FUZZY LOGIC APPROACH TO AIRPLANE PRECISION INSTRUMENT APPROACH AND
LANDING
Vahed Tavakoli Zadeh
B.S., Civil Aviation Technology College Tehran, Iran 2001
B.S., Embry Riddle Aeronautical University, 2005
THESIS
Submitted in partial satisfaction of
The requirements for the degree of
MASTER OF SCIENCE
in
MECHANICAL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2011
FUZZY LOGIC APPROACH TO AIRPLANE PRECISION INSTRUMENT APPROACH AND
LANDING
A Thesis
by
Vahed Tavakoli Zadeh
Approved by:
__________________________________, Committee Chair
Akihiko Kumagai, Ph. D.
__________________________________, Second Reader
Tien-I Liu, Ph. D.
____________________________
Date
ii
Student: Vahed Tavakoli Zadeh
I certify that this student has met the requirements for format contained in the University format
manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for
the thesis.
__________________________, Graduate Coordinator ___________________
Akihiko Kumagai, Ph. D.
Date
Department of Mechanical Engineering
iii
Abstract
Of
FUZZY LOGIC APPROACH TO AIRPLANE PRECISION INSTRUMENT APPROACH AND
LANDING
By
Vahed Tavakoli Zadeh
In the precision instrument approach and landing of an airplane where the uncertainty is very
frequent due to the high sensitivity of the activity to many factors that influence the behavior of
the pilots, Fuzzy logic can be used to produce estimates which take into account the vagueness of
the flight environment. In this situation, an important decision about the approach and landing of
the airplane under Instrument meteorological conditions is based on these conditions.
Instrument meteorological conditions (IMC) describes weather conditions that require pilots
to fly primarily by reference to instruments, and therefore under Instrument Flight Rules (IFR),
rather than by outside visual. Typically, instrument meteorological conditions are defined as bad
visibility and low ceiling.
In this thesis an analysis of the inputs under fuzzy logic approach is considered for a landing
of airplane in Instrument meteorological conditions. The success rate of landing is investigated,
when the visibility, pilot experience and air speed are given by a fuzzy function. The main
advantages of this approach are then discussed.
Precision instrument approach and landing simulations are used and the performance of the
fuzzy based system is evaluated with fuzzy logic toolbox under MATLAB’s Simulation Block
iv
Set which provides a complete set of tools for evaluating the success rate of landing under the
given inputs.
Around 100 approach and landings are simulated using Microsoft Flight Simulator. All these
flight simulation cases were applied to train the proposed fuzzy logic engine to calculate the
success rate of landing. After the proposed fuzzy logic engine has been fully developed, it has
been evaluated and then the evaluated results from the proposed fuzzy logic engine compared
with flight simulation data collected for evaluation. Comparison of the results from the developed
fuzzy based system and flight simulation results show that the proposed fuzzy engine can
successfully predict the success rate of landing under the given inputs.
_______________________, Committee Chair
Akihiko Kumagai, Ph. D.
_______________________
Date
v
ACKNOWLEDGMENTS
The author would like to acknowledge and thank: the support of Department of
Mechanical Engineering at California State University, Sacramento for providing the
computational resources, and Dr. Akihiko Kumagai and Dr. Tien-I Liu for their technical
expertise and guidance. Lastly, I would like to thank Dr Holl, Department Chair, for the
help to complete my Master in Mechanical Engineering.
Finally, I would like to thank my wife, Abbey, for her love, support, and
encouragement that has enabled me to get this far.
vi
TABLE OF CONTENTS
Page
Acknowledgments …………………………………………………………...………………...vi
List of Tables…………………………………………..………………………………………ix
List of Figures ………………………………………………………………………………....x
Chapter
1. INTRODUCTION …………………………. ……….…………………………………......1
2. DESCRIPTION OF THE PROPOSED FUZZY LOGIC …………………………………..5
2.1 Introduction …………………………………………………….……………………...5
2.2 The Proposed Fuzzy Inference System…….……................…………………………..9
2.2.1 Overview of Fuzzy Inference Process ……………………..……………………9
2.2.2 Step 1. Fuzzify Inputs ……………………………………………………….…10
2.2.3 Step 2. Apply Fuzzy Operator ……………………………………….………...10
2.2.4 Step 3. Apply Implication Method …………………………………….……....11
2.2.5 Step 4. Aggregate All Outputs …………………………………………………12
2.2.6 Step 5. Defuzzify ………………………………………………………………13
3. THE FIS MODLING AND SIMULATIONS ……………….……………………………14
3.1 Introduction …………………………………………………………………………..14
3.2 Modeling ……………………………………………………………………………...14
3.3 Loading Data ………………………………………………………………………....16
3.4 ANFIS Training ………………………………………………………………………20
3.5 The FIS Editor ………………………………………………………………………..22
3.6 The Membership Function Editor …………………………….……………………...23
vii
3.7 The Rule Editor ………………………………………………………………………26
3.8 The Rule Viewer ……………………………………………….……………………..27
3.9 The Surface Viewer …………………………………………….…………………….29
3.10 The FIS Evaluation ………………………………….………………………………32
4. CONCLUSION AND FURTHER STUDY ………………………………………………35
Appendix A The Matlab Structure Syntax.….………………………………………………...37
Appendix B Membership Function Plots and Surface Plot.………...………………………...41
Appendix C Flight Simulation Results…………………………………………….………….45
References ……………………………………………………………………………….……49
viii
LIST OF TABLES
Page
1. Table 1 The FIS and Simulation Results ……………..…………….…...……………....33
ix
LIST OF FIGURES
Page
1. Figure 1.1 Flight Simulation with MS Flight Simulator………………………………......3
2. Figure 2.1 A Graphical Example Of An Input-Output Map ……..…...………………......5
3. Figure 2.2 Roadmap For The Fuzzy Inference Process ……………..……………......…..6
4. Figure 2.3 Visibility Membership Function Curve ………………………………….........7
5. Figure 2.4 The Proposed Fuzzy Inference System ………..……………………...…. …..8
6. Figure 2.5 The Basic Structure of the Fuzzy Inference System ……………....……….....9
7. Figure 2.6 Visibility Input ……………………………………………………...………..10
8. Figure 2.7 Apply Fuzzy Operator AND ……………………………...……………........11
9. Figure 2.8 Apply Implication Method ………………………………...…………….......11
10. Figure 2.9 Aggregate All Outputs ……………………………………...………………..12
11. Figure 2.10 Defuzzify the Aggregated Output ………………………………………. ...13
12. Figure 3.1 The ANFIS Editor GUI Window …………………………………...……….15
13. Figure 3.2 Loading the Training Data Set …………………………………………..…..16
14. Figure 3.3 Loading the Checking Data Set ………………...……………………………17
15. Figure 3.4 The Model FIS Structure ………………………...…………………………..19
16. