 1.22 Topology of the ergatic information system in the form of a double-compound and tandem
connection of elementary structures
The feasibility of the method can be similar to flaw detectors that implement the
following methods: self-comparisons, comparisons with a standard, and absolute
measurements.
The extension of the scope of this method is supposed for analysis and synthesis
of self-organizing EIS in the field of controlling the movement of dynamic objects.
References
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Second half of 2017 (2018). Moscow, 122 p/145 p
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Russian Federation in 2010–2014". The order of the Government of the Russian Federation of
April 22, 2009, No. 554-r. Moscow, 48 p
3. Typical Operational Safety Survey (NOSS), 1st edn (2016) International Civil Aviation
Organization, 85 p
4. Safety management oversight guide, 2nd edn (2009) International Civil Aviation Organization,
318 p
5. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018 (2019).
Federal Air Transport Agency, Moscow, 89 p
6. Kleinrock L (2002) In: Neumann VI, Kleinrock L (eds) Theory of queuing (trans: Grushko II).
Mechanical Engineering, Moscow, 432 p
7. Human factors training manual, 1st edn (2008) International Civil Aviation Organization, 370
p
8. Zadeh LA (1981) Fuzzy sets and systems theory (Per. from English: Zadeh LA). VTsP, Moscow,
178 p
9. Peregudov FI (2009) In: Peregudov FI, Tarasenko FP (eds) Introduction to system analysis.
Higher School, Moscow, 367 p
10. Taran VA (1996) In: Ram VA (ed) Ergatic control systems. Mechanical Engineering, Moscow,
188 p
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1 Analysis of the Problem Functioning Modeling Ergatic Air …
11. Ponomarenko VA (2006) Psychology of the human factor in a dangerous profession—Krasnoyarsk: “Polikom,” 629 p
12. Anodina TG (1993) In: Anodina TG (ed) Process modeling in the air traffic control system.
Radio and Communications, Moscow, 345 p
13. Venikov VA (1976) In: Brooms VA (ed) Theory of similarity and modeling. Higher School,
Moscow, 479 p
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Moscow, 271 p
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Nauka, Leningrad, 270 p
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21. Darymov YuP (1981) Automation of air traffic control. G.A., Moscow, 667 p
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of the aviation transport system Russia. Samara, Samara State Aerospace University, 153 p
Chapter 2
The Methodology of Functional Control
of the Aircraft and Parrying Special
Situations
2.1 Analysis of Aircraft Failures and Malfunctions
by Aviation Systems and Groups of Causes
Improvement and creation of new armed forces have the purpose of achieving the
maximization of technical equipment while minimizing economic cost. At the same
time, the manufacturer faced with the dilemma between the technical complexity
and level of automation of the aircraft with one hand and the psycho-physiological
and intellectual capabilities of the crews on the other. Therefore, the appearance of
the DS on the board of the aircraft is caused, largely, the technical and ergonomic
imperfection of equipment that indirectly, through the actions of the pilot, leads to
accidents.
If the user manual for the aircraft of previous generations is how a crew of
20…30 °C, for modern aircraft, are more of them at times. The task of memorizing
the order of actions in each crew and their implementation in conditions of the high
physiological load is practically not feasible. This factor during the investigation of
aviation events converted to the following reasons:
• inadequate training of crew members associated with the DS;
• failure to provide skilled assistance to crews in the occurrence of DS in flight.
It is entirely not taken into account the physiological capabilities of the crew and
specialists of the Internal Affairs and the transience of the development of DS [1–5].
Thus, the development of means of information support of crew in particular
situations is a significant scientific problem, requiring a detailed analysis of the
causes and development of the asset, its classification, and the definition of clear
actions to minimize negative consequences.
Thus, in the aviation system, a critical factor is initially present that cannot be
localized entirely either by conducting simulations or by targeted inspections.
In Fig. 2.1, the distribution of AT failures in 2007–2018 in the Russian aviation
by the aviation systems in which the failure occurred is presented.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. V. Yakovlev et al., Conditional Function Control of Aircraft,
Springer Aerospace Technology,
https://doi.org/10.1007/978-981-16-1059-2_2
43
44
2 The Methodology of Functional Control of the Aircraft …
A and E - aircraft and engine; AE - aviation equipment; TLD - take-off and landing
devices; FHS - fuel and hydraulic systems; ACS - aircraft control system; REE radioelectronic equipment.
Fig. 2.1 Distribution of aircraft equipment failures by aviation systems in 2007–2018 in the aviation
of the RF
Thus, despite improvements in the aircraft in terms of reliability, testability, and
integration in their composition the means of information support of crew significant
reduction in the level of accidents occurs in the following several reasons:
• despite the comprehensive training of the members of the crew, their actions in the
DS do not allow to fully realize their knowledge and skills because of the rapidity
of the occurrence of a particular situation, because of incomplete information
about the state of the aircraft during flight;
• deviation from the general technical requirements for the formation of tactical
and technical tasks to create a new ACFT and conducting it testing significantly
reduces the level of flight safety;
• despite the existence of information systems on the occurrence of DS onboard
ACFT and for their improvement, they do not allow time to assist the crew during
transient events;
• a technical complication of the armed forces significantly increased the amount
of information circulating in a control system of the armed forces and left no time
for adequate assessment of the particular situation.
2.1 Analysis of Aircraft Failures and Malfunctions …
45
Installed on new ACFT system crew warning about the DS not allows us to:
• to reflect the causal relationships at the failure of elements of the armed forces
from the standpoint of the development of complex failures (i.e., when the failure
of one element leads to the failure of other elements of the armed forces);
• to estimate the amount of time to parry the DS depending on the flight conditions;
• under conditions of high intensity of receipt of information about the development of the DS to give adequate recommendations for responding to particular
situations;
• to give comprehensive recommendations on actions the crew to isolate and
troubleshoot complex failures in flight.
2.2 Decision-Making Model for Parrying Special Situations
Onboard an Aircraft
The crew’s decision-making model, when countering the DS onboard ACFT, understood as a formal representation of the crew’s actions and automatic actions of ACFT
systems aimed at minimizing damage.
The crew’s decision-making model when parrying the DS onboard ACFT is
presented in the form of a “decision tree”-type graph, in which the beginning
corresponds to the moment the DS appears (the decision-making peak characterizing the beginning of the DS development). The peak of the consequences, the
crew’s options and the aircraft’s automatic systems and possible consequences of
the selected actions. The functioning of the model begins with the assessment of the
critical time for the development of the DS based on the information received from
the onboard meters and based on the forecast for the development of a specific DS
in the form of the available time tˆavail from the DSIS knowledge base:
tcrit
⎧
⎪
tˆdist − tupd + tmode1 ,
⎪
⎪
⎨ˆ
t − tupd + tmode2 ,
= dist
⎪
tˆdist − tupd ,
⎪
⎪
⎩
0,
∗
∗
if Hcurr < Hopt
, Vcurr = Vopt
∗
∗
if Hcurr > Hopt , Vcurr = Vopt
∗
∗
if Hcurr = Hopt , Vcurr = Vopt
if tˆdist = 0
(2.1)
where:tcrit —time interval defining the boundary of the DS to catastrophic transition;
tmode1 —time to set the optimal altitude and create the optimal flight mode;
tmode 2 —time to lower to the optimum altitude and create the optimal flight mode;
tˆdist —time determined transition of the DS to catastrophic in the absence of optimal
actions to parry the DS;
Hcurr —current ACFT altitude;
∗
—the range of optimal aircraft heights for
Vcurr —current ACFT speed; Hopt
max
min
∗
<H <H
);
parrying DS (H
opt
opt
opt
min < V ∗ < V max ).
∗
—range of optimal ACFT speeds for parrying DS (Vopt
Vopt
opt
opt
46
2 The Methodology of Functional Control of the Aircraft …
The next step is to evaluate the possible options for parrying the DS by the criterion
of minimizing the time of parrying t par :
JT =
K
tpar → min.
(2.2)
i=1
where t par— time to perform DS parry operations.
The determination of t par for each DS is carried out based on a preliminary graph
analysis of the DS that has occurred, as well as based on the operating instructions
for the ACFT crew by summing up the time spent on the implementation of simple
actions t∂i :
tnapupi =
n
t∂i ,
(2.3)
i=1
where t∂i —the duration of the elementary action when parrying the DS;
n—the number of simple actions required to counter DS.
The use of the graph approach, in order to determine t par , allowed us to display
the events that determine the development of the DS on the aircraft and the reaction
of the crew of the aircraft and ATC specialists to it. We formally represent the DS in
the form of the following strata:
• stratum 1—failures of the aircraft elements;
• stratum 2—actions of the aircraft crew in the course of the operating system (input
information about the appearance of the operating system is information signals
from the built-in control system and its external manifestations);
• stratum 3—actions of air traffic control specialists in the course of DS.
The graph describing the DS is:
G = {V, E},
(2.4)
where V —graph vertices corresponding to DS development events on different strata;
E—edges of the graph, indicating transitions between events, loaded with an indicator
of the time of the event.
The synthesized graph G is analyzed to determine critical times on different strata
during the DS. On the graph, following the Dijkstra’s algorithm, the minimum path
is determined that characterizes the necessary and sufficient time to parry the DS
(t par ) [6, 7]. The authors analyzed more than 55 accidents in the form of graphsignal models for the development of the operating system, which led to another
result, namely the need to organize an information support system for the aircraft
crew and ATC personnel in the event of an operating system, characterized by the
timely provision of complete information on parrying the operating system based
on the development forecast DS. Presumably, the central part of the system should
2.2 Decision-Making Model for Parrying Special Situations …
47
Fig. 2.2 Dynamics of the development of an accident with the An-148 aircraft in graphical form
presentation
be concentrated onboard the ACFT with the maximum automatic response to the
control elements (without crew participation) when using duplicate systems or the
ability to restart non-duplicate elements with an efficient and clear display of the
aircraft crew. The involvement of ATC specialists to assist the crew is possible only
in cases where there is a margin of time (reserve of altitude and speed) for parrying
the DS.
The results of more than 50 accidents and aviation incidents were analyzed, as
an example, consider the description of the accident with the An-148 aircraft that
occurred on February 11, 2018 (Fig. 2.2, Table 2.1).
11.02.2018, at 14:27 local time (11:27 UTC), by day, during the scheduled flight
6B 703 Moscow (Domodedovo)—Orsk, the An-148-100V RA-61704 of Saratov
Airlines JSC crashed. As a result, the ACCID of the aircraft collapsed, all crew
members (4 people), aboard 2 ATB airline specialists, and 65 passengers died.
The crash of the An-148-100V RA-61704 aircraft occurred due to erroneous
actions of the crew at the stage of climb in conducive weather conditions with unreliable instrument speed readings caused by icing (blockage with ice) of all three RPMs,
which led to the loss of control over the flight parameters of the aircraft, translate it
into a dive and collision with the ground. An accident falls into the category of loss
of control in-flight (LOC-I) [7].
The outcomes of various options for the actions of the aircraft crew in the DS
estimated based on a synthesized decision tree, which allows, from the moment the
DS appears, to offer the optimal solution for the implementation of the sequence of
actions of the aircraft crew and automatic systems of the aviation complex minimizing
damage from a particular situation (Fig. 2.3).
Figure 2.4 shows a graph of the type “decision tree” synthesized for the abovedescribed accident with An-148 aircraft.
48
2 The Methodology of Functional Control of the Aircraft …
Table 2.1 Description of the vertices of the graph-signal model of the accident with An-148 aircraft
Graph
elements
Description of the event
V
E, c
V11
0:00
The crew commenced the takeoff. On integrated alarm information system “full
pressure receiver—1 no heating, full pressure receiver—2 no heating, landing
control center—3 is not heated, ice protection system is not prepared, Run-2 tool
pump 2—a failure”
V21
1:52
to IAIS the “INCREASE MODE MDU” (this the message remained until the end
of the flight)
V31
3:10
The analysis of the flight parameters at an altitude of 1100 m and speed…465
470 km/h starts to be a discrepancy between the calculated (actual) air speed with
the registered values of the speed: V [PR].1 (ICSP) coming from the IMP 1 (full
pressure receiver 1), and V [PR].2 (ppkr) coming from ppkr SVS (FPR 3)
V41
3:50
Airborne recorders were registered RI “Rate compare” and RK “V
[PR]—COMPARE” (registration lasted approximately 10 s, then stops)
V52
3:56
Report 2P: “Yes, okay, let me see (inaudible), 450?”. On CFI PIC speed from IMP
1 (PPD 1) was 457 km/h and different speed, which was observed by 2P on the
right KPI to the value of over 10 km/h. the speed of ppkr-SVS (PPD 3) was
considerably lower (≈430 km/h) than the speed indicated on CPD pilots. The
estimated (actual) speed was ≈490 km/h
V62
3:59
After the termination of the issuance of the alarm 2P reported: “Confirmed.
Equally, all stood up”
V71
4:50
The appearance of the RK “V [PR]—COMPARE” and alarm “SPEED
COMPARE”. The speed of ppkr SVS (full pressure receiver 3) continued to grow
and was already more speed from the IMP 1 (PPD 1), which rapidly decreased
V82
4:50
The deviation of the wheel on the dive and off SAU (autopilot)
V91
4:56
Check RK “V [PR]—COMPARE” stopped. According to the registered
information, from this point on has already been rejected speed from the IMP 1
and CFI PIC are beginning to appear speed from the IMP 3 (full pressure receiver
3). Was speed value from the Landing control center 3, this time was ≈480 km/h.
Thus, for 1-second speed on CFI PIC abruptly increased at ≈100 km/h
2
V10
4:56
Watching on the right CFI increased speed, 2P, most likely, tried to intervene in
the management, which caused the PIC indignation: “what are you doing?” 2P
proposed to decrease the operating mode: “Move the mode a little bit”
2
V11
5:01
Disconnected the autothrottle, and thrust lever was moved to position ≈17°
(land small gas (LSG) a (Thl) = 17°) with a subsequent increase in the mode up to
33–35° (mode 0.7 MP, a (Thl) ≥ 30°, a (Thl) = 51°)
1
V12
5:01
Registers a single command “NO RESERVE THE FBW (FOR Autopilot)”
2
V13
5:13
Move the thrust lever to the position of ≈20 (close to the flight small gas around
= 21 °C)
1
V14
5:17
Triggering of voice messages speed limit “SPEED is high”, the value of the speed
of ppkr SVS (FPR 3) was about 560 km/h, which exceeded the operating limits
for this phase of flight. Actual instrument speed—about 580 km/h
(continued)
2.2 Decision-Making Model for Parrying Special Situations …
49
Table 2.1 (continued)
Graph
elements
Description of the event
V
E, c
2
V15
5:18
2P: “Why are you pointing down? It was necessary to pitch up to lower the
speed… and you do down”
PIC: “I See, I see, I see.”
The PIC report on speed: “500”—confirms that at this moment the speed from
MVP 3 was already displayed on the left CFI, since the speed values from MVP 1
had decreased to 200 km/h by this time. The analysis showed that the speed from
MVP 3 to CFI PIC was displayed until the end of the flight
2
V16
5:22
The aircraft was transferred to the climb (2P: “Up”)
1
V17
5:35
At ppkr SVS (RPM 3) (if current values of about 480 km/h) due to further ice
(clogged with ice) 3 FPR began to fall speed values (up to 200 km/h and below)
2
V18
5:41
The aircraft was transferred to the crew for the reduction with near zero and
negative values of vertical acceleration. The operation of engines has been
increased
1
V19
5:45
For IAIS there was a message “landing GEAR OUT”
1
V20
5:48
RK “there is NO PROVISION to EDS (FOR ACS)” was replaced by RK “a
COMPLETE FAILURE of the EMF (FOR ACS)” with the simultaneous
occurrence of RK “a SIGN of the unreliability of the V [PR]”
2
V21
5:54
Seeing a further drop of speed on the left of the CRPD (“200 the speed…”), the
FAC repeatedly rejected steering column “by itself”, which led to an increase in
pitch angle to dive to 30 and reducing the vertical acceleration to 0 g
1
V22
5:58
At a height of ≈1500 m alarm EGPWS “TERRAIN AHEAD. PULL UP”. At this
point, the pitch angle was about 30° to the dive, the plane dropped with a vertical
velocity of 50 m/s
2
V23
6:00
In control of the plane intervened 2P (1200 m), while the actions of the pilots were
mixed: 2 pilot—take the wheel; KVS—steering wheel from itself
1
V24
6:04
The alarm “SPEED is GREAT”
2
V25
6:05
The geometric height of ≈300–400 m was additional movement starveling
columns on the dive (as a result of short-term vertical acceleration decreased to −
0.7 g), and immediately they were rejected almost completely on the pitch. Most
likely, the plane at this time came from the clouds, and the pilots found the fast
approaching land
1
V26
6:07
The aircraft pitch angle to dive at about a 30° right bank 25° collided with the
ground
3
V26
6:40
Dispatcher of sector M8 attempted call communication to the flight crew of the
An-148-100B RA-61704: “Saratov 703, are you here?”
Thus, the application of the developed model of decision-making by the crew
when parrying the DS onboard the ACFT allows us to estimate the time intervals for
the development and parrying of the DS in order to make informed decisions by the
ACFT crew to choose the best option to counter the particular situation.
50
2 The Methodology of Functional Control of the Aircraft …
Fig. 2.3 Crew’s decision-making model when parrying the DS onboard the ACFT in the form of
a graph like “decision tree”
Fig. 2.4 Decision-making model of the crew of the Yak-130 ACFT when parrying the DS in the
form of a graph like “decision tree”
2.3 Methods of Functional Monitoring of the State of the Aircraft …
51
2.3 Methods of Functional Monitoring of the State
of the Aircraft and the Organization of Information
Support for Decision-Making in Special Situations
The methodology of the functional control of the state of the aircraft and the organization of information support for decision-making in particular situations is a systematic
set of procedures implemented by the crew with the participation of DSIS to solve
the problem of parrying the DS. The use of criterion (1.16) provides for the selection
of the best option for the actions of the aircraft crew, minimizing the time of DS
retraction. An illustration of the developed methodology in the form of an presented
in Fig. 2.5.
The essence of the technique is to perform the following steps:
(1) Determination of the time of occurrence of the DS (based on a comparison of
the values of the vector of the current state of the nodes and assemblies of the aircraft
with the vector of reference values. The moment of occurrence of the event of the
provoking DS is determined to identify the DS and build the predicted trajectory of
development of the particular situation).
An analysis of the subject area showed that the currently used methods and models,
which are part of the information exchange model and describe the functioning
of the crew in the “aircraft–crew” system, do not allow developing models that
provide useful information support for the crew since each DS has a unique set flight
parameters and transience of development, which together affect the achievement of
a common goal—ensuring flight safety. In this regard, the transition to high-quality
indicators of the operation of the DSIS aircraft crew will significantly reduce the
time to parry the DS.
To solve this problem, a procedure has been developed for identifying the DS
and constructing a predicted development path for the DS, which is a set of fuzzy
production rules that describe the DS, which are: if z i (k) is a rule that determines
the unforeseen situation in the aircraft–crew system, and Fi1 —linguistic variables
characterizing the occurrence of the DS, where k are discrete time intervals, then the
corresponding analytical model of parrying the special situation is used:
Rule z1 (k):
if ACFT = (“Power plant” = ”good” & “automatic control system” = ”good”
& “hydraulic system” = ”good” & “DC power supply system” = ”good” & “AC
power system” = ”good” & “ fuel system “ = ” good “&” system for determining
the position in space “ = ” good “&” air signal system “ = ” good “&” integrated control system “ = ” good “&” electronic equipment “ = ” good “& “AT”
= ” serviceable” & “sighting and navigation system” = ”serviceable” & “system
Weapon management theme” = ”good” & “crew life support system” = ”good” &
“take-off and landing devices” = ”good” & “crew” = ”functional state” = ”normal” & “control actions” = ”normal” & “external environment” = “weather conditions” = “simple weather conditions” & “time of day” = “day” & “turbulence” =
“absent” & “icing” = “absent”) then “continued flight”.
Rule zt (k):
52
2 The Methodology of Functional Control of the Aircraft …
Fig. 2.5 Methods of functional monitoring of the state of the aircraft and the organization of
information support for decision-making in special situations
2.3 Methods of Functional Monitoring of the State of the Aircraft …
53
if ACFT = (“Power plant” = “lower engine RPM drop less than set” & “right
engine” = “good” & “height” = “less than optimal” & “speed” = “optimal”) then
(“turn off the left engine” & “increase the speed of the right engine “&” set of
optimal height “& …).
ẋi (t) = Ai xi (t) + Bi (t) + wi (t)
yi (t) = Ci xi (t) + vi (t), for i = 1 . . . I .
(2.4)
In expression (2.4):xi (t) = [x1 (t), x2 (t), . . . , xn (t)]T ∈ R 1×n —dynamic state
vector (aircraft), t ∈ k—continuous-time inside interval k i (k i —DS appearance
and recognition time interval); wi (t) = [w1 (t), w2 (t), . . . , wn (t)]T ∈ R 1×n —environment influence (wind speed and direction, atmospheric characteristics); yi (t)—
system outputs (characteristics of the observation equation); vi (t)—measurement
error; Fig —values of linguistic variables characterizing the occurrence of DS;
z 1 (k), z 2 (k), . . . , z g (k)—rules governing DS classification.
(1)
(2)
(3)
(4)
Determination of the critical time tcrit following (2.1) (determination of the
possibility of increasing the limit of available time for parrying the DS).
Generation of options for parrying the DS, based on the construction of a graph
in the form of a “decision tree” that defines the set of possible and valid options
for parrying the DS.
Selecting the optimal option for DS retraction (building a decision model and
using the criterion of the minimum path on the graph, the search for the optimal
option for DS retraction performed).
Carrying out DS parry operations and issuing recommendations to the crew
(automatic implementation of the selected DS parry option and issuing
recommendations to the crew).
The proposed method of functional monitoring of the state of the aircraft and
the organization of information support for decision-making in particular situations
based on:
• using a fuzzy model for identifying the DS and determining options for parrying
the DS;
• on the frequent use of the decision-making model and the graphical model of DS
parry to determine the best option for the aircraft crew actions, which selected
following the analysis of the decision tree formalizing the acceptable options for
the aircraft crew actions.
Thus, the developed methodology is the basis for the implementation of the
decision-making system of the aircraft crew to improve flight safety.
54
2 The Methodology of Functional Control of the Aircraft …
2.4 A Model of the Functioning of the Information Support
System for Decision-Making of the Aircraft Crew
in a Particular Situation
In order to determine the elements of the DSIS aircraft crew in the DS and the primary
information flows circulating in the process in parrying the DS, a model of the DSIS
aircraft crew in the DS has been developed.
The model of the DSIS functioning of the aircraft crew in the DS is built according
to the “client–server” scheme. Actual informational entities of the model (DS parry
options for specific types of aircraft, current information on aerodromes, meteorological conditions, etc.) should cover all existing aerodromes of the Russian Federation,
with the organization inside each in the form of a distributed information system,
with a data transmission channel allowing real-time transfer and processing of critical
information in the DS. The DMS FS server must process, store, and transmit updates
(aerodrome information cards, crew actions algorithm in the DS, etc.). The principle
of sending updates should be similar to the principle of automatic updates of antivirus products (e.g., Kaspersky Labs). The principle of updating DSIS aircraft crew
and DSIS ATC specialists at a particular aerodrome is carried out by the availability
of updates received from the DMS FS.
The model of the DSIS functioning of the aircraft crew in the DS shown in Fig. 2.6.
DSIS of the aircrew in the DS includes declarative and procedural parts. The
declarative part of DSIS sun consists of:
DBMS DSIS:
• knowledge base (expert information about parry DS);
• base models of the development of the operating system (information about the
options and parameters for the development of the DS);
• database (information about the operating parameters and operating limitations
of aircraft).
• Procedural part:
recognition module DS (signals from onboard measuring systems of the armed
forces come to the recognition engine information on the status of the armed forces
with an automatic check on the accuracy of the information survey method backup
systems, sensors, meters);
• classification module DS (the generated parameter vector state sun enters the classification module of the DS, by comparison with the reference state vector is the
classification of DS, classification of DS is in the base models of the development
of the operating system; in case of absence of classified DS, it becomes “conflict
state”);
• module parry DS (the formation of variants parry DS in the form of a graph
model and select the optimal variant by the criterion of minimum time parrying
with constraints from the database of operational parameters of the aircraft. The
2.4 A Model of the Functioning of the Information Support System …
55
Fig. 2.6 A model of the functioning of the DSIS aircraft crew in the DS. Note: 1—information
sheets of aerodromes, DS; 1 —updates of the knowledge base, model database; 2—updates of
the knowledge base, models and databases for the aircraft type; 3—information about the state of
the aircraft from onboard automated control system; 4—information sheet of the airfield, control
signals; 5—information about the state of the aircraft from onboard measuring systems; 6—information about the state of the aircraft from onboard measuring systems; 7—data on the options for
parrying the DS; 8—signal on the determination of the occurrence of the DS; 9—data from backup
systems, gauge sensors; 10—data about the DS; 11—information to the crew about the state of the
aircraft, actions to parry the DS, a request for automatic parry (information on the implementation of automatic actions based on the conditions of transient nature of the DS); 12—data on the
options for parrying the DS, operational parameters of the aircraft, etc..; 13—data on the current
DS and options for parrying; 14—data on the operating parameters and operational limitations of
the aircraft; 15—control actions of the aircraft crew; 16—information on the option of optimal DS
parry, request for automatic parry (information on the execution of automatic actions based on the
transient nature of the DS); 17—data on the best option to parry the DS
56
2 The Methodology of Functional Control of the Aircraft …
implementation of option parry DS may be in the form of contextual indications
to the flight crew or automatically).
Thus, a model of the functioning of DSIS of the aircrew in the DS will minimize
the time of occurrence of the critical information (in the form of instructions and
algorithms for countering negative influences in the operating system) onboard the
aircraft and on the working places of specialists of the Department of Internal Affairs.
The architecture of the information model used a distributed principle of combining
elements to maximize information availability and increase throughput.
References
1. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018 (2019).
Federal Air Transport Agency, Moscow, 89 pp
2. News on aviation accidents and aviation incidents for the first half of 2017. 2nd half of 2017
(2018). Moscow. With 122, p 145
3. The concept of the Federal target program “Ensuring the safety of flights of aircraft of state aviation of the Russian Federation in 2010–2014 years”. The government of the Russian Federation
of 22 April 2009, No. 554-R, Moscow, 48 p
4. Ponomarenko VA (2006) Psychology of the human factor in a dangerous profession. Polikom,
Krasnoyarsk, 629 p
5. Safety management oversight manual, 2nd edn (2009). International Civil Aviation Organization,
318 p
6. Ore O (1995) Theory of graphs. Nauka, Moscow, 336 p
7. Orlovsky SA (1998) Decision-making problems with fuzzy initial information. Nauka, Moscow,
194 p
Chapter 3
The Architecture of Safety Flights System
in the Airspace of the Russian Federation
3.1 The Role and Place of the Decision Support
Information System in the Structure of the Ergatic
System “Aircraft–Crew,” “Aircraft–Operator
of an Unmanned Aerial Vehicle”
The actual performance of the system “aircraft–crew” (“aircraft–operator of the
unmanned aerial vehicle (UAV)”) directly depends on the effective functioning of
its constituent parts. Local or inconsistent effects on each part of the system cannot
lead to the desired result—the achievement of values of indicators of the level of the
actual efficiency that is comparable to the potential level of efficiency of functioning
of system “aircraft–crew” (“aircraft operator–UAV”) for the intended purpose.
Crew operator (UAV) as an element of ergatic system “aircraft–crew” (“aircraft–
operator UAV”) the available control actions that are implemented by carrying out
various kinds of education and training of the human operator. Including the application of technical means of training (simulators), and in the course of operation–
effect on the state parameters of the human operator psycho-physical and chemical
methods, for example, feeding audio signals, electro-cutaneous stimulation, etc. [1–
3]. To implement the formation and the optimal control state of the system “aircraft–
crew” (“aircraft–operator UAV”) during the period of its intended functioning of the
decision-making system (DMS) (Fig. 3.1) should be provided with data containing
the following information:
• the current values of the state variables of the system “aircraft–crew” (“aircraft–
operator UAV”);
• the current values of variables characterizing external to the system environment;
• current values of the variables characterizing the results of the operation of the “aircraft–crew” system (“aircraft–UAV operator”) (including estimates of the level
of achievement of goals);
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. V. Yakovlev et al., Conditional Function Control of Aircraft,
Springer Aerospace Technology,
https://doi.org/10.1007/978-981-16-1059-2_3
57
58
3 The Architecture of Safety Flights System in the Airspace …
Fig. 3.1 Structure of the decision support information system. DCS—data collection system;
ADAS—airborne data acquisition system; DPS—data processing system; CAS—condition assessment system of ECS and the external environment functioning (EEF); SCHP—state change prediction system of ECS; RDS—recommendation development system for decision-making system of
the DMS; DB—a database of the state of the ECS and the EEF, which stores information characterizing the change in the state of the ECS and the EEF, as well as the dynamics of the results of
the operation of the ECS at the stages preceding the current one; KB—a knowledge base about
mathematical models of processes occurring in ECS and EEF
• the values of the state variables of the “aircraft–crew” system (“aircraft–UAV operator”) and the corresponding values of the variables characterizing the external
environment and the results of functioning at the stages preceding the current one;
3.1 The Role and Place of the Decision Support Information System …
59
• forecast of changes in the values of the state variables of the “aircraft–crew”
system (“aircraft–UAV operator”) for various combinations of variable values
characterizing the external environment;
• forecast changes in the performance indicators of the “aircraft–crew” system
(“aircraft–UAV operator”) and develop recommendations for the formation of
control actions.
The first two of the above requirements coincide with the general requirements for
information support for process control in the modern theory of automatic control.
The appearance of the remaining three requirements is because the processes of
managing the state of the “aircraft–crew” system have some features that significantly
distinguish them from the management of technical systems.
Thus, the unique properties of the state management processes of the ergatic
control system (ECS) led to the need to expand the functions of systems that
provide information management, improve data collection systems (DCS), and move
from them to another type of automatic information systems—decision support
information system (DSIS) ECS with a functional diagram shown in Fig. 3.1.
The analysis of the circuit in Fig. 3.1 shows that the structure of DSIS, along
with the traditional ADAS systems for information support, CAS and DPS, new
functional blocks included SCHPS state change prediction system, RDS recommendation development system for decision-making system, as well as a database
and knowledge base, which makes it possible to attribute information management
systems for ECS state management to systems with artificial intelligence, the theory
and practice of which has recently been considered the most promising direction in
cybernetics.
Thus, the analysis of the subject area, namely the effectiveness of the functioning
of polyergic systems (which is the “aircraft–crew” system), revealed the need to
integrate the decision support system for the aircraft crew in the DS into its structure.
This fact involves the development of a prototype of a unified flight safety system in
the airspace of the Russian Federation.
3.2 Development of the Russian Federation Safety System
Architecture in the Airspace
It is proposed to improve the flight safety of aircraft and to use an architecture that
includes:
• infrastructure for the exchange of data between aerodromes, flight safety services
(of various levels) and aircraft (it is recommended to combine elements of the
information system in a distributed network, and not according to a hierarchical
principle, which will increase the reliability and stability of data exchange);
60
3 The Architecture of Safety Flights System in the Airspace …
• a subsystem for updating knowledge and databases with relevant critical information (description of the DS, aircraft failures and malfunctions, erroneous
crew actions, etc., similar to that implemented by the anti-virus program update
service);
• a system of information support for the actions of the aircraft crew, which should be
located onboard the aircraft and duplicated at control centers (for issuing recommendations to the ATC officers and the aircraft crew in the event of a malfunction
of the DSIS).
It is assumed that the developed system should not have screening properties; i.e.,
she is not a superstructure to the existing system, improving some indicators. There
should be a subsystem integrated into the air traffic management system, united by
a single concept with the ability to respond flexibly to changing conditions. The
principle of its functioning can be determined by the prototype of the system, for
example, “human immunity,” i.e., a set of organs and individual cells that allow the
body to function in an aggressive environment.
Consider the functioning of the active safety management system (Fig. 3.2).
The database management system, as part of the flight safety system, is a systemforming element and implements:
• the function of collecting, storing processing, and updating particular information
about the BS and how to pair them;
• the function of collecting, storing the processing, and updating of “aerodrome
information sheets” (“aerodrome information sheets” is an array of particular
Fig. 3.2 Functioning diagram of an active safety management system
3.2 Development of the Russian Federation Safety System …
61
information of the ATIS type—automatic terminal information service about aerodrome crocs, data of its communications and radio equipment (MC and RTS)
flights, meteorological conditions, etc.);
• distribution of updates to the aerodrome database management system.
The aerodrome database management system implements:
• storage and updating of information about the DS and how to parry them;
• obtaining information about the development of the operating environment in the
area of responsibility of the aerodrome from the DSIS crew of the aircraft in the
DS and DSIS of ATC specialists;
• transfer of the “DS data sheet” to the flight safety system (FSS) database management system (“DS data sheet” is an array of individual information about the
particular situation that occurred in the area of responsibility of the aerodrome
received from DSIS aircraft crew in the DS and DSIS air traffic control specialists);
• the transfer of “data sheet of the aerodrome” in the database management system,
data FSS;
• the transfer of information in DSIS of the aircrew in a dangerous situation and
DSIS experts ATC (DS updates for a given aircraft type, data sheets of the
aerodrome).
DSIS of the aircrew in the DS carries out:
• receive specialized information (update in particular situations for a specific
aircraft type, the control signals from DSIS specialists of the Department of
Internal Affairs, data sheets of the aerodrome);
• the transmission of information, in real time, the development of fixed asset
management system database of the airfield and DSIS professionals ATC.
DSIS professionals ATC shall:
• receive specialized information (DS updates on aircraft, the control signals
from DSIS specialists of the Department of Internal Affairs, data sheets of the
aerodrome);
• obtaining information about the development of a particular situation in the area
of responsibility of our police department from DSIS of the aircrew in the DS;
• transmission of the control signals, in real time, in DSIS of the aircrew in the DS;
• transfer datasheet of the aerodrome in real time, in DSIS of the aircrew in the DS;
• the transmission of information, in real time, the development of fixed asset
management system database DSIS airfield.
Thus, the architecture of the unified system of safety of flights in the airspace of
the Russian Federation has the properties of stability, reliability, performance and
will ensure on the one hand timely updating of critical information on the ground,
and on the other hand, the collection of information on the status of airfields, aviation
incidents and accidents to establish instructions and algorithms of actions of the crew
in the DS.
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3 The Architecture of Safety Flights System in the Airspace …
3.3 A Model for the Optimal Placement of Critical
Information Entities in a Unified Safety System
The organization of information support for the aircraft crew is understood as the
presentation of decision-making at various levels of the hierarchy, aggregation of critical information in the nodes of an active flight safety management system, ensuring
prompt access to critical information and its reliability, consolidation of data on a DS
in the FSS, organization of optimal access to data and their protection: the proposal
of technology for coordinated updating of a single information base for universal
access.
The task of distributing data for parrying the DS in the active safety system developed is the equivalent task of placing information in the nodes of a distributed information and computer network (DCN). The task in the general case is multi-criteria.
Various objective functions can serve as criteria for minimization or maximization
(e.g., minimizing the time of delivery of a request and response to a DCN, minimizing
information circulating in a network, etc.) [4–7].
The total cost of implementing a query to the DS database in a unified flight safety
system in the airspace of the Russian Federation includes the following elements
[4–7]:
communication costs (Z c );
the costs of local processing (Z lp );
system costs (Z sc );
costs of conflict resolution (Z cr ).
Formally, the total costs of system resources can be represented as:
Z s = Z c + Z lp + Z sc + Z cr .
(3.1)
In a single system of safety of flights in the airspace of the Russian Federation, the
major part of the total cost accounted for communication costs. The costs of conflict
resolution and systemic costs in work are not considered because at the design stage,
and there is no information needed to determine the quantitative characteristics of
these costs. In developing the model focused on optimal distribution of information
in a single system of safety of flights in the airspace of the Russian Federation, the
assumption will be made about the optimal choice of mechanisms to access remote
data, local processing, and algorithms lock when sharing.
The main objective of the developed methodology is to convert the original
logical structure integrated into a distributed database, which must meet the following
requirements:
• to ensure the preservation of semantic properties of the information of the domain
elements and relationships between them, are recorded in the conceptual schema
of the data;
3.3 A Model for the Optimal Placement of Critical Information …
63
• take into account software capabilities and different modes of operation of
automation systems, frequency characteristics of the calls of components of the
extraordinary mathematical and software of informational funds.
A distributed database is a collection of multiple interrelated databases distributed
in a computer network. The control system, the distributed database, is defined as a
software system that allows us to manage the database so that its distribution was
transparent to users.
The technology of distributed databases disseminates fundamental for database
management concept, data independence on Wednesday. Several forms of transparency achieve this: network transparency (the transparency of the distribution)
transparency replication transparency fragmentation.
Transparency of the network means that users are dealing with a single logical
image of the database (DB) and access distributed data just as if they were stored
centrally.
In the distributed database management system of flight safety (DBMS FS),
data and applications that access them can be localized on the same node, thereby
avoiding or decreasing the need for remote data access. Moreover, since each host
runs fewer applications and stored a smaller portion of the database, we can also
reduce competition in access to information and resources. The system consists of
many (possibly empty) of nodes and a nonempty set of data nodes. Data nodes have
means for data storage, and the nodes receive requests—no; they only run programs
that implement a user interface for access to data stored in the data nodes. The logical
nodes are independent computers (servers) that have their operating system and can
run independently of the application. The most important distinguishing feature—a
loosely coupled environment, where each node has its operating system and operates
independently.
For each data node can act in two modes:
• on the initiative of a client node;
• at the initiative of the host server.
In each of these modes, the information can come:
•
•
•
•
single (in the form of the original data);
periodically (at regular intervals of time);
schedule (through unequal, but known in advance the time intervals);
stochastically (random time).
Typical queries have several classification features (Figs. 3.3, 3.4 and 3.5):
• in terms of impact on information stored in a database: query to read data and
requests to modify data;
• the source of the request: application and system;
• the number of participating in the execution of the query nodes: standalone and
distributed;
• at the place of coordination of the request: local and remote;
• by the method of forming the request: formalized and non-formalized.
64
3 The Architecture of Safety Flights System in the Airspace …
Fig. 3.3 Local autonomous request
Fig. 3.4 Remote autonomous request
Fig. 3.5 Remote distributed request
The node is characterized by the following information:
• information placed in a node and used to solve problems by other nodes;
• the information generated inside the node and used to solve problems on the node
(local);
• the information generated within the node and used by other nodes.
The information generated on a node should be understood as information that
appears on a node once or repeatedly (but its occurrence is inherent only to this node).
The information generated on the node will be further considered as non-moving.
Data channels, in general, are described by a tuple of characteristics. The following
are used for description: throughput at a given error probability (Rer ), average
3.3 A Model for the Optimal Placement of Critical Information …
65
message delivery time, etc. Delivery time is a function of the amount of information transmitted. We consider the channel capacity unchanged in the interval of the
solution to the problem. Then, as the weight coefficient characterizing the arc, we
introduce an indicator of the form:
Ψ =
1
,
C
(3.2)
where C—bandwidth of the channel connecting adjacent nodes (C > 0).
The so-called bottleneck determines the channel capacity between two nonadjacent nodes, i.e., transit section having a minimum throughput or a maximum
weight coefficient. Therefore, the channel estimate between two non-adjacent
nodes will be:
Ψ = max(Ψe , e ∈ ),
(3.3)
where e—channel connecting two adjacent vertices, —the path from the source
node to the destination node.
To solve the problem of optimal placement of fragments of a distributed database
(DDB) in the nodes of an active flight safety system, it is necessary to formalize
the concepts: essence, task, distributed information, and computer network. These
concepts will allow us to formulate the optimal placement problem and propose
algorithms for its solution.
Next, we move on to solving the problem of the optimal placement of informational entities in the flight safety system in the airspace of the Russian Federation. In
the flight safety system in the airspace of the Russian Federation, the access time to
information (action instructions) is critical, so the task of optimally placing critical
information in the nodes (servers) of the system in question is urgent.
The model for placing informational entities in the flight safety system in the
airspace of the Russian Federation can be formalized and presented in the following
form (Table 3.1).
Information entity (S) is an object of the real world, information about which
stored in a database. An attribute of an information entity (A) is a named characteristic
of an entity that is relevant in a given subject area.
This IE is designed to solve a complex of tasks
B = {bp , p = 1, …, P} defined by regulatory documents, using information about
instances of the information entity S stored in the DCN nodes:
S = sr1 ,...,rW , r1 = 1, . . . , R1 , . . . , r W = 1, . . . , RW , w = 1, . . . , W
(3.4)
or
S=
Sr1 ; Sr1 =
Sr1 ,r1 ; . . . ; Sr1 ,...,rW −1 =
Sr1 ,...,rW ,
(3.5)
66
3 The Architecture of Safety Flights System in the Airspace …
Table 3.1 Description of the mathematical model for placing informational entities in a unified
system of flight safety in the airspace of RF
Description of entities
Math record
Many entities used in the “aircraft–crew”
“aircraft–UAV operator” system, defined as
special situations:
• AT failures
• crew actions leading to a particular situation
• the impact of external factors
S = {sr1,…,rW ; r 1 = 1, …, R1 ; r W = 1, …,
RW ; w = 1, …, W };
Sr 1
Sr 1,...,r W −1 =
S=
Sr 1 ;
=
Sr 1,r 1 ;
..
.
Sr 1,...,r W
Description of the essence of all levels except
the last (w = 0, …, W − 1):
• failures (violations) in the operation of
aircraft systems
• the aircraft goes beyond the operational
parameters of piloting
S r1,…,rw = {<Aj,(r1,…,rw) > ,<S r1,…, S r1,…,rW >
∈ S, j = 1, …, J (r1,…,rW −1) }
Description of the essence of the last level W:
intervals of operational parameters
characterizing the regular operation of units
and assemblies of the aircraft
S r1,…,rW = {<Aj,(r1,…,rW )> , j = 1, …,
J (r1,…,rW ) }
The set of attributes describing the objects of
A = {Aj,(r1,…,rW ) , j = 1, …, J (r1,…,rW ) }
the set S: specific parameter values that
describe the functioning of the components and
assemblies of the aircraft at the time of the
occurrence of an individual situation
where S—many entities used in solving problems; r 1 = 1, …, R1 , …, r W = 1,
…, RW , w = 1, …, W is the index number of the entity that determines its place
in the dependency hierarchy; i.e., independent entities—level w = 1—have a single
index (e.g., s1 , s2 , …, sR1 ), and entities that are included as sub-entities in the previous
level—level w = 2—have a double index (e.g., s1,1 , s1,2 , …, s1,R2 , etc.); ∪—operation
of quasi-union, which allows to obtain the essence of the previous level according to
the rule:
Sr1 ,...,rw−1 = {< A j,(r1 ,...,rw−1 ) >, < Sr1 ,...,rw >}
= {< A j1 ,(r1 ,...,1) >, < S j1 ,(r1 ,...,1) } ∪ . . . ∪ {< A jr w ,(r1 ,...,rw ) >, < S jr w ,(r1 ,...,rw ) }
= {< A j1 ... jw ,(r1 ,...,rw ) >, < S j1 ... jw ,r1 ,...,rw > |Sr1 ,...,rw−1 .A j ∗ = Sr1 ,...,rw .A j1∗ & . . .
. . . &Sr1 ,...,rw−1 .A j ∗ = Sr1 ,...,rw .A jw∗ }.
(3.6)
The principle of constructing indexes of entities used in the system is shown in
Fig. 3.6.
3.3 A Model for the Optimal Placement of Critical Information …
67
Fig. 3.6 Hierarchical entity model
Entities of any level, except the last, are described in the form:
sr1 ,...,rW −1 = {< A j,(r1 ,...,rW −1 ) >, < sr1 ,...,rW >, j = 1, . . . , Jr1 ,...,rW −1 },
sr1 , . . . , sr1 ,r1 ,...,rW ∈ S,
(3.7)
where Aj —attribute of this entity, sr1,…,rW —entities (sub-entities) of other (lower)
levels, and entities of the last level in the form:
sr1 ,...,rW = {< A j,(r1 ,...,rW ) >, j = 1, . . . , Jr1 ,...,rW }.
(3.8)
The entity description view is informational reference guides.
Let us further consider the description of the system from the point of view of the
distribution of entities among nodes of a graph of the type “decision tree.”
Suppose that in each lth node a strictly defined set of problems is solved due to
the special situation in flight:
Fl = fl,n , n = 1, . . . , Nl , l = 1, . . . , L , Fl ⊂ B.
(3.9)
The cost of delivering an information entity from a source node to the node on
which the problem solved has the form:
Ψl,n,k (lu (Φ)) = max Ψl,n,k,κ , κ ∈ l,lu ,
(3.10)
68
3 The Architecture of Safety Flights System in the Airspace …
where l,lu —least-cost path connecting the source node and the destination node;
κ—arc belonging to this path.
Table 3.2 describes the elements of a mathematical model for the placement of
information during the operation of an active safety management system.
Table 3.2 Description of the elements of a mathematical model for the placement of information
entities in a unified system of flight safety in the airspace of the RF
Elements of the mathematical model
Math record
G network
G = (V, E)
The set V of vertices (nodes) of the
network G
V = {vl , l = 1, …, L}
The set E of arcs of the network G
E = {em , m = 0, …, M}
Γ = vl l Weighting matrix
H κ
The set B of problems solved by the system B = {bp , p = 1, …, P}
The set F l of problems solved in the lth
node
F l = {f l,n , n = 1, …, N l }, l = 1, …, L, Fl ⊂ B
Q = ql,n The set of Dl,n entities used to solve the nth Dl,n = dl,n,k , kl,n = 1, . . . , K l,n
∗
problem in the lth node
, Dl,n , n = 1, . . . , Nl , l = 1, . . . , L
= Dl,n
∗ of non-moving entities used to
∗ = d∗
∗
∗
The set Dl,n
Dl,n
l,n,k∗ , kl,n = 1, . . . , K l,n , n =
solve the nth problem in the lth node
1, . . . , Nl , l = 1, . . . , L
Frequency characteristics of the task
Frequency characteristics of an entity
Dl,n = {d l,n,k , k l,n = 1, …, K l,n }, n = 1, …, N l , l =
1, …, L
U = u l,n,k The set F of entities placed in nodes
F = {F l , l = 1, …, L},
The set Dl,n of relocatable entities used to
solve the nth problem in the lth node
L
Fl =S
l=1
The set Fl of entities located in the lth node F = {ϕ , x = 1, . . . , X } = F ∗ , F , l =
l
l,x
l
l
l
1, . . . , L
The set of Fl * non-relocatable entities
located in the lth node
∗ , x ∗ = 1, . . . , X ∗ }, l = 1, . . . , L
Fl∗ = {ϕl,x∗
l
A set of Fl ~ roaming entities located in the F l = {ϕ l,x , x = 1, …, X l }, l = 1, …, L
lth node
The set of H l,n,k attributes describing the
H l,n,k = {hl,n,k,i , i = 1, …, I l,n,k }, k l,n = 1, …, K l,n ,
kth entity in solving the nth problem in the n = 1, …, N l , l = 1, …, L, Hl,n,k ⊂ A
lth node
ith attribute is characterized by a tuple
hl,n,k,i = {<l,n,k,i ,
The volume of the ith attribute of the kth
entity when solving the nth problem in the
lth node
Y l,n,k,i
l,n,k,i ,
Yl,n,k,i >}
3.3 A Model for the Optimal Placement of Critical Information …
69
Based on the description of the model elements, we obtain a function that characterizes the information flows in the information system when performing distributed
queries, in the form:
L
K l,n
Nl
Z (F) =
Il,n,k
u l,n,k Ψl,n,k (lu (F))ρl,n,k
ql,n
l=1 n=1
k=1
Yl,n,k,i ,
(3.11)
i=1
where Ψl,n,k (lu (F))—the cost of delivering the required entity from the source node
with number li to the destination node with number l (l = li ).
Solving the problem of placing entities in the nodes of a unified flight safety
system in the airspace of the RF, we pose the following restrictions:
• the same informational entity in the network cannot be located in different nodes
Xl
L
φl,x = ∅;
l=1 x=1
Xl
L φl,x = S;
(3.12)
l=1 x=1
• nodes have limited resources for storing information:
Nl
K l,n
Il,n,k
ρl,n,k
n=1 k=1
Yl,n,k,i ≤ Λl ,
(3.13)
i=1
where l —volume, including the volume occupied by non-roaming entities, allowed
to place data in this node; ρl,n,k —the number of instances of this entity.
The first limitation based on the fact that the optimal placement of information
does not provide for its duplication. At the same time, the question arises of the
reliability of information storage, which requires the use of extraordinary measures.
Therefore, in order to ensure the reliability of information storage, it is supposed to
have backup nodes on which current replicas of fragments of a distributed database
with critical information will be stored.
The second limitation is related to the hardware capabilities of nodes that provide
their resources for information placement. This restriction allows we to manipulate
the node load ( l ) information. For nodes that are not able to provide their resources,
this value is 0.
Based on the preceding, the task of allocating entities by nodes can be formulated
as follows: determine such a distribution (F) of entities by nodes of a unified flight
safety system in the airspace of the Russian Federation that minimizes the objective
function (the total processing time of requests when solving the entire set of tasks at
a given time interval) (3.11) under the constraints (3.12) and (3.13):
70
3 The Architecture of Safety Flights System in the Airspace …
Fopt → min Z (F).
F
(3.14)
This task belongs to the class of integer programming problems, a feature of which
is the optimization of the structure of a unified flight safety system in the airspace of
the Russian Federation with an implicit dependence of the objective function on the
deployment variable and the presence of restrictions.
Thus, the developed mathematical model for placing critical information in a
unified flight safety system in the airspace of the Russian Federation allows us to
solve the problem under consideration and use the properties of the objective function
and the constraints set to reduce the space of the source data. The task of distributing
and placing information in the nodes of a unified flight safety system in the airspace
of the Russian Federation cannot be solved by the direct combinatorial method even
on relatively small numbers of nodes and entities, since the search for its solution
has an exponential time complexity, which requires the development of methods that
lead to a decrease in dimension source data and, accordingly, reducing the space of
possible solutions.
3.4 The Concept of the Creation and Development
of the Air Navigation System of Russia
The concept of creating and developing the Air Navigation System of Russia is
described in detail in [8].
The air navigation system (ANS) should be a single system for organizing the
use of airspace and air navigation services for users of the airspace of the Russian
Federation, including areas of its international responsibility, in the interests of its
practical use by all users, ensuring national security and developing the economy
of the Russian Federation. The system should be based on the integrated interaction
of man, technology, facilities, and services, with the support of promising onboard,
ground, satellite means, and air navigation systems. Belonging to ANS means that:
• the activity of the service/system, in whole or in part, is aimed at solving the
problems of the ANS;
• coordination of the activities and development of these services/systems in the
interests of air navigation services to airspace users is carried out by Rosaeronavigation, regardless of whether the services/systems are directly subordinate to
it and regardless of their departmental affiliation.
Part of ANS should log in ground, airborne, and satellite facilities and systems:
•
•
•
•
communications, navigation, landing, surveillance;
aviation and space search and rescue
of aeronautical information;
meteorological services;
3.4 The Concept of the Creation and Development …
71
• technical support and trained personnel by established rules and procedures, organizing airspace and air navigation servicing of users of airspace of the Russian
Federation.
In the active tasks and area of responsibility, the ANS is a system of a higher
hierarchy level than the current EU ATM. It should be designed based on a typical
technical architecture that provides the functional and organizational integrity of the
system and the integration of all its elements, in compliance with relevant international standards and recommended practices of ICAO and regulatory acts of the
Russian Federation. The system shall provide organizational, information, and technical interoperability, as well as multilevel interaction systems of the relevant bodies
of air traffic management (ATM) (flight control) airspace users, including automated.
In addition, the ANS needs to interact with a Federal System of Reconnaissance
and Control Over Airspace (FSR and COA), military automated control systems,
automated systems for meteorological services to air navigation, and other systems,
information that can be used or transferred to/from the ANS, in the interest of the
organization of airspace use and air navigation services users.
The creation and development of ANS should provide all users with timely access
to required airspace, and maintenance, and aircraft operators will allow creating
conditions for maintaining the planned time of departure and arrival, including
providing flights for general aviation. ANS should give users the possibility of
selecting preferred routes of flight to maintain the required level of safety of air
traffic. The development of ANS should be based on [8] international standards
and recommended practices, taking into account methods of air navigation planning
ICAO.
The establishment of the air navigation system of Russia will allow to:
• to ensure adequate state regulation of using the airspace of the Russian Federation;
• to eliminate departmental fragmentation of military and civil ATM agencies,
and insufficient coordination of development of systems of communication and
radio engineering maintenance of flights, onboard flight control, and navigation
systems, the system of aerospace search and rescue, aeronautical information
services, meteorological services;
• to optimize the process control of ANS in the light of national interests in the
use and control of the airspace, based on economic development of the Russian
Federation;
• to upgrade technical support of air navigation in the airspace of the Russian
Federation and the enlargement of ATM centers;
• to provide air navigation services aircraft using advanced equipment and technologies by the method of “from gate-to-gate” taking into account tendencies of
development of the airfield network of the Russian Federation;
• to ensure a single economic and technical policy of ANS in the use and control of
the airspace of the Russian Federation, to achieve the standardization of technical
means and systems of dual use, reduce development costs and operation;
72
3 The Architecture of Safety Flights System in the Airspace …
• to reduce unproductive losses of the users to improve the security of air traffic and
the economic efficiency of airspace use including, when flying in the far North,
Siberia, and the Far East;
• to reduce the negative impact on the environment gas emissions, engines, noise,
and electromagnetic radiation terrestrial means of support of flights;
• to increase the attractiveness and flexibility of use of airspace for domestic and
foreign users;
• to accelerate the integration of the ANS into the world aeronautical system.
The system of indicators and target indicators promising ANS should include
requirements set by the state based on the demands of airspace users, as well as
resulting from them, more detailed indicators that relate to various components and
characteristics of the system.
The leading government indicators of ANS should be:
• national security in the sphere of the use and control of the airspace of the Russian
Federation;
• air traffic safety;
• the bandwidth of the air navigation system;
• the efficiency of the air navigation system;
• the availability of air navigation system;
• aviation safety in the field of air navigation;
• environmental protection;
• the compatibility of air navigation systems.
Indicators at the level of ANS should be developed, taking into account standards
and recommended practices to ICAO and to reflect the quality of its subsystems and
components, their degree of interaction, level of technical equipment, and compliance
with international and domestic standards.
The airspace of the Russian Federation is a resource of ANS used in the interests
of citizens, economy, and national security of the Russian Federation. Any limits
ATS airspace must be temporary. The primary task of the ANS in this direction is
the introduction of the classification of the airspace of the Russian Federation and
methods of air traffic services for each class of airspace, the relevant international
standards, and recommended practices of ICAO.
The introduction of flexible use of airspace of the Russian Federation should
ensure that the transition to the use of the principles of an area navigation route
and in terminal areas, and the future, should be implemented the ability to perform
autonomous flight along the optimal trajectory in the airspace, designed for “freeflying.”
Promising ANS should allow us to decide to provide users with preferred, from
the viewpoint of saving fuel, route and flight level in realtime, based on the automated
interaction of ANS with aircraft operators and airport services.
Following international standards and recommended ICAO practices, an air traffic
safety management system should be introduced in the Russian Federation. Conditions must be provided under which the frequency of aircraft accidents, directly or
3.4 The Concept of the Creation and Development …
73
indirectly related to the functioning of the air navigation system, did not increase
with increasing light intensity, and if possible, decreased. An analysis of the state of
air traffic safety and the development of a program of specific measures to ensure it
should be carried out on a systematic basis. Each implemented ANS element should
be subjected to a specific analysis of its impact on security, both as a separate element
and as a component of a more extensive holistic system.
To reduce the negative impact of the human factor on air traffic, safety within
the framework of a promising ANS is necessary to provide the required level of
automated support for the dispatcher.
Assessment of air traffic safety should be carried out continuously at the stages
of the creation and development of ANS. ANS facilities, technical means, and the
process of processing aeronautical information must be certified (meet established
state requirements), and its personnel must be certified.
ANS should be a unified technical policy, providing for the modernization of ATM
systems to ensure the operation of all types of aircraft only domestic equipment and
ensure that the national interests of the Russian Federation, national and international
standards. Given the new principles of functioning of the ANS, based on the integration of perspective ground-based, airborne and satellite facilities, and air navigation
systems, is necessary to develop and implement an agreed by all stakeholders of
the technical architecture that defines the functional relationship of these tools and
systems, interaction protocols, and to ensure harmonized development of terrestrial,
airborne, and satellite parts of the system.
Directions of development of technical base ANS must comply with the provisions
of the CNS/ATM concept, ICAO, and be:
(1)
In the field of communications.
It must be a network of air communication based on the integration of perspective
ground-based, airborne, and satellite communications systems and data links, which
provides secure automated interaction of system components and the airspace user
at all stages of the flight in real time.
(2)
In the navigation pane.
The evolutionary transition to advanced navigation systems, including ground-based
and satellite means of support operations, both on the route and in the terminal area,
including approach and landing should be provided.
(3)
In the region of interest.
Modernized traditional surveillance system with a system of state recognition and
secured their merging into a unified automated radar system of the FSR and the
COA should be implemented. At the same time, it should implemented a new kind
of surveillance—automatic dependent surveillance—with the integration of information on the air situation from the traditional and advanced tools and surveillance
systems.
74
(4)
3 The Architecture of Safety Flights System in the Airspace …
In the field of air traffic management.
A system of air traffic services high level of automation, including the use of artificial intelligence for the detection and development of solutions to resolve conflict
situations must be created. In the conditions of the growing intensity of air traffic,
these systems must minimize the Download Manager to the normative level and the
implementation of flights on their preferred trajectories due to the flexible management of airspace, improved information provision, and automated interaction with
all major components of the ANS.
It must be a multi-tiered system of planning of air space use and air traffic management, the operation of which will be implemented in conjunction with air traffic
control and management systems arrivals and departures of aircraft in real time. As
a result, it needs to be implemented on the principles of air traffic service “from
gate-to-gate,” as well as bandwidth control ANS.
It must provide information and technical interoperability of ATM systems with
automated systems of appropriate ATS units (flight control) airspace users, information items, dual-use unified automated radar system of the FSR, and the COA and
other military automated control systems using the information of ANS.
(5)
In the field of avionics.
Perspective avionics which allows optimizing the modes of the aircraft for the application of four-dimensional area navigation and the exchange of necessary information
via the “ground-board-ground” and “board-board” needs to be embedded. Aircraft
must be equipped with warning systems collisions with other aircraft and ground
systems for the public recognition, and autonomous separation and implementation
of airspace technology “free flights.”
(6)
In the field of meteorological services to air navigation.
Operational practice of meteorological services for air navigation automated systems
for monitoring, gathering, processing, storage, and dissemination of meteorological
information (including onboard weather), including a system for determining the
slipstream, wind shear that is compatible in performance with technical devices
and systems of air navigation must be created and implemented. There should be
developed standardized communications protocols, automated systems, and means
of ATM and meteorological services to air navigation.
(7)
In the field of aeronautical information.
Automated systems for the collection, processing, storage, and dissemination of
aeronautical data, providing of ANS and airspace users of the Russian Federation of
aeronautical information anytime, anywhere, in a consistent format, electronically
and/or on paper must be created.
3.4 The Concept of the Creation and Development …
(8)
75
In the field of search and rescue.
Along with the introduction of satellite systems and equipment of all aircraft, automatic radio beacons transmit distress signals in an emergency, rescue and life support
must be provided for the creation of a new aviation search and rescue complex.
Given the strategic importance of the ANS, the high cost, and large amounts
of introducing advanced technology for air navigation purposes, it is necessary to
ensure the priority in its creation and implementation of domestic producers. In
exceptional cases, external components are allowed to use while creating tools and
ATM systems. Also, the objects of ANS should be executed in a secure execution.
The development and introduction of advanced equipment and systems in support
of ANS should be carried out by the Air Navigation Plan of the Russian Federation.
To prevent equipment ANS of diverse technical facilities and software necessary to
implement projects of modernization and development of the system and its components on the principles of systemic integration under a binding agreement with the
Rosaeronavigation.
The integration of ANS into the global air navigation system should be carried
out following the Global ATM Operational Concept and the Global Air Navigation
Plan for ICAO CNS/ATM systems, taking into account the national interests of the
Russian Federation. As an initial stage, a set of works on harmonization and subsequent integration of the ANS with the systems of CIS member states and Western
Europe should be implemented. For this purpose, differences between the regulatory
legal documents of the Russian Federation and international standards recommended
practices ICAO rules and procedures should be eliminated as much as possible.
In the short term, it is necessary to ensure the interconnection of the airways of
the Russian Federation with the network of routes developed on an ongoing basis by
an international group of experts on the development of transit routes in the eastern
part of the ICAO European Region. The aircraft equipment of Russian airlines with
onboard equipment should be carried out, taking into account the recommendations
adopted by the European Commission of Civil Aviation and approved by ICAO that
determine the requirements for onboard equipment.
References
1. Babiychuk AN (ed) (1988) Medical aspects of civil aviation safety. Air Transport, Moscow, 360
p
2. Ponomarenko VA (2006) Psychology of the human factor in a dangerous profession. Polikom,
Krasnoyarsk, 629 p
3. Human factors training manual, 1st edn (2008). International Civil Aviation Organization, 370
p
4. Mauder J (ed) (1981) Operations research. Moscow, 667 p
5. Krasovsky AA (2005) Mathematical modeling and computer training systems. VVIA them.
NOT. Zhukovsky, Moscow, 255 p
6. Sovetov BYa (1985) Sovetov BYa, Yakovlev SA (eds) Modeling systems. Higher School,
Moscow, 271 p
76
3 The Architecture of Safety Flights System in the Airspace …
7. Taran VA (1996) Ergatic control systems. Mechanical Engineering, Moscow, 188 p
8. The concept of the creation and development of the Air Navigation System of Russia. Approved
by the Decree of the Government of the Russian Federation (2006)
Chapter 4
A Mathematical Model for Constructing
a Conflict-Free Flow of Aircraft
in the Zone of the Near Zone Officer
Responsibility (Circle Dispatcher)
The method of organizing information support for the officer of the near zone (circle
dispatcher) in detecting and resolving potential conflict situations is a combination
of a model for constructing an aircraft delay maneuver for a given interval and
algorithms for constructing a conflict-free flow in the conditions of priority and
priority service modes [1].
4.1 Features of Information Support During the Formation
of the Flow of Aircraft During Approach
The process of forming an aircraft stream in the near zone is a complex process
consisting of a large number of separate operations for processing information about
aircraft and their motion parameters.
Among many of these operations, we can distinguish the main ones that make up
the basic structure of the process [2]:
•
•
•
•
establishing the sequence of landing and takeoff;
regulation of spatial and time intervals between aircraft while maintaining safety;
control of aircraft flight at heading and glide path;
landing, takeoff.
Following the sequence of operations, the process can be represented in the form
of a diagram consisting of the following five functional elements:
(1)
(2)
(3)
(4)
(5)
waiting area;
approach pattern;
maneuverable zone (zone of extension of the trajectory);
pre-landing straight line;
runway.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. V. Yakovlev et al., Conditional Function Control of Aircraft,
Springer Aerospace Technology,
https://doi.org/10.1007/978-981-16-1059-2_4
77
78
4 A Mathematical Model for Constructing a Conflict-Free Flow …
Let us briefly describe the purpose of each element.
The waiting area is a drive or “buffer” for delays in the case when the flow of
incoming aircraft exceeds the capacity of the aerodrome zone. The waiting area is
used if it is necessary to carry out delays that cannot be realized in a maneuverable
area.
An approach pattern is an established route in the area of an aerodrome along
which the aircraft flies from the point of entry into the area of the aerodrome to the
exit to the pre-landing line.
The maneuvering zone is intended for the implementation of the necessary spatial
intervals between aircraft approaching to achieve the maximum CPTY while maintaining flight safety. Depending on the organization of the airspace and the intensity
of the decline, either an unordered or an ordered flow from the waiting area enters
the maneuvering zone. The regulation of spatial intervals between aircraft is carried
out by changing (lengthening) flight paths. In this zone, one of the most difficult
operations of the ATC process is carried out. Its effectiveness largely depends on
the accuracy of the forecast of the development of the air situation in the area of the
aerodrome, the timeliness of the commands of the officer of the near zone by the
pilot, and the accuracy of the navigation aids of the air traffic control, because in the
next step; i.e., on the pre-landing straight line, regulation of intervals is practically
impossible [3].
The base leg (BL) is a common path coinciding in the plan with the axis of the
runway. The straight length for modern aircraft is about 12–18 km.
The runway is designed for takeoffs and landings. The condition for its safe
operation is that during the take-off or landing on the runway, the simultaneous
presence of two aircraft is unacceptable. The runway capacity depends on the time
the runway is occupied by arriving aircraft and on the combination of incoming
aircraft. They are determined by the quality of the runway surface, the configuration
of taxiways adjacent to the runway and their number, meteorological conditions, type
of aircraft, etc. To ensure flight safety during successive landings on one lane, it is
necessary that at the moment when the aircraft landing releases the runway at the
taxiway (TWY), the aircraft landing approach must be at a height from which the
ACFT can go to the second circle. The minimum value of the height from which the
ACFT of this type can go to the second circle is called the critical height of departure
to the second circle. Runway occupancy time (or landing time) is understood to
mean:
H
+ trunway ,
tlanding = trunway
(4.1)
H
where trunway
—flight time of the aircraft from the critical departure altitude to the
second circle until the runway touches;
trunway —the runway time of the aircraft on the runway, taking into account the
taxiing time to the TWY.
4.1 Features of Information Support During the Formation …
79
Therefore, to ensure landing safety, the minimum interval between aircraft should
be sufficient to land the first aircraft (time taken to land tlanding ) before the second
aircraft has crossed a critical point of departure to the second circle.
The average runway busy time can be calculated using the following expression:
trunway =
2Lr un
L ar c
L add
+
+
,
Vtan + Vs
Vs
Vs
(4.2)
where L run —dry concrete run length in standard conditions until reaching the exit
speed on the taxiway—Vñ õ ;
Vtan —the average speed of the aircraft of this group at the time of landing;
L arc —arc length;
Rα
L arc = π180
◦ ,
where R—runway taxiway radius;
α—runway contact angle;
L add —runway additional run length.
From the expression (4.2), it can be seen that the runway travel time substantially
depends on the rate of descent to the taxiway. If taxiways located at an angle of
90° to the runway axis, then Vs is small and trunway is large. If there are high-speed
taxiways, i.e., TWY, adjacent to the runway at an acute angle, then the descent speed
can be increased, and trunway , therefore, reduced. The run time of an aircraft along a
runway also significantly depends on the location of the taxiways. The calculations
showed that it is most advisable to position high-speed taxiways at distances from
the runway end for aircraft of the IL-62 type—2200 m, for aircraft of the IL-18,
TU-134, TU-154 type—1200 m.
The minimum interval between aircraft landings and total throughput is determined as follows (if this random variable has a normal distribution) [4]:
Tlanding = p tlanding + κrunway σrunway ,
λ=
1
1
=
,
Tlanding
p tlanding + κrunway σrunway
(4.3)
(4.4)
where p—probability vector of being in the aircraft zone of various classes;
tlanding —runway occupation time vector of various classes;
κrunway —coefficient from the tables for the normal distribution function for the
selected minimum value of the probability of going to the second circle.
σrunway —runway standard deviation.
Thus, it is evident that increasing the throughput capacity of the pre-landing
direct and air space of the near zone as a whole is possible by minimizing the
intervals between aircraft at the landing course (no less than a safe interval) achieved
by quickly establishing the sequence of aircraft landing and take-off, as well as
by adjusting the spatial and time intervals between aircraft during approach with
maintaining safety requirements.
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4 A Mathematical Model for Constructing a Conflict-Free Flow …
4.2 Justification of the Need to Develop a Method
and Models for Organizing Information Support
for the Near Zone Officer (Circle Dispatcher)
in the Detection and Resolution of Potential Conflict
Situations
Safety and regularity of aircraft flights are one of the leading indicators of the effectiveness of the air transport system, which determines largely the level of organization, clarity, and coherence of the work of aviation enterprises and aviation departments, as well as their services, which interact in the process of preparing for flights
and air traffic control. Chapter 1 presents the results of safety analysis in the zone of
responsibility of the near zone officer (NZO) in the form of a distribution of flight
incidents in his zone of responsibility. The results of this analysis prove the relevance
of the need to automate the activities of the officer of the near zone (circle dispatcher)
to control dangerous proximity when approaching aircraft based on the development
of methods and analytical models for organizing information support [5].
The problem of ensuring safety and regularity in planning air traffic generated, as
a rule, by the uneven distribution of aircraft flows in space and time. At the stages
of preliminary planning of aircraft flows, this is primarily due to various restrictions
on the use of a network of airspace elements and leads to the fact that in the process
of implementing the plan some sectors of the near zone are overloaded. As a result,
during specific time intervals, the NZO cannot, due to lack of time, calculate and
ensure the optimal flight modes of aircraft, while taking into account the whole range
of requirements for safety, regularity, and economy of flights [6].
The use of aircraft delays in waiting areas as a means of ensuring flight safety
inevitably leads to a violation of regularity upon arrival. Failure of regularity, in
turn, can complicate the situation in the area of the aerodrome due to the possible
accumulation of a large number of aircraft and lead to a violation of the regularity
of departure.
Violation of flight regularity negatively affects the efficiency of all services that
ensure the implementation of the flight plan. It should also be taken into account
that the process of violation of regularity has the property of a “chain reaction”;
that is, violation of regularity, having arisen in a specific sector of the near zone,
can spread to other aerodromes through schedules of aircraft turnover and cause air
traffic disorganization. The solution to the problem of ensuring regular flights in these
conditions is possible only by automating the processes of organizing and controlling
air traffic flows based on the use of computer technology and optimization methods.
The efficiency of air traffic ensured by reducing the cost of CA operations. Costeffectiveness of flights as the central part of ensuring the efficiency of aviation is
a matter of concern for almost all airline services, such as aviation engineering,
operation of radio equipment, flight, navigation, aerodrome, and weather services.
The role and proportion of the service in ensuring flight efficiency increase with
4.2 Justification of the Need to Develop a Method and Models for Organizing …
81
increasing volume work on the transport of passengers and goods. However, the task
of increasing the efficiency of air traffic in the challenging operating conditions of
the EIS ATC is not easy.
In real conditions, in the ATC system, there are airspace restrictions, adverse
weather conditions, restrictions on the height and intervals of movement, limitations
on the capabilities of the person who is the FMT specialist, who is generating the
aircraft flow, etc. Under the influence of these restrictions, additional air costs arise
for ensuring air traffic safety flights.
To improve the efficiency and economy of air traffic, the following main
organizational measures are carried out [7]:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
the development and implementation of a rational network of routes and traffic
patterns that reduce the distances travelled by aircraft;
the rational division of airspace into sectors of the airborne forces and the
division of responsibilities between control centers, allowing to increase the
throughput of the elements of the air traffic control system;
rational flight planning, which eliminates the overload of the ATC system EIS
elements;
the development of rational rules for deciding on a flight based on the analysis of meteorological conditions at the landing aerodrome and alternate
aerodromes;
the rational organization of taxiing routes to the executive start before departure and the release of the runway after landing to reduce the employment
time of the runway;
rational control of the movement of aircraft on the airfield, allowing to reduce
the time of unproductive work of engines on the ground;
the choice of the optimal direction of the runway taking into account the meteorological conditions of flight in the area of the aerodrome and the existing
intensity of the flows of arriving and departing aircraft;
improving the accuracy and reliability of technical means of navigation and
radar control of air traffic to create objective conditions for reducing aircraft
separation standards;
the introduction of automation tools for processes of formation of aircraft
flows in order to increase the objectivity of the analysis of the state of the
air situation, improve the quality of decisions and reduce the workload of the
FMT specialist;
improving the qualifications and professional skills of flight personnel and
FMT specialists.
For each of these, organizational measures have been developed, methods of
increasing the efficiency of air traffic. Several such methods are embedded in the
practice of individual airlines and recommended for dissemination in the form of best
practices. Significant economic benefits can be obtained by optimizing the forming
processes flow entirely in terms of negative impacts. Calculations show that the
discontinuation of the sun in a large airfield site because of the sudden deterioration of
weather conditions formed unnecessarily significant losses providing care entirely on
82
4 A Mathematical Model for Constructing a Conflict-Free Flow …
spare airfields. Subjectivism in the decision-making of commanders on the selection
of other airport results, in addition to a sharp increase in the total flight time, even
to more congestion of some airports, which entails a whole chain of losses, such
as increasing the time of preparation of aircraft for departure, the complication of
supply of crews, in connection with the restrictions on sanitary norms of working
time.
The redistribution of responsibilities between the flight crew and officials of the
traffic service in the direction of active participation of the system of air traffic control
in making decisions about the distribution of airborne aircraft spare airfields involving
the preparation of decisions of computers will provide a significant increase in the
efficiency of air traffic in terms of crashes.
Along with the examples of apparent reserves of increase of efficiency of air traffic,
there are potential savings, which at first sight are not visible. Thus, the implementation of scientifically based standards for traffic flow management system in the
terminal area, in addition to increasing the safety of air traffic, leads to substantial
economic effect. Sources of effect can be [8]:
• reducing the cost of waiting for landing in the airspace of the aerodrome area by
eliminating the overload of the airfield airspace during peak hours;
• reducing the cost of waiting for landing and take off by increasing the capacity of
the aerodrome area when implementing organizational and technical measures,
the need for which is justified by the methodology for determining the capacity.
The effect from the first source formed when the hourly intensity of the stream
of arriving aircraft changes during the day by redistributing the arrival time of part
of the aircraft to other, less busy hours. If we know the number of aircraft λk (k
= 1.24) arriving at the airport every hour during the day before the introduction of
capacity standards, as well as the stream of aircraft redistributed taking into account
the capacity, with intensity λ∗k (k = 1, 24), then the economic effect of the introduction
bandwidth standards:
Q=ω
24
(λk yk − λ∗k yk∗ ),
(4.5)
k=1
where ω—average costs for 1 min of flight delay in the airspace of one aircraft in
the studied area of the aerodrome;
yk , yk∗ —the average landing is waiting time determined using the waiting
characteristic at a flow rate of arriving aircraft equal to, respectively λk and λ∗k .
The effect of the second source formed when the waiting characteristics of a given
aerodrome change with the introduction of organizational and technical measures
that increase the capacity of the aerodrome area. If, during the implementation of
such measures, the parameters x̄ and σ of the distribution of the controlled landing
intervals changed from the initial values to the new values and then the economic
effect of the implementation of the estimated organizational and technical measures.
4.2 Justification of the Need to Develop a Method and Models for Organizing …
83
The effect of the second source formed when the waiting characteristics of a given
aerodrome change with the introduction of organizational and technical measures
that increase the capacity of the aerodrome area. If during the implementation of
such measures, the parameters x̄ and σ of the distribution of the controlled landing
intervals changed from the initial values of x̄0 and σ0 to the new values of x̄∗ and σ∗ ,
then the economic effect of introducing the estimated organizational and technical
measures:
Q=ω
24
λk yk .
(4.6)
k=1
where ω—average costs for 1 min of flight delay in the airspace of one aircraft in
the studied area of the aerodrome;
yk , yk∗ —the average landing is waiting time determined using the waiting
characteristic at a flow rate of arriving aircraft equal to, respectively, λk and λ∗k .
The difference between the values of the average waiting time for landing before
y0 (λk ) and after y∗ (λk ) the implementation of the evaluated measures:
yk = y0 (λk ) − y∗ (λk ) = λk
B02 − B∗2 − λk (B02 x̄∗ − B∗2 x̄0 )
,
2(1 − λk x̄0 )(1 − λk x̄∗ )
B02 = x̄02 + σ02 , B∗2 = x̄∗2 + σ∗2 when λk <
(4.7)
1
,
x̄0
where ω—average costs for 1 min flight delays in the airspace of one aircraft in the
studied area of the aerodrome;
yk , yk∗ —the average landing is waiting time determined using the waiting
characteristic at a flow rate of arriving aircraft equal to, respectively, λk and λ∗k .
Calculations show that at aerodromes with high traffic intensity, a significant
economic effect can be obtained [9]:
(1)
(2)
(3)
(4)
(5)
(6)
when introducing new taxiways, reducing runway occupancy time by arriving
and departing aircraft;
with increasing accuracy of keeping crews of specified flight modes along
trajectories in the area of the aerodrome;
upon the introduction of computer technology to predict the estimated moments
of the landing of the arriving aircraft;
when introducing air traffic control systems increase the accuracy and
reliability of radar control of aircraft movement;
upon the introduction of automation tools for planning the approach sequence;
when optimizing the regulatory landing intervals and the corresponding
algorithms.
The economic effect can also be obtained by training FMT specialists in actions
by reasonable, rational procedures for planning the sequence of take-off and landing,
as well as the optimal values of the planned intervals of movement.
84
4 A Mathematical Model for Constructing a Conflict-Free Flow …
Thus, increasing the efficiency of air traffic is based on a set of interconnected
organizational and technical measures for the implementation of which appropriate
scientifically based methods are being developed.
4.3 Determination of the Space and Trajectories
of the Aircraft During Approach Conflict-Free Flow
Formation
At the present stage of the development of the Civil Aviation Administration of
the Russian Federation, an urgent need is to carry out flights in a safe and orderly
manner. That is dictated by the currently achieved and predicted values of flight intensity, tactical and technical data of the aircraft shortly, and continuously increasing
requirements for the quality of their tasks.
To determine the boundaries of the space and trajectories of the aircraft in the zone
of responsibility of the NZO, which exclude the development of a conflict between
the aircraft, an analysis of the zones and sectors in the area of the aerodrome is carried
out. An idea of the high zones and sectors given by the analysis of a typical scheme
of the aerodrome area is shown in Fig. 4.1.
The structure of the aerodrome zone includes flight routes, aerobatic zones,
training grounds, approach procedures, and other elements.
In its activities, NZO solves the following tasks:
• direct formation of a conflict-free flow of aircraft at all stages of flight;
• maintaining safe intervals between aircraft and taking timely measures to prevent
aircraft collisions on the ground and in the air;
• assisting aircraft crews in the event of particular incidents in flight and distress.
The officer of the near zone performs its functions throughout the flight shift
without the right to replace, and pauses for rest are not provided for by the regulations
of his activity.
The remote nature of the activities of NZO forces him to interact with the images,
replacing the sun and environment information model of the environment and sun.
Information model, in the minds of the NZO, is reflected in the way adequate to
the task that is set before him, and, together with previously obtained knowledge,
experience and is used to build the model, responsible for the activities of the officer
of the near zone.
Current conditions the activities of the NZO are caused by several factors that
have an essential impact on the information process flow of the sun [10, 11]:
(1)
(2)
extrapolation of the aircraft motion (information on a continuously moving
aircraft enters discretely; it is necessary to resort to the prediction of this
movement);
the dynamic processes of air traffic management [often by several armed forces,
the parameters of which rapidly change through time (course, speed, altitude)].
4.3 Determination of the Space …
85
Fig. 4.1 Variant of the airspace structure in the zone responsibility of the near zone officer
(3)
Officer of the near zone in your consciousness reflects the traffic situation as a
whole and of its parts; movement perceived ACFT NZO in connection with the
movement of other aircraft; the dynamic is a constant change of air situation,
flight parameters of the aircraft, meteorological conditions, etc.);
efficiency of processes in air traffic (NZO is subject to the time limit; the
increase of flight speeds and flight intensity require a quick response, heightened attention, plastic thinking; entirely perform the movement with high speed
86
(4)
(5)
(6)
4 A Mathematical Model for Constructing a Conflict-Free Flow …
on the established schemes with limited bandwidth that requires constant monitoring to maintain safe longitudinal, lateral, and vertical intervals between
aircraft);
the complexity of the process of formation of aircraft stream (is the solution of
the NZO several independent (competing) tasks vary in their importance and
nature. Often the way of solving the problem is missing or need to change the
shortcut that will lead to the solution of problems such a situation characterized
as problematic. The flow of aircraft performing the approach and resolution of
this conflict at the time of arrival on the runway simultaneously for multiple
aircraft—one of the main competing tasks solved by the officer of the near
zone);
the need for constant psychological preparedness for the occurrence of individual cases caused by the influence of negative factors (the occurrence of
equipment failures, errors of specialists of the flight management group,
high loads require the officer of the near zone of constant readiness and
mobilization);
work in conditions of interference (interference in the radio network, when
aircraft detected on the screens of all-round visibility indicators, work in
conditions of discomfort).
The formation of the conflict-free flow of aircraft in the near field is a complex,
highly dynamic process implemented by the NZO in terms of the high workload.
Technical means that as part of the EIS, ATC has a decisive influence on the
professional activity of the officer of the near zone. The workplace of the officer of
the near zone equipped with the remote indicator of landing system (RILS) which
allows the simultaneous pairing:
•
•
•
•
•
with the landing radar and control of NZO;
review radar;
automatic direction-finding equipment;
with radio communication HF, VHF, UHF ranges;
with short-range navigation SHORAN.
RILS provides:
surveillance specialist group flight management for air environment on the
external indicators and the combination of radar situation on the screens of the
indicators of the circular review with the display lines of bearing;
• displaying navigation information, additional digital information on the aircraft
(tail number (callsign), altitude, remaining fuel from aircraft equipped with
aircraft by the defendants (RSA), as well as its operational update at the same
time for six aircraft (according to the number of units auto-tracking).
On-screen indicators operating modes surveillance radar (SR) and SHORAN, the
following information is displayed:
Analog radar information corresponding to the radar system (radar);
4.3 Determination of the Space …
87
• labels range, and azimuth.
Information required from the specialists of the group management of flights during
the flights in the terminal area (routes, flight areas, the scheme of approach, polygon,
route, course line, and glide path, etc.) applied collotype press [12] manually.
RILS has several significant disadvantages:
• there is no combination on one indicator of information from several sources
about the position of the aircraft;
• there are no support forms for the aircraft, which necessitates switching the
attention of the officer of the near zone between the PPI and NID;
• there is no cartographic information on the PPI, HI, GPI (information about the
position of the aerobatic zones and the axis of the routes is applied by a collotype
press, which in the presence of parallax significantly worsens the control of the
position of the aircraft on the trajectory);
• insufficient operational capabilities to bring aircraft into auto-tracking (up to six
aircraft);
• there are no zones for automatic entry of aircraft into auto-tracking;
• the insufficient size of indicators of jobs of NZO specialists;
• there is no possibility of adjusting the position of the indicators (height, tilt,
rotation).
Thus, the officer of the near zone carries out its activities in the conditions of
dividing attention between different sources of information, with limited awareness
of the spatial position of aircraft and low accuracy characteristics of information
display facilities.
4.4 A Model for Constructing an Aircraft Delay Maneuver
for a Given Interval
The development of a model for constructing an aircraft maneuver for a delay for
a given interval is due to the need for prompt assistance in the formation of an
aircraft flow, monitoring the correctness of maneuvers, and predicting the situation.
Its application, by including the NZO workstation in the decision support information
system, will minimize the time for making the right decision by the officer of the
near zone; create the necessary conditions for the formation of a conflict-free flow of
aircraft during the approach. The model proposes to use as a criterion the minimum
delay time when performing aircraft maneuvering while resolving a conflict between
aircraft. A geometric illustration of the developed model is presented in Fig. 4.2. By
the model for constructing an aircraft delay maneuver, the initial data are determined:
S—distance to the lighthouse; V —is the speed of the aircraft (actual); TA—turning
angle (TA= 90 − TA1 ); TA1 —first turning angle; β—aircraft roll angle; R—turning
radius; Ω—angular velocity; {x0 , y0 }—beacon coordinates (ACP); {x, y}—aircraft
initial coordinates.
Fig. 4.2 Trajectory of the aircraft delay maneuver for a given interval
88
4 A Mathematical Model for Constructing a Conflict-Free Flow …
4.4 A Model for Constructing an Aircraft Delay Maneuver for a Given Interval
89
To organize effective informational support for NZO, in the event of a conflict
between aircraft in this area of responsibility, it is necessary to carry out calculations
to build a maneuver of aircraft delay for a given interval. These calculations include
the following steps [6, 7]:
• the choice of the angle of heel of the aircraft from the following conditions:
β=
β = 15, tdelay ≥
β = 30, tdelay ≤
tturn
2
tturn
2
(4.8)
• turning radius determination:
R=
V2
,
g · tgβ
(4.9)
V
· β.
R
(4.10)
• angular velocity determination
Ω=
1.
Straight line (a, b):
ya,b = kx + b,
(4.11)
where k = −tg(TA1 );
b = R;
x = 0, 100, 200, 300 . . .
2.
The construction of the circle of the first turn:
• we find the coordinates of the center of the pivot:
X = R sin(T A1 );
Y = Rcos(T A1 ) + R.
(4.12)
• finding the coordinates of point A of the intersection of the line (a, b) and the
circle of the first turn:
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4 A Mathematical Model for Constructing a Conflict-Free Flow …
X A = R sin(T A1 );
YA = R − Rcos(T A1 ).
2.
(4.13)
Building a straight line (c, d) (the first linear portion of the aircraft delay
maneuver):
yc,d = kx + b,
(4.14)
where k = tg(T A1), b = y A − kx A .
Find the length of the straight section AB and denote it by d. For this, an iterative
procedure for selecting a parameter will be used. At the initial stage, we can assign
d = 0. The coordinates are respectively equal:
xd = d cos(T A1 ) + R sin(T A1 ) and yd = y A + d sin(T A1 ).
3.
(4.15)
Determination of the coordinates of point B (beginning of the second turn):
x B = x A + d cos(T A1 ),
(4.16)
y B = yd .
The distance between the centers of the turns defined as:
Sx. = 2R sin(T A1 ) + d cos(T A1 ).
4.
(4.17)
Plotting line e, f (line orthogonal to the line (c, d) at point B of the beginning
of the second turn)
ye,f = kx + b,
(4.18)
where k = −tg(90 − yp1),b = yd − kxd .
The location of the center of the second turn determined from the coefficients k,
b of the line (e, f ) and the coordinates of point B:
x2turn = x B + R sin(T A1),
y2turn = kx + b.
(4.19)
4.4 A Model for Constructing an Aircraft Delay Maneuver for a Given Interval
5.
91
The construction of the circle of the second turn:
• the change in the angle of the second turn carried out in the range from 270 to
450°;
• calculate the coordinates of the point (X ∗∗ , Y ∗∗ );
• determine the distance from the center of the second turn to FD:
SFD =
2
y2turn
+ (Sx − x2turn )2 ;
(4.20)
• determine the ratio of the coordinates of the center of the second turn and the
value of the distance from the center of the second turn to FD:
y2turn
2
y2turn
+ (Sx − x2turn )2
;
(4.21)
• then using the obtained expression (4.21), we calculate a part of the angle at the
top of the FD:
⎛
⎞
γ = 90 − arccos⎝ y2turn
2
y2turn
+ (Sx − x2turn
⎠ · 180 ;
π
)2
(4.22)
• determine the ratio of the radius of the turn and the distance from the center of
the second turn to FD:
R·
2
y2turn
+ (Sx − x2turn )2
y2turn
;
(4.23)
• using the resulting expression, we calculate the total angle at FD:
⎛
η = γ + arcsin⎝
R·
2
y2turn
+ (Sx − x2turn )2
y2turn
⎞
⎠ · 180 ;
π
(4.24)
92
4 A Mathematical Model for Constructing a Conflict-Free Flow …
• calculate the coefficient of the line:
kline =
6.
η·π
;
180
(4.25)
Building a straight line (g, h) (from point C to the control point of the aerodrome
(ACP)):
ye,f = kx + b,
(4.26)
2
where k = −tg( y2turn
+ (Sx − x2turn )2 );
b = Sx k.
The coordinates of point C are defined as:
xC = x2turn +
R 2 − (R − cos(γ ))2 ;
yC = y2turn + R cos(γ ).
(4.27)
(4.28)
The length of the linear section of the straight CD will be equal to:
SC D =
7.
(xC − Sx )2 + (yC − S y )2 .
(4.29)
Determining the execution time of the aircraft delay maneuver:
tdelay = tfly −
S
;
V
(4.30)
where S—straight distance from the start point of the maneuver to the ACP;
V —aircraft speed (actual);
tfly = tta1 + t AB + tta2 + tC D .
The application of the developed model for constructing the aircraft delay
maneuver for a given interval allows us to fully determine the numerical values
of all sections of its delay trajectory subject to existing restrictions and submit them
to the NZO for making decisions on the formation of a conflict-free aircraft flow [9].
4.5 The Method of Organizing Information Support for the Near …
93
4.5 The Method of Organizing Information Support
for the Near Zone Officer (Circle Dispatcher)
in the Detection and Resolution of Potential Conflict
Situations
4.5.1 Description of the Method of Organizing Information
Support for the Officer of the Near Zone (Circle
Dispatcher) When Detecting and Resolving Potential
Conflict Situations Between Aircraft Landing
Based on the conditions that determine the structure of the aerodrome traffic zone
(ATZ) and the parameters of aircraft movement, it assumed that if there is one aircraft
in the ATZ, the time spent in the airspace is tn (the time from the moment the aircraft
appears in the airfield before landing). When there are n ≥ 2 in the aerodrome zone,
and conflicts arise regarding the violation of safe intervals when the aircraft arrives
at the end of the runway tn , the aircraft participating in the conflict resolution will
be increased by the delay time tdelay necessary to form a safe time interval between
the aircraft and determine the aircraft’s location in the queue, which in turn orders
in time the entire set of aircraft located in the airfield.
A directive solution to the problem of forming a conflict-free flow of aircraft,
implemented through the professional skills of NZO, does not allow for the operational management of aircraft with minimizing the time intervals for arrival at the
runway.
The method for detecting and resolving potential conflict situations between
aircraft approach is a systematic set of actions implemented by the NZO with the
participation of DSIS to solve the problem of constructing a conflict-free aircraft
flow during approach by the criterion of the minimum presence of aircraft in the near
zone
JT =
K
ti → min.
i=1
The use of criterion JT involves minimizing the time tn during the formation of the
flow and the delay time tdelay maneuver of the aircraft on the set of decision options
adopted by the NZO and, as a result, reducing the total time spent by the aircraft in
the airfield.
The essence of the method is to perform the following steps [13–15]:
1.
2.
Determining the time before boarding the aircraft for all landing approaches.
Determination of the time difference between the arriving aircraft and the aircraft
of the formed stream:
94
4 A Mathematical Model for Constructing a Conflict-Free Flow …
tn = tn + tdelay ,
tn−1 − tn + tsafe , tn−1 > tn ;
0, tn−1 < tn , tn−1 − tn ≥ tsafe ;
=
⎪
⎪
⎪
⎪
⎩ t − t − t , t < t , t − t < t ,
safe
n+1
n
n
safe
n
n−1
n−1
(4.31)
⎧
⎪
⎪
⎪
⎪
⎨
tdelay
(4.32)
where tn —time before nth boarding ACFT, n = 2, . . . , N ;
N —number of aircraft in the initial stream;
tn−1 —time before the landing of the (n − 1) aircraft, taking into account the time
delay;
tdelay —aircraft delay time in the airspace of the aerodrome zone;
tsafe —safe time level between aircraft.
3.
Determining the time delay to resolve a potential conflict:
t = tn−1 − tn .
4.
Formation of options for a conflict-free flow of aircraft, taking into account the
delay time:
• determination of the position of the incoming aircraft relative to the generated
flow:
t > tn − for the nth ACFT;
t < tn − in front of the nth ACFT,
(4.33)
where t—time before landing;
• identification of conflict between the ACFT:
tn − t < tsafe − there is a conflict;
t − t > tsafe − there is not a conflict. ;
n
(4.34)
• determination of intervals between aircraft tn−1 − tn in the stream of ACFT;
• search for possible locations of movement of conflicting ACFT:
tn−1 − tn ≥ 2tsa f e .
(4.35)
4.5 The Method of Organizing Information Support for the Near …
5.
95
Determination of aircraft maneuver for its delay for a given interval:
tn−1 − tn ≤ 2tsafe ,
K
tni → min, i = 1, K ,
(4.36)
(4.37)
i=1
where tni —the time spent by the ACFT during the formation of the flow in the
aerodrome zone, taking into account the delay to resolve the conflict;
K—the number of options for actions implemented in the formation of a conflictfree flow in the airfield.
tdelay = tTA1 + tstr1 + tTA2 + tstr2 ,
(4.38)
tdelay → min,
(4.39)
∠turn
,
Vangle
(4.40)
L1
,
V
(4.41)
∠turn + ∠gen
,
Vangle
(4.42)
L2
,
V
(4.43)
tTA1 =
tstr1 =
tTA2 =
tstr2 =
where tn —total delay time of all aircraft approaching;
tdelay —delay maneuver execution time;
tTA1 —first turn time;
tTA2 —second turn time;
tstr1 —first straight flight time;
tstr2 —second straight flight time;
∠turn —aircraft turning angle;
∠gen —general angle at the final destination;
Vangle —angular velocity;
V—aircraft speed;
L 1 —length of the first straight section;
L 2 —the length of the second straight section.
96
4 A Mathematical Model for Constructing a Conflict-Free Flow …
Fig. 4.3 Interpretation of the organization of information support for NZO in the formation of a
conflict-free flow of aircraft
6.
The formation of the aircraft final flow.
Figure 4.3 presents an interpretation of the application of the method for detecting and
resolving potential conflict situations between aircraft approaching and the model for
constructing an aircraft delay maneuver for a given interval to organize information
support of the NZO during the formation of a conflict-free aircraft flow.
The calculated values of the aircraft motion parameters calculated in the analytical
model for constructing the aircraft delay maneuver for a given interval, following
the method steps, are converted into information functions, represented by the set of
commands recommended by the NZO, for influencing the aircraft crew. Such teams
are formed both for one aircraft and for the aircraft stream, if necessary [14].
Information functions, represented by a set of generated DSIS NZO commands in
the form of flight courses, delay time, the spatial position of the start and endpoints
of turns, ensure the formation of a conflict-free flow of aircraft.
The proposed method of organizing NZO information support in detecting and
resolving potential conflict situations is based on:
• on the joint use of the EE representation model, which is selected by the analysis
of the task tree and DSIS;
• using a logical–linguistic model that allows us to fend off a specific set of negative
influences, forming information functions, in the form of a sequence of commands,
and choosing an analytical model for constructing a maneuver to delay the aircraft
for a given interval.
4.5 The Method of Organizing Information Support for the Near …
97
Thus, the developed method is the basis for the implementation in the information
support system of decision-making for the workplace of the officer of the near zone
to increase the reliability and safety of the aircraft in the airfield.
4.5.2 Organization of Information Support for the Officer
of the Near Zone (Circle Dispatcher) When Forming
the Aircraft Queue Without Priority
Consider the example of organizing information support for the officer of the near
zone during the formation of a conflict-free flow of aircraft in the airfield, based on
the method of organizing information support for the officer of the near zone when
detecting and resolving potential conflict situations between aircraft approaching, as
presented in Sect. 4.5.1.
To organize information, support for NZO is necessary to determine the initial
conditions. There is a group of aircraft flying toward the aerodrome for approach.
Each aircraft has its own time before landing and a certain amount of fuel onboard
[13, 15]. It is necessary:
•
•
•
•
determine the sequence of aircraft landing;
resolve existing and potential conflict situations between the armed forces;
calculate time delays for each aircraft;
comply with safety requirements, residual fuel limits, and service priorities.
An analysis of Fig. 4.1 shows that the shape of the airfield zone within which the
movement of the aircraft regulated can be of any shape, and its boundary, depending
on several circumstances, varies from several tens to several hundred kilometers.
It assumed that outside the aerodrome zone, aircraft fly to the aerodrome in radial
directions. Aircraft arrive at the approach area with occasional deviations from the
schedule. In this case, when approaching the glide path between some of them may
be an interval that is less safe, and flow control must be performed.
The process of regulating the input stream is as follows:
(1)
(2)
the conversion of random intervals between arrivals of the aircraft in an ordered
flow at the final stage of the approach;
preventing the possibility of aircraft approaching each other less than a
predetermined distance (see Fig. 4.4).
At high traffic intensities, a queue of waiting for aircraft clearance may be formed.
Restrictions on the density of intervals between aircraft on a landing course is
obtained from the following considerations. Landing is not possible if the intervals
between them are less than the minimum safe.
Consider a situation where six aircraft sequentially arrive in the airspace of the
aerodrome area, which corresponds to the average density and intensity of air traffic,
and the order of entry into the airspace is not defined. The arrival of aircraft in the
98
4 A Mathematical Model for Constructing a Conflict-Free Flow …
Fig. 4.4 Conversion of the initial stream of aircraft in an ordered sequence
near zone is carried out sequentially by ACFT No. 1 → of ACFT No. 2 → of ACFT
No. 3 → of ACFT No. 4 → of ACFT No. 5 → of ACFT No. 6; the aircraft, with the
shortest flight time to the runway, is the first to land without delay. Other aircraft,
according to increasing values of time before landing, follow the first. ACFT No. 1,
ACFT No. 2, ACFT No. 3, ACFT No. 4, ACFT No. 5, ACFT No. 6, we designate t1 ,
t2 , t 3 , t 4 , t 5 , t 6 .
For a specific example, we give the temporary values before landing the set of
aircraft presented in Table 4.1.
We will regulate the flow of six successively arriving aircraft, if the interval
between them should not be less safe tsafe = 120 s. Define the delay time for aircraft
for which this condition is not satisfied at the time of entry into the near zone.
We use formulas (4.33) and (4.34) and obtain the following results presented in
Table 4.2.
Table 4.1 The initial data for the formation of the flow of aircraft
Time to
landing (s)
ACFT No.
1 (t1)
ACFT No.
2 (t2)
ACFT No.
3 (t3)
ACFT No.
4 (t4)
ACFT No.
5 (t5)
ACFT No.
6 (t6)
420
660
870
900
1020
1380
Table 4.2 Aircraft time delays
Conflict
ACFT delays
(s)
Time before
boarding (s)
ACFT No.
1
(t1)
ACFT No.
2
(t2)
ACFT No.
3
(t3)
ACFT No. 4 ACFT No. 5 ACFT No.
(t4)
(t5)
6
(t6)
No
No
No
There is
with ACFT
No. 3
0
0
0
90
90
0
420
660
870
990
1110
1380
There is
with ACFT
No. 4
no
4.5 The Method of Organizing Information Support for the Near …
99
Table 4.3 Attributes of aircraft No. 7 relative to the flow of six aircraft
ACFT
No. 1
(t1)
ACFT
No. 2
(t2)
ACFT
No. 3
(t3)
ACFT
No. 4
(t4)
ACFT
No. 5
(t5)
ACFT
No. 6
(t6)
ACFT No.
7
(t7)
Time to
landing (s)
420
660
870
990
1110
1380
830
Conflict
No
No
No
No
No
No
There is
with ACFT
No. 3,
ACFT No.
4
It can be seen that the aircraft of ACFT No. 1, ACFT No. 2, ACFT No. 3, and
ACFT No. 6 follow the established approach procedures without delay, and ACFT
No. 4, ACFT No. 5 must be delayed by 90 s each.
We will simulate a situation when, after resolving existing conflicts, another
aircraft flies into the near zone. Let us designate it as aircraft No. 7 with a time
before landing t7 = 830 s. It is necessary to adjust the flow of aircraft, taking into
account the new disturbance (taking into account aircraft No. 7) and determine the
sequence of approach. To do this, determine the position of the aircraft No. 7 relative to the generated flow according to the formula (4.37) and search for conflict
situations according to the formula (4.38) (Table 4.3).
It can be seen that, according to landing time, ACFT No. 7 falls into the time
interval between arrival times on runways of ACFT No. 2 and ACFT No. 3; given
that ACFT No. 2 and ACFT No. 3 are in an ordered flow, it is necessary to determine
the potential location of ACFT No. 7 in ACFT flow. We find the intervals between
the ACFT in the flow and look for a gap for which condition (4.37) is satisfied. If
such a gap is not found, then we move ACFT No. 7 to the end of the queue at a
distance tsafe from the aircraft closing the queue (see Table 4.4).
The time interval suitable for condition (4.38) is between ACFT No. 5 and ACFT
No. 6 (Fig. 4.5), while the time before landing for ACFT No. 7 will increase from
830 to 1230 s. The total delay time of all aircraft is the sum of the delays of each
aircraft at the stages of regulation and the formation of the queue of aircraft coming
in for a landing (see Table 4.5).
Thus, restriction (4.38) is satisfied when T gen = 580 s and NZO; to make a decision,
the following sequence of aircraft approach is proposed:
Table 4.4 Search for ACFT No. 7 locations
|t1–t2|
|t2–t3|
|t3–t4|
|t4–t5|
t (c)
240
210
120
120
|t5–t6|
Move
–
–
–
–
+
Grouped t delay (c)
–
–
–
–
1230
270
100
4 A Mathematical Model for Constructing a Conflict-Free Flow …
Fig. 4.5 Aircraft queuing without service priority
Table 4.5 Total aircraft delay time
T delay
ACFT
No. 1
T delay
ACFT
No. 2
T delay
ACFT
No. 3
T delay
ACFT
No. 4
T delay
ACFT
No. 5
0
0
0
90
90
Time to
420
landing (s)
660
870
990
1110
Aircraft
delays (s)
T delay
ACFT
No. 6
T delay
ACFT
No. 7
T gen
0
400
580
1380
1230
ACFT No. 1 → ACFT No. 2 → ACFT No. 3 → ACFT No. 4 → ACFT No. 5 →
v No. 7 → ACFT No. 6.
4.5.3 Organization of Information Support for the Near Zone
Officer (Circle Dispatcher) in the Formation
of the Queue of Aircraft with a Priority of Service
at the Incoming Aircraft
Consider another example where an incoming aircraft takes precedence over other
aircraft in the queue. Priority is a sign that determines the order of service. The
priority will be taken into account if there is a conflict between the incoming aircraft
and any other in the stream. We take the initial data from clause 4.5.1. In Table 4.1,
there is a conflict between ACFT No. 3 and the flying ACFT No. 7. Since ACFT No.
7 has priority, its trajectory does not change, and the search for a suitable interval
in the aircraft flow will be performed for ACFT No. 3. Therefore, the preliminary
flow of aircraft approaching landing is ACFTNo. 1 → ACFT No. 2 → ACFT No.
7 → ACFT No. 4 → ACFT No. 5 → ACFT No. 6. Movement of ACFT No. 3 is
possible only after ACFT No. 7; therefore, we consider only three potential intervals
(Table 4.6).
From the calculations, it follows that ACFT No. 3 will be moved between the
ACFT No. 5 and the ACFT No. 6 (Fig. 4.6). Based on this, the following delays for
4.5 The Method of Organizing Information Support for the Near …
101
Table 4.6 Search for aircraft locations No. 3
|t1–t2|
|t2–t|
|t–t4|
|t4–t5|
t (c)
0
0
160
120
|t5–t6|
Move
0
0
–
–
+
Grouped t delay (c)
0
0
–
–
1230
270
Fig. 4.6 Queuing with priority service at the flown in aircraft
the aircraft will be generated and presented in Table 4.7.
The total delay time of the aircraft will be 540 s. NZO; to make a decision, the
following sequence of aircraft approach is proposed:
ACFT No. 1 → ACFT No. 2 → ACFT No. 7 → ACFT No. 4 → ACFT No. 5 →
ACFT No. 3 → ACFT No. 6.
Table 4.7 Total delay time for priority queue
T delay
ACFT
No. 1
T delay
ACFT
No. 2
T delay
ACFT
No. 3
T delay
ACFT
No. 4
T delay
ACFT
No. 5
T delay
ACFT
No. 6
T delay
ACFT
No. 7
T gen
360
Delay (s)
0
0
360
0
0
0
0
Time
before
boarding
(s)
420
660
1230
990
1110
1380
830
102
4 A Mathematical Model for Constructing a Conflict-Free Flow …
4.5.4 Organization of Information Support for the Officer
of the Near Zone (Circle Dispatcher) When Forming
a Queue of Aircraft with a Priority of Service
and Taking into Account Fuel Residues Onboard Each
Aircraft
This section describes an example of the organization of information support in the
formation of a conflict-free flow of aircraft with the priority of service for an incoming
aircraft and taking into account the remaining fuel onboard each aircraft. One of the
essential safety criteria is accounting for the remaining fuel on board the aircraft. If
any aircraft has less a fuel balance than the minimum allowable for landing, then this
aircraft has an obvious priority over other aircraft. It is often necessary to set delays
in the formation of the aircraft flow, and some delays may not be feasible, since a
situation may arise when the aircraft, after performing the maneuver, may not have
enough fuel to land [15]. Add the remaining fuel to the initial data (see Table 4.8).
The minimum amount of fuel required for landing aircraft, we denote Umin and
assign it a value of 500 kg. Fuel consumption is λ = 6.5 kg/s. We determine the
maximum delay time for each aircraft according to the following formula:
tdelay max =
U − Umin
;
λ
For ACFT No. 1 tdelay max = 3800−500
≈ 507.69 s;
6.5
2430−500
For ACFT No. 2 tdelay max = 6.5 ≈ 296.92 s;
For ACFT No. 3 tdelay max = 1981−500
≈ 227.85 s;
6.5
For ACFT No. 4 tdelay max = 4586−500
≈ 628.62 s;
6.5
5941−500
For ACFT No. 5 tdelay max = 6.5 ≈ 837.08 s;
For ACFT No. 6 tdelay max = 2743−500
≈ 345.08 s.
6.5
Now, we analyze the possibility of the expected delays (Tables 4.9 and 4.10). The
Table 4.8 The remaining fuel at the time of entry into the aerodrome zone
ACFT No. 1 ACFT No. 2 ACFT No. 3 ACFT No. 4 ACFT No. 5 ACFT No. 6
Fuel
residues
(kg)
3800
2430
1981
4586
5941
2743
|t–t4|
|t4–t5|
|t5–t6|
Table 4.9 Delay feasibility of ACFT No. 3
|t1–t2|
|t2–t|
t (s)
0
0
160
120
Move
0
0
–
–
+
Grouped t delay (s)
0
0
–
–
1230
270
4.5 The Method of Organizing Information Support for the Near …
103
Table 4.10 Delay values of ACFT No. 3
Delay (s)
t delay.
ACFT
No. 1
t delay.
ACFT
No. 2
t delay.
ACFT
No. 3
t delay.
ACFT
No. 4
t delay.
ACFT
No. 5
t delay.
ACFT
No. 6
t delay.
ACFT
No. 7
t gen
0
0
360
90
90
0
0
540
Yes
No
Yes
Yes
Yes
Yes
Is the delay Yes
feasible?
feasibility or impracticability of delays is determined based on the condition (4.38).
It can be seen that for given values of fuel residues, it is impossible to move ACFT
No. 3 in the interval between ACFT No. 5 and ACFT No. 6. Therefore, it is necessary
to move ACFT No. 3 to the place of ACFT No. 4 and move ACFT No. 4 in turn
(Fig. 4.7) in search of a suitable interval (Tables 4.11 and 4.12), taking into account
restrictions (4.34)–(4.36).
Fig. 4.7 Queuing with a service priority at the flown in aircraft and taking into account the remaining
fuel onboard each aircraft
Table 4.11 Delay feasibility of ACFT No. 4
|t1–t2|
|t2–t|
|t–t3|
|t3–t5|
t (s)
0
Move
–
Grouped t delay (s)
–
|t5–t6|
0
0
120
–
–
–
+
–
–
–
1230
270
Table 4.12 Delay values of ACFT No. 4
t delay.
ACFT
No. 1
t delay.
ACFT
No. 2
t delay.
ACFT
No. 3
t delay.
ACFT
No. 4
t delay.
ACFT
No. 5
t delay.
ACFT
No. 6
t delay.
ACFT
No. 7
t gen
zadepka, (c)
0
0
120
330
90
0
0
540
zadepka
ocywectvima?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
104
4 A Mathematical Model for Constructing a Conflict-Free Flow …
Since all delays are feasible and the total delay time is T = 540 s, the NZO is
proposed, for decision-making, the next sequence of aircraft landing approach:
ACFT No. 1 → ACFT No. 2 → ACFT No. 7 → ACFT No. 3 → ACFT No. 5 →
ACFT No. 4 → ACFT No. 6.
Thus, the developed method of organizing informational support for the officer of
the near zone in detecting and resolving potential conflict situations can be successfully used in DSIS EIS ATC. Expected results from the implementation will improve
the quality of aircraft services and the level of air traffic safety.
References
1. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018/Federal
Air Transport Agency, Moscow, 89 p (2019)
2. Voshchinin AP (1989) Optimization in the face of uncertainty. Voshchinin AP—M.: Technique,
224 p
3. Darymov YuP (1981) Automation of air traffic control. Darymov YuP, G.A. Moscow, 667 p
4. Danilov VB (2012) Flight safety. Danilov VB—Samara, Samara State Aerospace University,
148 p
5. Dubov YuA (1996) Multicriteria models of the formation and selection of system options.
Dubov YuA, Travkin SI—M.: Nauka, 294 p
6. Information releases on aviation accidents and aviation incidents for the first half of
2017/Second half of 2017. Moscow, 122 p/145 p (2018)
7. Kini RL (1999) Decision making under many criteria: preferences and substitutions. Keeney
RL, Rife H—M.: Radio and Communications, 560 p
8. Orlovsky SA (1998) Decision-making problems with fuzzy initial information. Oryol SA—M.:
Nauka, 194 p
9. The final report on the results of the investigation of the accident. Interstate Aviation Committee,
180 p (2019)
10. Pisarenko VN (2017) The method of ensuring flight safety at the present stage of the state of
the aviation transport system of Russia. Pisarenko VN, Koptev AN— Samara, Samara State
Aerospace University, 153 p
11. Guidance on the organization of safety oversight (2009) International Civil Aviation Organization, 2nd edn, 318 p
12. Councils BYa (1985) Modeling systems. Sovetov BYa, Yakovlev SA—M.: Higher school, 271
p
13. Airbus A318/A319/A320/A321 Flight Crew Operating Manual (FCOM), vol 1, Systems
Description. Airbus, France, 1088 p (2011)
14. Ammerman HL (2003) FAA air traffic control operations concepts, vol VI, ARTCC/HOST
En route controllers, report number DOT/FAA/AP/86-01. Washington, Federal Aviation
Administration, 312 p
15. Atkinson JM (1988) Analysis of mental processes involved in air traffic control. Ergonomics
14:565–570
Chapter 5
Formation of Solutions for Optimizing
the Activities of the Landing Zone Officer
(Landing Dispatcher)
5.1 Building a Model of a Guaranteed Aircraft Landing
Approach
One of the variants of optimization of activities of FOO is to determine the space
within which it can exercise control of aircraft flight, confident in the positive effect of
the decision. Pre-trajectory of the ACFT relative to a given trajectory can be divided
into two phases: the phase of the approach according to the available technical means
and the area of the corrective maneuver for the withdrawal of the armed forces in a
specified area accurate landing on the runway (after establishing visual contact with
the runway) [1].
The landing operation in order to stop the ACFT in the conditional region M (see
Fig. 5.1) ensures the flight crew with the appropriate training, when you perform a
corrective maneuver landing force in the strip accurate landing.
The area of M is the area around the point lying on the trajectory of the sun on
the height of the decision. It is the pilot that should adjust the flight path of the
ACFT, if the deviation does not exceed the allowable limits, or if they exceeded to
go to the second round. The borders of this space are determined by the linear lateral
deviations of zmax and deviations in height H max , as well as deviations V max from
a given flight speed. If at the time of establishing visual contact with the runway on
removing L man , the aircraft has a velocity vector V oriented parallel to the axis of
the runway; on the z-axis, there is some boundary point zmax , from which it is still
possible to perform two paired, coordinated turn at a precise conclusion entirely on
the runway for an existing roll.
If, by the indicated time, the velocity vector is deviated from the direction of the
runway axis by an angle exceeding ε, then it is impossible to perform a corrective
maneuver from the point zmax to ensure the correct withdrawal of the aircraft to the
runway. The influence of flight speed and its deviations V from a given approach
speed is manifested through the radius of the corresponding coordinated turns with
the same roll. The dimensions of the region M also depend on the removal of the
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. V. Yakovlev et al., Conditional Function Control of Aircraft,
Springer Aerospace Technology,
https://doi.org/10.1007/978-981-16-1059-2_5
105
106
5 A. V. Yakovlev et al.
Fig. 5.1 Uqactki ppedpocadoqno tpaektopii poleta BC
beginning of maneuvering. To take into account the parameter z max , the guarantee
approach is applied, taking into account the worst values f the angle ε:
ε=
+3◦ ;
−3◦ .
(5.1)
The values of permissible lateral deviations at the transition point to visual flight
are:
⎤
⎡
2
2
2V ⎣ 1 + cos(r )
L man g tg(β) ⎦
z max prem =
− 1−
+ z 0 , (5.2)
g tg(β)
2
2V 2
where V is the average flight speed of the aircraft on the approach path; g is the
acceleration of gravity; β is average roll of coordinated turns; is the angle of
inclination of the trajectory; L man is maneuvering distance; z0 is the allowable
linear lateral deviation of the aircraft from the axis of the runway at the time of
landing.
At the final stages of the approach, stringent requirements are imposed to maintain
a given flight speed to ensure the necessary stability and controllability of the aircraft;
actual errors do not exceed, as a rule, 5% [2, 4]. The results of calculating the region of
permissible deviations for V pc = 450 km/h, V ar = 320 km/h are presented in Fig. 5.2
and allow us to conclude that the presented model gives an idea of the FOO about
the possibility of approaching (independent approach) of the aircraft for landing if
the sun is inside the specified zone.
5.1 Building a Model of a Guaranteed Aircraft Landing Approach
107
Fig. 5.2 The zone of permissible deviations in the horizontal plane
The main disadvantages of the model are:
• calculations based on averaged aircraft motion parameters (V, β);
• lack of information from FOO about the approach path for subsequent control of
the correctness of the construction of the aircraft approach;
• lack of information about the coordinates of the “point of change of course of the
aircraft.”
In the presented model, it is seen that at ranges exceeding 10,000 m, it is possible
to ensure that the aircraft approaches from almost any direction.
5.2 Defining a Set of Safe Approach Paths
In the control system with multiple calculations of the trajectory by the final state, a
family of nominal trajectories is used, each of which can satisfy the final conditions.
At each moment in time, the corresponding nominal trajectory is calculated, passing
through the point on the trajectory where the aircraft is located. Control commands
are formed so that the aircraft can withstand this nominal trajectory [3].
One of the types of descriptions of nominal trajectories is polynomials with
coefficients satisfying the required conditions.
Function
s(τ ) = −τ + a2 τ 2 + a3 τ 3 , τ = t − T
(5.3)
108
5 A. V. Yakovlev et al.
Fig. 5.3 Tpaektopii bezopacnogo zaxoda na pocadky
satisfies the final conditions s(0) = 0, ṡ(0) = −1 for any values of the coefficients
a2 and a3 . Trajectory parameters are determined from sM and ṡ M measurements and
using conditions:
s M (τ0 ) + τ0 = τ02 τ03
ṡ M (τ0 ) + 1 = 2τ0 3τ02
a2
.
a3
(5.4)
Solving Eqs. (5.3), (5.4) and substituting the coefficients a2 and a3 in the nominal
function, we determine the following dependence:
2
2
3
τ
τ
τ
τ
sc (τ ) = −τ + 3
−2
−
[s M (τ0 ) + τ0 ] + τ
[ṡ M (τ0 ) + 1].
τ0
τ0
τ0
τ0
(5.5)
The control system with multiple calculations of the trajectory by the final state
allows us to create a family of trajectories shown in Fig. 5.3.
If the controlled system has a finite number of states, it is necessary to determine
the optimal ACFT control parameters to find the best solution to the problem of determining the desired flight path and then perform a comparison using the optimization
parameter and determine the best control method.
5.3 Determining the Optimal Safe Approach Path
One approach to determining the optimal trajectory is to solve the problem of phased
optimization of some intermediate objective functions to achieve the desired result
[4]. The primary method for solving such problems is the dynamic programming
method, which allows obtaining a common (resulting) optimum by phased (multistep) optimization. The general form of the optimization function can be represented
as the following expression:
5.3 Determining the Optimal Safe Approach Path
109
n
f (x1 , x2 , . . . , xn ) =
f j x j → max
(5.6)
j=1
under restrictions
n
f j (x j ) ≤ b, a j > 0, x j ≥ 0.
(5.7)
j=1
Substantially, task (5.6)–(5.7) can be interpreted as the problem of the optimal
investment of some resources j, reduced to a single dimension (e.g., fuel) using the
coefficients aj in various processes (projects, operating modes, etc.) characterized by
functions f j , i.e., such a distribution of a limited amount of resource b that maximizes
the total profit. Imagine a situation where it is solved sequentially for each process.
If, at the first step, it was decided to invest x n units in the nth process, then, in the
remaining steps we can distribute the b-ap x p units of the resource. Abstracting from
the considerations based on which the decision was made in the first step, it will
be quite natural to act so that in the remaining steps, the distribution of the current
volume of the resource occurs optimally, what is equivalent to solving the task:
n−1
f j (x j )
max
(5.8)
j=1
under restrictions
n−1
a j x j ≤ b − an xn , a j > 0, x j ≥ 0.
(5.9)
j=1
The maximum value (5.8) depends on the size of the distributed residue, and if
the remaining amount of the resource is denoted by ξ , then the quantity (1.8) can be
expressed as a function of ξ :
n−1
n−1 (ξ ) =
f j (x j ),
max
n−1
x1 ,...,xn−1 :
(5.10)
a j x j ≤ξ j=1
j=1
where index n − 1 indicates the remaining number of steps. Then, the total income
obtained because of the decision made in the first step and the optimal decisions
made in the remaining steps will be:
n (x n )
= f n (xn ) + n−1 (b − an xn ).
(5.11)
110
5 A. V. Yakovlev et al.
If it were possible to influence x p , then, in order to get the maximum profit, we
would have to maximize n in the variable x p , i.e., find n (b) and solve the task
max
0≤xn ≤ abn
n (x n )
= max { f n (xn ) + n−1 (b − an xn )} = n (b).
0≤xn ≤ abn
(5.12)
As a result, we obtain an expression for the value of the objective function of the
task with the optimal stepwise process of making decisions about the distribution of
the resource. It, under the construction of this process, is equal to the global optimum
of the objective function
⎧
⎨
n
f j (x j )
max
x1 ,...,xn ⎩
j=1
⎫
⎬
⎭
= n (b),
(5.13)
i.e., the value of the objective function in the simultaneous distribution of the resource.
If, in expression (5.13), we replace the values of b with ξ and n with k, then it
can be considered as a recurrence formula that allows us to sequentially calculate the
optimal values of the objective function for the distribution of the resource volume
ξ in k steps:
k (ξ ) = max { f k (xk ) + k−1 (ξ − ak xk )}.
0≤xk ≤ aξ
(5.14)
k
The value of the variable xk at which the considered maximum reached is denoted
by x̂k (ξ ). For k = 1, formula (5.13) takes the form
1 (ξ ) = max f 1 (x1 ),
0≤x1 ≤ aξ
(5.15)
1
i.e., it allows the direct calculation of functions 1 (ξ ) and x̂1 (ξ ).
Using (5.15) as a recursion base, using (5.14), we can successively calculate k (ξ )
and x̂k (ξ ), k ∈ 2 : n. Putting ξ = b at the last step, by (5.11), we find the global
maximum of function (5.13), equal to n (b), and the component of the optimal plan
xn∗ = x̂n (b). The resulting component allows you to calculate the unallocated balance
in the next step with optimal planning: w, and, in turn, find x. As a result of such
calculations, all components of the optimal plan will be successively found.
The task of constructing an optimal aircraft trajectory of approach is reduced to
solving the problem of withdrawing aircraft from its current position [5, 6], for the
minimum time, to the line of the landing course; thereby, the aircraft at point s0 at
time t 0 and having speed V 0 is necessary to bring sk to a given point, and its speed
should be brought to the value of V k . The flight time along a curved path from point
s0 to point s1 , from point s1 to point s2 , at constant speed V is known. It is required
to find the optimal path of movement from point s0 to point sk at which the total
5.3 Determining the Optimal Safe Approach Path
111
Fig. 5.4 The process of moving a point from the initial state s0 to the final sk
flight time will be minimal. Based on the assumption, the entire flight process can
be divided into a series of successive elementary steps (steps), at any of which the
aircraft changes speed.
Let us depict the state of the aircraft by a point on the plane V0T, where the
abscissa corresponds to the speed V and the ordinate corresponds to the flight time
of the aircraft T. Then, the process of moving the point from the initial state s0 to the
final sk will be displayed on the plane V0T with some step broken line (Fig. 5.4).
This trajectory will characterize the control of changes in coordinates and velocity.
Of all the possible trajectories, one must choose one on which the value of the selected
criterion (time) will be the smallest.
To solve the problem by dynamic programming is necessary to divide the flight
segment |s0 , sk | into n1 equal parts and the speeds |V 0 , V k | on n2 equal parts. Thus,
during the first step of the process, there is either a change in the distance by s =
sk −s0
0
or a change in speed by V = Vkn−V
and the total number of steps in the
n1
2
process of transferring an aircraft from state s0 to sk will be m = n 1 + n 2 .
The total number of all possible trajectories is quite large; therefore, their simple
enumeration is unacceptable, and therefore, the Bellman optimality principle is applicable. Since the final state of the sk system is known, the process of constructing the
optimal trajectory starts from the end.
It follows from the Bellman optimality principle [7] that if the system located at
some intermediate point sr and the endpoint is known, then the optimal strategy is the
one that transfers from the point sr to the final sk along the optimal trajectory, which
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5 A. V. Yakovlev et al.
corresponds to the least time expenditure. Since this is true for any intermediate point,
we conclude that the optimal trajectory has this property—each section (fragment)
of it makes an optimal trajectory. We apply this conclusion to construct an optimal
trajectory moving from the endpoint sk . We can move to the point sk only from two
neighboring points b1 and b2 , and only in one possible way, and therefore, there is
no choice of the optimal control at the last step—it is the only one. The obvious
drawback of using the dynamic programming method to form the optimal flight path
is the lack of the possibility of forming a flight path with access to the landing line
with the flight path equal to the landing one.
5.4 A Mathematical Model for Constructing an Optimal
Approach Path
5.4.1 The Principle of Maximum Performance in Solving
the Problem of Parrying Deviations from the Landing
Course
When solving the problems of predicting the location of aircraft in the process of
flight control and ATC (e.g., identifying conflict situations in other tasks), a more
detailed description of the movement of control objects or the so-called microscopic
model of air traffic is used. The simplest system of equations is a system that describes
the plane motion of the aircraft relative to the selected fixed coordinate system:
Ẋ g = VB cos(ϕ) + W cos(ϕw );
Ẏg = VB sin(ϕ) + W sin(ϕw );
g tg(γ )
ϕ̇ =
.
VB
(5.16)
where
Va
ϕ
W
ϕw
g
γ
aircraft airspeed;
heading angle;
wind speed;
drift angle;
acceleration of gravity;
roll angle.
The first two equations—kinematic, the third—describe the balance of forces in
lateral motion in a coordinated U-turn. The simplicity of relations (5.16) limits the
possibility of using them for modeling air traffic and studying processes in air traffic
control systems that occur in real time. To solve problems such as accurate prediction
of the danger of aircraft collisions, substantiation of separation standards, analysis
5.4 A Mathematical Model for Constructing an Optimal Approach Path
113
of the influence of atmospheric conditions on flight safety, the system of equations
should reflect, as far as possible, the dynamic characteristics of the aircraft and the
properties of their control and aircraft navigation systems. However, when using such
systems of equations, reflecting not only the change in coordinates and flight speeds
but also the parameters of motion around the center of mass, the requirements for the
speed of computing complexes of automated air traffic control systems (AS ATC)
significantly increased.
Acceptable results can be achieved by describing the motion of the aircraft as a
material point, taking into account wind disturbances, limiting itself to an auxiliary
system of differential equations for characterizing the motion of the aircraft around
the center of mass.
The main tasks of operational ATC are:
• tasks of flight planning and air traffic, i.e., calculation of schedules and flight
paths;
• control tasks (direct control) relative to the calculated flight paths.
The first group of tasks relates to the deterministic tasks of constructing optimal
aircraft motion programs taking into account several restrictions on the phase coordinates due to the need to ensure safety, regularity, and economy of air traffic. In
this case, it is assumed that the controlled object is not under the influence of any
perturbations, and all state variables are known or can be accurately measured.
The second group of problems is solved based on the assessment of real trajectories
of the aircraft and the synthesis of optimal control actions, i.e., represents the problem
of controlling the state x(t) of the object, which in control theory formulated as the
problem of determining the method of forming the control vector u(t).
To select the optimal flight path or to assess the quality of behavior of a controlled
object, a specific indicator or quality criterion is introduced. If the selected programs
or control signals should ensure the achievement of the extreme value of this indicator,
then this task is called the optimal control task. The solution to the optimal control
problem consists of finding an algorithm for the formation of the control vector
u(t), which ensures the extreme value of the quality indicator. One of the main tasks
of automated flight control systems in the aerodrome area is the task of ensuring
maximum throughput. Therefore, as a criterion for optimizing the flight program
(trajectory) when constructing an approach maneuver, the most applicable is the
time spent by the aircraft in the control zone, namely:
tk
It =
dt = (tk − t0 ) → min .
(5.17)
t0
According to Pontryagin, the variational task of minimizing the functional (5.17) is
called the optimal speed task. A particular case is a task of determining the trajectory
of the minimum transit time of a specific region when the speed of movement depends
on the phase coordinates of the location of the controlled object in this region.
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5 A. V. Yakovlev et al.
With a constant flight speed in the landing zone and the absence of wind, the
optimal trajectory for plane motion, described by a system of equations, consists of a
sequence of circular arcs, the minimum allowable radius, i.e., the trajectory will take
the form of a “turn-turn.” In this case, the optimality criterion will have the form
n
It =
ti → min,
(5.18)
i=1
where t i —travel time ith section; i = 1, 2—parcel numbers.
The coordinate system of the XOY is selected to solve this problem.
Determination of the optimal speed path is performed using the maximum principle of Pontryagin [6], which consists in the fact that the Hamiltonian of the system
of Eq. (5.19) reaches a maximum:
ẋ = V cos(ϕ);
ẏ = V sin(ϕ);
g tg(γ )
ϕ̇ =
.
V
(5.19)
where V —the ground speed of ACFT; ϕ—heading angle; g—acceleration of gravity;
γ —roll angle.
When solving Eq. (5.19), the following conditions chosen as boundary conditions:
x(t0 ) = x0 ; y(t0 ) = y0 ; ϕ(t0 ) = ϕ0 ;
x(tk ) = xtk ; y(tk ) = ytk ; ϕ(tk ) = ϕk .
(5.20)
In general, an aircraft entering a control zone has a heading −π ≤ ϕ 0 ≤ π. We
accept that the endpoint of the desired trajectory is the entry point to the glide path of
descent. The landing course is determined from the condition of the aircraft entering
the landing zone with a course close to the landing, i.e.,
ϕ K = ϕ0 ± ε.
To determine the optimal speed trajectory, we use the maximum principle of
L. S. Pontryagin, which consists in the fact that the Hamiltonian of the system of
Eq. (5.21):
H = λ1 (V cos(ϕ)) + λ2 V sin(ϕ) + λ3
g tg(γ )
,
V
(5.21)
where [λ1 ] = s/m, [λ2 ] = s/m, [λ3 ] = s/rad, reaches a maximum
H (λ1 , λ2 , λ3 , ϕ, γ ) = 1 under optimal control, i.e., with a specific law of change in
5.4 A Mathematical Model for Constructing an Optimal Approach Path
115
the angle of heel γ (t) = γ ∗ (t). Helper variables entered λ1 , λ2 , λ3 are determined
by the following system of equations:
dH
= 0;
dx
dH
λ̇2 = −
= 0;
dy
dH
λ̇3 = −
= V (λ1 sin(ϕ) − λ2 cos(ϕ)).
dϕ
λ̇1 = −
(5.22)
Whence it follows that λ1 = const; λ2 = const. The maximum principle means
that there is a nonzero solution to system (5.22) for which the condition (t 0 , t k ) holds:
g tg(γ )
λ1 (V cos(ϕ)) + λ2 V sin(ϕ) + λ3
V
g tg(γ )
.
= max λ1 (V cos(ϕ)) + λ2 V sin(ϕ) + λ3
V
Thus, only the last term in Eq. (5.22) depends on the control function γ (t), and
the maximum Hamiltonian achieved under the following conditions:
γ ∗ (t) = γnorm sign(λ3 ),
(5.23)
Otherwise, the ACFT performs a full turn, and output to the landing pattern
is impossible. For finding the law of change in time, of course, the ACFT and its
coordinates, we integrate the system of Eq. (5.19) for γ = γnorm . From the conditions,
ϕ(t0 ) = ϕ0 and ϕ = t.
Integrating the system of Eq. (5.19) for γ = γnopm , we get the laws of change in
time of the flight course of the ACFT and its coordinates:
ẋ =
(V cos(ϕ))dt ⇒ x =
1
V sin( t + ϕ0 ) + c1 ;
(5.24)
(V sin(ϕ))dt ⇒ y = −
1
V cos( t + ϕ0 ) + c2 ;
(5.25)
ẏ =
ϕ̇ =
g tg(γnorm )t
gtg(γ )
dt ⇒ ϕ = ±
+ ϕ0 =
V
V
t + ϕ0 ,
(5.26)
where = ± g tg(γVnorm ) — angular velocity of turn.
From expressions (5.24)–(5.26) for t 0, we obtain the integration constants:
c1 = x0 −
V sin( t0 + ϕ0 )
= x0 −
V sin( t0 + ϕ0 )
gtg(γt0 )
V
= x0 −
V 2 sin(ϕ0 )
; (5.27)
g
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5 A. V. Yakovlev et al.
c2 = y0 +
V cos( t0 + ϕ0 )
= y0 +
V cos( t0 + ϕ0 )
gtg(γt0 )
V
= y0 +
V 2 cos(ϕ0 )
.
g
(5.28)
Having constructed the trajectory of motion in the selected coordinate system, we
can see that it is an elongated arc of a logarithmic spiral, and in the case of a special
solution γ = 0, a straight line. If the trajectory is a combination of conjugate arcs
of logarithmic spirals, then γ = γnorm , and from expressions (5.21) and (5.22), we
obtain the following expression for finding the function λ3 (t) :
λ1 (V cos(ϕ)) + λ2 V sin(ϕ) +
V
(−λ1 cos( t + ϕ0 ) + λ2 sin( t + ϕ0 )) = 1
(5.29)
λ1 V cos( t + ϕ0 ) + λ2 V sin( t + ϕ0 ) + λ3
= 1.
(5.30)
Find λ3 :
λ3 =
1
V λ21 + λ22 cos( t + ϕ0i − ψ) ,
(5.31)
where ψ = arctg(λ1 /λ2 ); ϕ0i —initial course for the i-th constancy interval γ (t).
The increment of the argument ti determines the duration of each interval ti of
the constancy of the control function = t i , which maintains the positive value of
the expression in square brackets in Eq. (5.31). For the characters of λ3 and Ω must
match the expression in square brackets in (5.31) can only be positive or go to zero
during the switching control.
Since the optimal trajectory has straight-line segments that are output to the
endpoint O is only possible on the left (Ω < 0) or right (Ω > 0) steer. Depending on
the initial conditions, the sign i can be positive or negative. Therefore, in the worst
case [when the signs Ω(t 0 + 0) i Ω(t k − 0)], the function has two switches, in
this case, and with a larger number of switches (a significant distance from the line
landing course), the trajectory is not optimal as it can be shortened by replacing the
arcs of a logarithmic spiral line segments. Except for some special cases, a special
administration (straight section) may not be in the initial and final sections of the
optimal trajectory. Indeed, after the linear part of the full revolution of a logarithmic
spiral, since t i = 2π, output to the landing pattern is impossible if the spiral does not
pass through the point O of output to the landing pattern. Every point of the zone
of approach to the airfield can build up to four trajectories that satisfy the optimality
conditions, because of the first and last intervals t, the control function γ ∗ = ±γnorm .
Therefore, to determine the absolute minimum, we need to compare the time of flight
for each of these trajectories, defining it using numerical simulations. So, the optimal
5.4 A Mathematical Model for Constructing an Optimal Approach Path
117
path out of the armed forces from any point of the airfield area at the entrance to it
with any course in the starting point of the reduction on the glide path-planning in the
landing pattern is generally composed of mutually conjugate arcs of a logarithmic
spiral, except [8]:
• the starting point (x 0 , y0 ) located on one of the arcs of the logarithmic spiral
passing through point O, and the initial course ϕ0 coincides with the tangent to
the arc of the logarithmic spiral at this point;
• the starting point is on the extension of the runway axis, and ϕ0 = ϕ K , in this
case, the path degenerates into a straight line (case of a special solution).
For other initial conditions, the number of switchings of the control function γ (t)
depends on the number of sign changes of the function λ3 (t) in the time interval
(t 0 , t k ). The need to control the movement of aircraft relative to programmed paths
(landing course lines) arises because, under the influence of disturbances, inaccuracies in piloting and aircraft navigation, as well as errors in setting initial conditions
and differences in aircraft characteristics from the calculated ones, movement parameters deviate from programmatic ones. We note that the Pontryagin maximum principle is a necessary optimality condition for performing the numerical simulation.
The question of the existence of admissible (optimal) controls is each time decided
following a specific situation.
5.4.2 Aircraft Movement Model During Approach
for Landing with a Decrease in Speed and Two Turns
Since the deflection of the ACFT from the landing course line systemic random, it
seems appropriate simulation to determine the most probable boundaries of arising
deviations with maximum values of errors of the aging rate and the roll forces in the
process of turn to the landing pattern.
The ACFT movement in the landing zone performed with decreasing flight speed
of the ACFT in the prescribed program, wherein the roll rotates, in the case to
compensate the lateral deviation limited to, as a rule, the value of 15º.
One of the options technology is changing the interaction of the pilot (crew), and
the landing zone officer is to establish the route of reducing control points in which
the pilot (crew) of the ACFT together with the landing zone determines its position
relative to the limit line of descent and makes a decision on keeping or changing the
course of decline (entry direct, the entry on the scheme through the DLRB, etc.).
In the intermediate control points, the landing zone officer (landing dispatcher)
recommends a method of landing; the decision is depending on the magnitude limit
of the trajectory and given the variances in the previous passage control points.
Certain types of human activities involve decision-making in the form of implicit
components, although the decision-making process often is regarded as a sensory,
sensory motor, or even cognitive and that directly applies to the process of ATC,
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5 A. V. Yakovlev et al.
where entities of the group management of flights/pilots (the crew) have to resort
to forecasting, for example, the trajectory of the landing. Thus, the process can
be viewed as a sequence of actions and decisions by using additional information
because of the process—minimizing the time of ATC for the safe running of the
whole system.
Such tasks are characterized by incompleteness, ambiguity, the uncertainty of
initial information and used the rules in its transformation, and it is necessary to assess
the environment to forecast the behavior of objects (ACFT) and the development of
the situation, to evaluate possible actions and choose the best, etc.
In the described activities of so-called combined installation (“safety - time”),
when along with the requirement of the inadmissibility of errors when entering the
sun on the landing, you also need to perform actions when responding to deviations
of the aircraft from the predetermined trajectory for the minimum time.
Creating algorithms and models to assist in the operational management of the
armed forces control the correct operation and predicting the situation will minimize
the time for making the right decisions.
Based on the above, is the apparent necessity:
• theoretical and experimental substantiation of the rational trajectory of the aircraft,
which would provide the crew an opportunity to reserve time for keeping the
required limits in routine flight and increase his readiness for the solution of
management tasks in extreme conditions;
• development of algorithms for the detection of unsafe flight conditions at the stage
of decline of the armed forces and formation on their basis of preventive measures
and establishment of systems of support of decision-making using simplified
mathematical models of flight of the aircraft.
The length of the aircraft on landing performed with the execution of several
maneuvers is required for precise and straight falling into the zone of allowable
deviation from the landing course. The aircraft is moving at a constant speed, and
the role will have a constant radius of the circle in the entire trajectory. Turn on
the required number of degrees or double-page spread is a line of circles shown
in Fig. 5.5. Therefore, for their characteristics, the following parameters are used:
radius (R) and angle of turn.
The maneuver for performing a double turn during approach is characterized by
the fact that at the place of changing the direction of the turn (point O), the radii of
the end of the first half of the turn and the beginning of the second half of the turn
are equal.
The calculation of the radius of the circle along which the ACFT moves is carried
out using the following expression [9, 10]:
Rt =
Vt2
g tan(γnorm )
(5.32)
5.4 A Mathematical Model for Constructing an Optimal Approach Path
119
Fig. 5.5 Aircraft approach path with two turns at constant speed
where V t is the current ground speed of the aircraft, m/s; g is the acceleration of
gravity, m/s2 ; γnorm —necessary to complete a turn, deg.
ACFT flight at the approach stage is characterized by a decrease in speed, which
is continuously monitored. Therefore, with accuracy sufficient for practical calculations, we can assume that the motion of the aircraft is equally slow; under these
conditions, the turning radius will change (Fig. 5.6). The acceleration is determined
using the initial and final speed of the ACFT, as well as the length of the flight path.
Because the ACFT decreases speed, the acceleration will have a negative sign. To
calculate the acceleration, we use the formula [10]:
a=
V 2 − V02
,
2·S
(5.33)
where
V
V0
S
final speed, m/s;
initial speed, m/s;
distance from start to endpoint of movement, m.
The turning radius with a decrease in speed and negative acceleration will naturally
decrease.
To find the angle of rotation is necessary to determine the angular velocity of the
aircraft using formula (5.34) [10]:
ω=
g · n γ · sin γ
,
V · cos (5.34)
where g—free-fall acceleration, m/s2 ; n γ —overload; γ —roll required to complete
a turn, deg.; V —aircraft speed, m/s; —pitch angle, deg.
The angular velocity (5.34) is measured in m/s; the angular velocity in deg/s is
determined using the following expression:
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5 A. V. Yakovlev et al.
Fig. 5.6 Aircraft approach path with two turns at decreasing speed
t
=
Vt
,
Rt
(5.35)
where
Vt
Rt
Rt
βt
L1
O
αt
X 0, Y 0, X β , Y β
current aircraft speed, m/s;
current radius of the circle of movement, m;
aircraft turning radius at time t, t, t = 0, 0.01, 0.02, …, n, (m);
ACFT turning angle in the first half of the maneuver at time t;
linear lateral deviation of ACFT from the line of the landing course;
the ACFT rotation direction change point (change of aircraft roll
sign);
ACFT turning angle in the second half of the maneuver at time t;
the aircraft rotation of the coordinates centers (center of the
logarithmic spiral).
The rotation angle β is determined as follows:
βt =
t
t
(5.36)
5.4 A Mathematical Model for Constructing an Optimal Approach Path
121
where
t
Ωt
turn realization time, s;
angular velocity, rad/s.
Thus, knowing the basic parameters of the aircraft motion is possible to build a
model of its flight with a turn at a certain angle, for which it is necessary to determine
the radius of the circle of the trajectory, the angular speed of the turn and the angle
itself.
5.4.3 Aircraft Double Turn Modeling
The main feature of double-turn modeling is the determination of the angles in the
first and second parts of the maneuver. Since the motion of the aircraft is equally
slow, and the radius of the circle of the trajectory of movement decreases, the angles
of the first and second turns will be unequal.
The primary flight parameters necessary for constructing the ACFT approach
trajectory is presented in the form of initial data, which include:
V
V0
G
γnorm
nγ
L1
L2
α
final speed of maneuver, m/s;
initial speed of the maneuver, m/s;
free-fall acceleration, m/s2 ;
roll required to complete a turn, deg.;
overload;
pitch angle, deg.;
lateral linear deviation, m;
distance to runway, m;
angle of deviation of the ACFT course from the landing course, deg.
The movement of the aircraft is considered in a rectangular coordinate plane. The
y-axis is the line of the landing line; the x-axis is the line of lateral deviation from the
runway. The origin of the runway is taken as the origin of coordinates; the trajectory
of movement should be located in the fourth quarter of the coordinate plane because
a turn is performed at a value of no more than 90°.
Aircraft motion modeling is performed with a resolution of 0.01 s. At each
moment, there is a change in the speed of aircraft; it is characterized by negative
acceleration, a change in the radius of the flight curve, the angular velocity, and the
angle of rotation. Following this, there is a change in the coordinates of the trajectory. Coordinates (x, y) will decrease. The first part of constructing the double-turn
trajectory is to determine the value of the angle of the turn in the first half of the
maneuver.
The angle of the first turn is found by comparing the simulated radius when
turning through the angle β t at each moment of time Rβ t and the radius obtained by
the calculation method Rβ∗ . When both radii become equal, we determine the value
of the desired angle. Rβ t , which is as follows [9–11]:
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5 A. V. Yakovlev et al.
Rβ∗ = Rβt =
R0 − L 1 κ
,
cos(βt )
(5.37)
where
Rβ t —
R0 —
L 1—
κ—
βt —
calculated radius at a time t, t = 0, 0.01, …,n, m;
radius at a time t = 0, m;
lateral linear deviation, m;
coefficient characterizing the deflected deviation for the first turn;
turning angle at time t, deg.
The value of (L 1 · κ) characterizes the moment of shifting the course (the point
of the beginning of the second turn). The functional dependence of κ on the lateral
deviation L 1 is found by numerical simulation and has the form:
k = 0.4722 + 2.295 × 10−5 L 1 − 4.666 × 10−9 L 21
quad + 5.305 × 10−13 L 31 − 2.428 × 10−17 L 41
(5.38)
The value of the desired turning angle βt is determined by the moment of
coincidence of the simulated and calculated radii:
Rβ∗ = Rβt .
(5.39)
The construction of the flight path when turning at an angle βt is possible only by
determining the coordinates of the aircraft location at each time t using the following:
yt = Rt · sin(βt );
xt = Rt · cos(βt ),
(5.40)
where Rt —radius at time t, t = 0, 0.01, 0.02,…, n, m; βt —turning angle at time t,
deg.
Thus, it is possible to construct the trajectory of the aircraft during the first turn
and find the coordinates of the point of course shifting, from which the second turn
will begin. Denote this point - O (x Rβ∗ , y Rβ∗ ).
To determine the trajectory of the second turn is necessary to find the reflection
of the arc of the logarithmic spiral relative to the tangent to this spiral at point O
() symmetrically. Knowing the equation that describes the curve of motion of the
aircraft and the point of passing the course O, we construct the tangent at this point.
The equation of the tangent to the graph of the function F(x) at the point (x 0 , y0 ) is
as follows:
y = f (x) + f (x) · (x − x0 ),
while f (x)—angular tangent coefficient.
(5.41)
5.4 A Mathematical Model for Constructing an Optimal Approach Path
123
For a function depending on two variables F(x, y), the tangent equation will have
the form:
f (x)(x Rβ∗ , y Rβ∗ ) · (x − x Rβ∗ ) + f (y)(x Rβ∗ , y Rβ∗ )(y − y Rβ∗ ) = 0.
(5.42)
Using Eq. (5.42), we construct the tangent to the graph of the function at point O
(x Rβ∗ , y Rβ∗ ).
The next step is to find the coordinate of a point already on a symmetric curve.
For this, it is necessary to find the tangent coefficient and the angle of inclination of
the perpendicular straight line to the x-axis, using the following expressions:
q=−
∂f ∂f
/ ;
∂x ∂y
φ = ar ctg(− f (y)/( f (x)),
(5.43)
(5.44)
where φ—tilt angle of straight.
The coordinates of a symmetrical curve are defined as follows:
xt = xα + 2 · d · cos(φ);
yt = yα + 2 · d · sin(φ),
(5.45)
where xα , yα —projections of the coordinates of a trajectory point on a tangent; d—
distance from the point of the path to the tangent, m; φ—tangent of the slope of the
tangent.
Thus, a curve is constructed that is symmetrical with the initial curve of the aircraft
motion relative to the tangent at point O. The described operation must be done for
each point. Knowing the coordinates of each point of the symmetrically reflected
curve, we find the intersection of this curve with the line of the landing course.
A double turn is simulated for the shortest aircraft access to the landing line using
the presented sequence of actions. The trajectory of the aircraft when performing
a double turn is based on the flight coordinates of the first and second turns. The
coordinates of the constructed trajectory must satisfy certain restrictions, based on
which the decision is made to use the constructed trajectory.
The final phase and result of the developed model are the decision on whether
or not to perform a maneuver on approaching the aircraft. A definite conclusion
is adopted when the constructed trajectory of the aircraft falls within regulatory
restrictions. The latter is taken into account in the algorithm for constructing the
flight path.
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5.5 Development of a Set of Problem-Oriented Programs
and Simulation Confidence Assessment
The aircraft trajectory control algorithm during approach is the determination of the
sequence of FOO actions necessary to obtain a solution to the problem of ensuring
a given level of safety at the aircraft landing stage. The algorithm for constructing
the aircraft trajectory during an approach is characterized by branching and multi
variance that is due to the presence of a significant number of restrictions associated
with the aircraft landing, as well as various options for aircraft departure relative
to the landing course. One of the main criteria for branching the algorithm is the
position of the aircraft and its course at the time of exit to the landing area relative to
the LH. The scheme of the aircraft trajectory control algorithm during the approach
is shown in Fig. 5.7. The structure of the latter allows us to cover all the necessary
restrictions, as well as various options for the aircraft to enter the area of the landing
course. The first limitation, which is the criterion for branching the algorithm, is the
entry of aircraft into the landing radar visibility area (LRVA). It determines the further
movement through the stages of the algorithm. If the aircraft exit point does not fall
into the necessary restriction, then a decision is made to go to the second circle,
which allows the aircraft to take a more favorable position relative to the landing
course when performing a second approach. In the opposite case, the coordinates of
the appearance of aircraft in the landing zone become one of the initial indicators
necessary for calculating the trajectory of the aircraft landing.
The flight course of the aircraft is a determining factor in the multivariance of the
algorithm. The aircraft can have a course equal to or unequal to the landing, and the
flight rate not equal to the landing rate differs in the direction: toward the landing
course and away from it. Depending on the course with which the aircraft entered
the line of sight, a model for constructing the aircraft trajectory is being developed.
After modeling the approach trajectory, a check made to find all the trajectory points
in the visibility range of the landing radar. The procedure for calculating the flight
path of the aircraft is crucial in the general algorithm of the decision support system.
The structural diagram of the functioning of the procedure for calculating the flight
path of an aircraft is presented in Figs. 5.8 and 5.9.
To determine the parameters of the aircraft flight path is necessary to have the
aircraft removal values to the runway, the lateral deviation of the aircraft relative to
the line of the landing course, the roll of the aircraft, the initial and final value of the
aircraft flight speed, in and out of the landing zone, which is acceptable in accordance
with regulatory documents (at the entrance to the landing zone and landing), as
well as the error of maintaining the flight speed on the trajectory of the landing
course. The next stage of the algorithm is finding the acceleration, which determines
the parameters of the trajectory in a given time interval. Next, the procedure for
calculating each point of the aircraft flight path and the roll point of the aircraft roll
is called up. Then, the lines are built:
• permissible deviations from the line of the landing course;
• zone of visibility of the RNL;
5.5 Development of a Set of Problem-Oriented …
Fig. 5.7 Block diagram of
the algorithm for
determining the parameters
of the aircraft flight path
125
126
Fig. 5.8 Implementation
algorithm flight path
calculation procedures
aircraft
5 A. V. Yakovlev et al.
5.5 Development of a Set of Problem-Oriented …
Fig. 5.9 Implementation algorithm calc procedures
127
128
5 A. V. Yakovlev et al.
• A zone is providing an optimal approach by two turns.
The next step in the algorithm is to display the calculated lines and trajectories,
as well as the deviation of the aircraft from the line of the landing course after the
end of the maneuver, the removal of the aircraft to the runway after the end of the
maneuver, the coordinates of the roll point and the course at this point.
The trajectory calculation procedure is an iterative computational process
consisting of three stages:
• construction of the first half of the trajectory to the point of roll change;
• finding the tangent to the flight path of the aircraft at the roll point;
• construction of the second half of the trajectory.
Creating algorithms and models to assist in the operational management of the
aircraft, monitoring the correct operation, and predicting the situation will minimize
the time to make the right decision.
5.6 Assessment of the Complexity of the Algorithmic
Ensure of the System Decision-Making Support
for the Workstation of the Landing Zone Officer
(Landing Dispatcher)
The complexity of the algorithm for determining the parameters is estimated in two
stages:
• performance assessment in the course of solving the problem of constructing the
optimal flight path of an aircraft;
• checking the performance of the algorithm, taking into account the existing
restrictions.
When evaluating, we will consider the following:
• the considered algorithms have two types of operations: operations of addition
type and operations of comparison type;
• addition type operations and comparison type operations have the same duration.
In the algorithm for determining the flight path parameters of an aircraft, the
total number of operations is 58. The first half of the trajectory is calculated in 26
operations and the number of iterations of the first half of the trajectories is 3565.
The second half of the trajectory is calculated in 32 operations, and the number of
iterations of the second half of the trajectories is 3579 [5–7]:
N
k=
σ (N − i) = σ N
i=1
(N − 1)
2
(5.46)
5.6 Assessment of the Complexity of the Algorithmic Ensure of the System …
129
The complexity of the algorithm is estimated - O(N 2 ). Analysis of the research
results shows that the algorithm for determining the parameters of the aircraft flight
path allows us to obtain a given path in the shortest time since it has complexity
O(N 2 ).
5.7 Construction of a Landing Approach Zone
and Recommendations to the Officer of the Landing
Zone (Landing Dispatcher) on Aircraft Control Using
the Decision Support System
By numerical simulation, a safe approach zone with two conjugate turns is defined
(Fig. 5.10), which allows the officer of the landing zone to make a timely decision
on the possibility of an emergency landing, or on the need to go to the second round.
The boundary of the safe approach zone corresponds to the maximum parameter
of the linear lateral deviation of the aircraft (X max ), for which it is still possible to
perform two paired coordinated turns to accurately bring the aircraft to the landing
course under the existing roll restrictions without a straight section of the path when
moving away from the runway corresponding to L man .
It can be seen that up to a distance of 9 km from the runway, the safe entry zone
exceeds the size of the zone of responsibility of the officer of the landing zone, which
expands its ability to control aircraft flight. It was determined that after a distance
Fig. 5.10 Area providing a safe approach by two paired turns
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5 A. V. Yakovlev et al.
of 9 km to the runway, there are segments of the control zone of the officer of the
landing zone, and if they fall into it, he must decide on the formation of the escape
path to the second circle, since it is impossible to enter the aircraft for landing.
5.8 Software Development of a Decision Support System
for an Automated Workstation of a Landing Zone
Officer (Landing Dispatcher)
Based on the developed method, mathematical model, and algorithms, the software
was created for the decision support system for the automatized working station
(AWS) of the officer of the landing zone (Fig. 5.13), which implements:
• display of the current state of control objects;
• definition and mapping of zones ensuring the safe approach of aircraft;
• the formation of the optimal trajectory of the aircraft approach for landing with the
display of the exact location of the roll change, as well as the landing trajectory,
taking into account the allowable deviations of the aircraft speed keeping;
• displaying information about the execution time of the first and second half of the
maneuver;
• display of the course at the point of roll change, range to the runway, and lateral
deviation at the end of the maneuver.
The software was created using the Delphi Rapid Application Development Environment for Windows 9x, XP operating systems. The program uses modern interface
elements (contextual prompts, graphic buttons, etc.), new information technologies.
The software includes:
1.
Input data input panel (Fig. 5.11), which contains the following main elements:
•
•
•
•
•
input of the initial speed of the ACFT;
entering the final speed of the ACFT;
input the roll angle of the ACFT;
enter the value of the allowable error of the aircraft flight speed;
the landing course of the landing aerodrome with the possibility of changing the
direction of approach of the ACFT;
• image scale on the main control panel;
• entering the line of entry of the ACFT into the zone of responsibility of the officer
of the landing zone;
• aircraft deviation from the landing line at the time of calculating the optimal
approach path.
Here, the basic information can be directly entered to form the optimal aircraft
approach path, as well as additional information in the form of the allowable error of
5.8 Software Development of a Decision Support System for an Automated …
131
Fig. 5.11 Input panel for source data
the aircraft’s flight speed, which is usually provided for by the norm, which allows
obtaining the approach paths corresponding to the extreme values of speed keeping
flight crew of the aircraft.
2.
The panel of the output of results (Fig. 5.12), which contains information for
the formation of control actions by the officer in the landing zone:
•
•
•
•
•
ACFT heading at the roll point;
deviation of the ACFT from the landing course at the end of the maneuver;
the time the ACFT performed the first and second half of the maneuver;
the position of the roll point of the ACFT relative to the landing course and runway;
removal of the ACFT from the runway after the end of the maneuver.
3.
The main control panel (Fig. 5.13), which displays:
•
•
•
•
zone of responsibility of the officer of the landing zone;
zone of permissible deviations of the ACFT from the line of the landing course;
a zone ensuring the safe approach of the aircraft for landing by two paired turns;
the optimal trajectory of the aircraft landing for taking into account the allowable
error in maintaining the speed of flight;
• the point of change of the roll of the ACFT.
Here, the aircraft’s deviation from the landing course line is directly determined,
the optimal aircraft approach path is built, and the officer of the landing zone chooses
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5 A. V. Yakovlev et al.
Fig. 5.12 Results output panel
the most suitable options for solving the aircraft landing approach (the ACFT to land
on the optimal approach path, formation of the ACFT departure path to the second
circle).
A convenient graphical interface allows the officer of the landing zone to monitor
the current situation in his area of responsibility, quickly develop options for solving
the problem of approaching the aircraft in case of deviation from the trajectory of the
landing course, choose the most suitable ones, and form commands for controlling
the aircraft.
Presentation to the landing zone officer of the execution time of each of the halves
of the turn, together with the display of the place of change of the roll of the turn,
makes it possible to control the flight of the aircraft and control its location on the
optimal path in the event of an onboard navigation system failure.
The indication of the zone, ensuring the safe approach of the aircraft to the landing
by two paired turns, significantly expands the capabilities of the officer of the landing
zone to manage in his area of responsibility, providing a decision on the withdrawal
of the aircraft to the line of the landing course along the optimal path within the zone
of responsibility until the distance of 9 km from the runway.
After the removal of 9 km to the runway, the ability to bring the aircraft to the
landing course at a distance of at least 4 km to the runway (location of the DLRB)
is significantly reduced, which can be seen from the presented zone configuration,
which ensures the safe landing of the aircraft.
5.8 Software Development of a Decision Support System for an Automated …
133
1 - the current state of the control object; 2 - the boundaries of the zone that
ensures the safe approach of the aircraft for landing; 3 - the optimal trajectory of
the aircraft approach for landing with the display of the exact location of the roll,
as well as the trajectory, taking into account the allowable deviations of the
airspeed; 4- performing the first and second half of the maneuver; 5 - course at the
point of roll change, range to the runway and lateral deviation at the end of the
maneuver; 6 - the area of responsibility of the FOO
Fig. 5.13 A fragment of the interface of the AWS FOO
The program does not require any specific software products. It usually works
on a PC with a processor having a clock frequency = 800 Hz, an 8 MB graphics
card, 128 MB RAM, and Windows 9x (XP) operating environment. It most optimally
works with a processor having a clock frequency = 1.8 kHz, a 64 MB graphics card,
256 MB RAM.
5.9 Reliability Assessment of the Model for Constructing
an Optimal Approach Trajectory
It was required to assess the characteristics of the developed system of support of
decision-making, having in its composition the optimal trajectory and the differences
between the existing control methods.
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5 A. V. Yakovlev et al.
There were three series of experiments involving the control of aircraft using the
system of support of decision-making, the control of aircraft to the command of the
officer landing zone, independent execution of the flight crew of the landing. The
total number of experiments in each series was 32. The initial aircraft position in
the landing zone was the distance from the end of the runway 20 km lateral distance
from the line landing course 4000 m.
The first stage of the statistical studies is conducted to determine differences
between sample averages of the deviations from the line landing course in three series
of experiments. Determined the leading statistical indicators in the form of mathematical expectation of a linear lateral deviation from the line of the landing course at
the end of the maneuver the aircraft on the line landing course, variance, deviation,
distribution of random variables as a test for hypotheses about the difference, the
average deviation was used Student’s t-test for independent samples.
The main statistical indicators are summarized in Table 5.1. Insignificant values of
asymmetry and kurtosis which are close to zero allow putting forward the hypothesis
of normality of the distribution. The second stage of statistical research is to prove the
hypothesis about the normality of the distribution, as a condition for the application
of the Student’s t-test. The distribution can be considered normal if the values of the
asymmetry and kurtosis do not exceed twice their average standard deviations σ as i
σ ex , t.e. (As /σ as ) ≤ 2 i (E x /σ ex ) ≤ 2.
To more thoroughly test the hypothesis of a normal distribution, we compared the
frequencies of the actual distribution with the frequencies of the normal distribution
using the χ2 criteria at a 5% significance level, and the tabular value of the χ2 criterion
was 18.307.
The calculation results are presented in Table 5.2.
Since the actual values of the χ2 criteria for all populations do not exceed the table,
and the asymmetry and kurtosis do not exceed their double mean square deviations,
the distribution of linear deviations from the line of the landing course at the end of
the maneuver, the distribution can be considered standard with a significance level
of P ≤ 0.05.
Table 5.1 Statistical indicators of experimental studies
Statistical indicator
FOO
Crew
DSS
A mathematical model for
calculating the parameters of the
aircraft trajectory taking into
account changes in its
aerodynamic characteristics
MoBU , m
101.25
104.25
3.594
4.352
DBU ,m
94.438
137.938
79.273
75.687
BU , m
9.718
11.745
8.904
8.699
As
0.068
0.092
0.121
0.005
Ex
0.113
0.795
0.069
0.095
MoD , m
8350.4
10,560.7
12,818.3
12,540.7
5.9 Reliability Assessment of the Model …
Table 5.2 Checking the
normality of the distribution
(P ≤ 0.05)
135
Criterion
FOO
Crew
DSS
As /σ as
−0.973
−1.313
−1.722
E x /σ ex
0.139
0.983
−0.209
1.511
5.857
0.393
χ2
Note χ2
tabl.
= 18.307
We revealed a difference between the average deviations from the line of the
landing course at the time of the end of the maneuver, for which we considered the
null hypothesis that the wide variances of the considered sets are equal to each other.
To solve the problem of comparing variances, we used the F-criterion (R. Fisher’s
criterion), at a 5% significance level, and the tabular value of the F-criterion was
1.822 for the degree of freedom 31. The actual values of the F-criterion obtained by
comparing all variances are presented in Table 5.3.
It can be seen that all calculated values of the F-criterion do not exceed the
tabulated value; this indicates the absence of grounds for rejecting the null hypothesis
of equality of variances.
A comparison was made of the average linear deviations from the line of the
landing course at the time of the end of the maneuver using the Student’s t-test. Due
to the insignificance of differences between the average deviations from the line of the
landing course when controlling the approach by the officer of the landing zone and
the crew of the aircraft, the null hypothesis of the equality of the average H0: M(crew)
= M(FOO) was independently tested at a significance level of 0.05. The estimated value
of zmon. . is amounted to 1,113. By hypothesis, the competing hypothesis has the form
M(crew) = M(FOO) ; therefore, the critical region is two-sided. The right critical point
is:
Φ(z cr ) =
1 − 0.05
1−α
=
= 0.475,
2
2
Z cr. = 1.96, as much as zmonit. ≥ zcr. , there is no reason to reject the null hypothesis.
Therefore, there are no differences between the average deviations from the line of
the landing course when controlling the approach by the officer of the landing zone
and the crew of the aircraft.
Subsequently, hypotheses were put forward on the equality between the average
deviations from the landing line when managing the approach by the landing zone
officer and using the decision support system to bring the aircraft to the landing line
when deviations occur, as well as on the equality between the average deviations
Table 5.3 The actual values
of Fisher’s criterion are
obtained in the comparison of
all variances
FOO
Crew
DSS
FOO
–
1.46
1.74
Crew
1.46
–
1.191
DSS
1.74
1.191
–
136
5 A. V. Yakovlev et al.
from the line of the landing course for an independent approach to the landing of the
crew of the aircraft and in the case of applying the decision support system.
As competing hypotheses, the officer of the landing zone and the crew of the
aircraft put hypotheses forward about the excess of average values when controlling
the approach over the average value of deviations when controlling the flight of the
aircraft using the decision support system. Hypotheses tested at a significance level
of 0.05 (zkr. = 1.64):
1
2
H0 : M(Crew) = M(DSS) , H1: M(Crew) > M(DSS) .
zmonit. = 38.635, as much as zmonit. ≥ zcr. , We reject the null hypothesis; therefore,
the average deviation of the aircraft from the line of the landing course when
using the decision support system is less than the average deviation during the
independent call of the aircraft–crew.
H0 : M(FOO) = M(DSS) , H1: M(FOO) > M(DSS) .
zmonit. = 38.99, as much as zmonit. ≥ zcr. , We reject the null hypothesis; therefore,
the average deviation of the aircraft from the landing line when using the decision
support system is less than the average deviation when controlling the approach
by the officer of the landing zone.
The use of statistical methods in the study made it possible to confirm the adequacy
of the developed model if applied as part of the decision support system of the AWS
of the landing zone officer.
The results of the experiment and their comparative analysis are presented in
Fig. 5.14.
Fig. 5.14 Assessment of the reliability of the simulation and the gain on based on the use of DSS
5.9 Reliability Assessment of the Model …
137
Figure 3.8 shows that the average value of deviations of the aircraft from the
landing course line when using the developed mathematical model (DSS) is significantly less than the average value of deviations when the aircraft–crew independently
enters the landing area, as well as by commands of the landing zone officer. Statistical
indicators of the DSS modeling data and the full dynamic mathematical model are
almost identical. However, the proposed DSS model is implemented in real-time and
provides operational control of the aircraft, which is almost impossible when using
a fully dynamic model.
Comparative characteristics of the existing management system and DSS as part
of the AWS FOO are presented in Table 5.4.
Analysis of the results allows us to draw the following conclusions:
• the introduction of a decision support system in the workplace of the officer of
the landing zone will improve the safety of the aircraft landing approach based
on the construction of an optimal landing path;
• the use of a decision support system during flights enables the officer of the landing
zone to improve the management and control of aircraft flight at the most critical
stage–landing.
Thus, the use of statistical methods in the study made it possible to confirm the
adequacy of the developed model and justify the need for its application as part of
the decision support system for the AWS of the landing zone officer.
5.10 Development Of The Technology For The Operation
Of Air Traffic Control (Flight Control) Service
Dispatchers During Flights In Special Conditions
And Individual Cases In Flight
The technology for the operation of air traffic controllers (ATS) on international air
routes and regional airlines (RA) is open for international flights within the airspace
of the Russian Federation. As well as ATS in the airspace outside it assigned to
the Russian Federation, are developed with taking into account the requirements of
regulatory legal documents of the Russian Federation, Standards and Recommended
Practices of the International Civil Aviation Organization (ICAO).
In this case, the following issues should be considered [11]:
(1)
(2)
(3)
(4)
(5)
general provisions;
preparation for duty and reception of duty;
the boundaries of the transfer of ATS;
air traffic services procedure;
how ATS occurs when flying in special conditions and individual cases in flight.
The general provisions indicate:
• sources based on which technologies developed;
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5 A. V. Yakovlev et al.
Table 5.4 Comparative characteristics of the existing information reporting system and DSS FOO
The way to present or use
information in the workplace of
the officer of the landing zone
Existing system (VISP-75,
VISP-97, KSRP-A)
DSS FOO
Building and displaying the
optimal trajectory of the aircraft
in the event of a deviation from
the line of the landing course
–
+
The method of withdrawal of
aircraft on a landing course
FOO by the method of
successive approximations
Automated by plotting a
2-turn trajectory
Decision-making on aircraft
retreat to the second round
FOO following the level of
training and preparedness
Automated at the time the
aircraft enters the landing
zone
The method of calculating the
parameters of the flight path of
the aircraft (beginning and end
of a turn)
By visual estimation
Automated
The degree of participation of
All necessary calculations,
the landing zone officer in the
issuance of executive
management of the aircraft flight commands and control of the
flight path
Issuance of executive
commands and control of
aircraft flight path
Calculation accuracy
Following the specified
requirements
Following the preparedness of
the FOO
Information that determines the –
parameters of the optimal
trajectory of the aircraft:
– the direction of a turn
– regulatory roll of a turn
– the exact location on the flight
path of the aircraft of the point
of change of the direction of
the turn
– aircraft heading at the point of
change of direction
– lateral deviation of the aircraft
from the line of the landing
course at the end of the
maneuver
– removal of aircraft from the
runway at the end of the
maneuver
+
Indication of zones ensuring a
safe approach to the aircraft
+
–
(continued)
5.10 Development of the Technology for the Operation …
139
Table 5.4 (continued)
The way to present or use
information in the workplace of
the officer of the landing zone
Existing system (VISP-75,
VISP-97, KSRP-A)
DSS FOO
Indication of the execution time
of each part of the maneuver, to
ensure the aircraft approaches
the landing in the event of a
failure of the navigation and
flight system
–
+
Training of the officer of the
landing zone in the approach of
the aircraft in the event of a
deviation from the line of the
landing course during
preparation for flights
–
+
Analyzing to determine the
–
possibility of an aircraft
approaching, taking into account
the characteristics of the airfield
+
Analysis and review processes of –
the actions of the landing zone
officer according to the
completed flight plans
+
• the features of the organization, the possibilities, and conditions for combining
the functional responsibilities of dispatchers engaged in ATS;
• general provisions for the development and application of the technology of the
dispatcher.
In preparation for duty and reception of duty indicated [11]:
• issues with which the dispatcher obliged to familiarize themselves with the
briefing at the workplace;
• questions or information requiring clarification;
• the procedure for the transfer of duty and its execution;
• the conditions under which the flight director can delay duty and make a
substitution.
ATS transfer boundaries are carried out as follows [11]:
• the boundaries of districts, zones, and sectors (directions) of ATS with indication
of reference points, geographical coordinates;
• given the boundaries of the reception and transmission of ATS in the vertical and
horizontal planes.
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5 A. V. Yakovlev et al.
The air traffic services procedure disclosed dispatcher work content:
• when receiving (transmitting) air traffic control from an adjacent point dispatcher,
as well as when flying AML;
• with flight routes in the ATS area (zone);
• when sent to the alternate aerodrome;
• when using secondary radar (VRL) (where available);
• at ATS aircraft performing international flights (if any).
When providing ATS during flights in special conditions and individual cases in
flight, the contents of the work of the dispatcher during ATS in special conditions
and individual cases in flight are disclosed, taking into account local conditions and
peculiarities of ATS.
The interaction between air traffic control (flight control) controllers [11] is shown
in Fig. 5.15.
Figure 5.16 shows a diagram of the actions of air traffic control (flight control) air
traffic controllers during aircraft flights in the icing zone, thunderstorms and heavy
rainfall, heavy chatter, increased electrical activity of the atmosphere, and dust storm
[11].
Analysis of the data presented in Fig. 5.16 shows that for the effective operation
of dispatchers in areas of adverse weather conditions, it is necessary to:
(1)
(2)
(3)
have reliable information about the meteorological situation;
be able to predict dangerous meteorological phenomena;
make the right decisions in adverse conditions
meteorological conditions: send the aircraft to the waiting area or close (limit
flights) or send the aircraft to the alternate aerodrome.
It should be noted that in addition to the safety factor in this situation, it is necessary
to take into account the economic factor. In the case of short-term adverse weather
Fig. 5.15 Interaction between air traffic control (flight control) controllers. Note: FOA— flight
operations assistant; FOO—flight operations officer ppovepit napicanie vezde; NZO—near
zone officer
5.10 Development of the Technology for the Operation …
141
Fig. 5.16 Actions of air traffic control (flight control) controllers during aircraft flights in the
icing zone, thunderstorms and heavy rainfall, heavy chatter, increased electrical activity of the
atmosphere, and dust storm
conditions, the aircraft should be sent to the waiting area and not to the alternate
aerodrome. Moreover, it makes no sense in this case to close flights.
The requirements for air traffic services (flight control) dispatcher can be defined
as follows:
d → min
γ ≥ γ0 ,
(5.47)
where d—it is an indicator of material losses from inaccurate information or an
erroneous forecast of a meteorological phenomenon or an incorrect decision due to
the “human factor” γ —safety indicator γ0 —its minimum value. Today, according
to ICAO requirements, the probability of a plane crash should not be more γ0 =
5 × 10−9 .
The error of air traffic control (flight control) controllers when flying aircraft in
an area with adverse weather conditions can result from errors in the transmission
of meteorological information, a priori errors associated with the forecast of the
meteorological situation and an error in making decisions.
In general, the probability of a dispatcher error can be described by the following
formula:
P = α · β · p(),
(5.48)
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5 A. V. Yakovlev et al.
where α—the probability of error in the transmission of meteorological information
β—the probability of an error associated with an incorrect weather forecast —
event of dispatcher making a wrong decision p()—the probability of the dispatcher
making the wrong decision. For example, an indication for an aircraft to move to
a waiting area under long-term exposure to hazardous meteorological conditions
affects flight safety, and an indication for an aircraft to fly to an alternate aerodrome
at a time when only a short-term hazardous meteorological phenomenon observed
leads to unjustified temporary and, as a result, economic losses.
Under the forecast weather conditions, errors of the first and second kinds are
possible.
We denote by ε the probability of the event that the meteorological phenomenon
is recognized as short-term, although it is contractual.
We denote by δ the probability of the event that the meteorological phenomenon
is recognized as long-term, although, in fact, it is short-term.
In this case, the receipt of incorrect meteorological information can also affect
the incorrect decision of the dispatcher.
Thus, (5.48) can be represented as follows:
P = α · (ε + δ) · pcond. () + ·(ε + δ) p()
+ α · (1 − ε − δ) · pcond. () + (1 − α) · (1 − ε − δ) p(),
(5.49)
where pcond. ()—this is the conditional probability of a controller error when
receiving incorrect meteorological information.
Figure 5.17 shows the actions of air traffic control (flight control) dispatchers in
an attack on an aircraft–crew [11].
Fig. 5.17 Actions of air traffic control (flight control) controllers in an attack on an aircraft–crew
5.10 Development of the Technology for the Operation …
143
In this situation, for the dispatcher to work effectively, the following is required:
(1)
(2)
(3)
the transfer of reliable information about the incident;
the correct assessment of the air situation;
the correct decision of the dispatcher.
Further, the probability of a controller error can be obtained based on formulas
(5.48) and (5.49).
References
1. Anodina TG (1993) Modeling of processes in the system of air traffic control. In: Radio and
communication, 345 p
2. Analysis of the state of flight safety in civil aviation of the Russian Federation in 2018/Federal
air transport Agency, Moscow, 89 p (2019)
3. Danilov VB (2012) Safety. Samara, Samara state aerospace University, 148 p
4. Krasovskii AA (2005) Mathematical modeling and computer systems education and training.
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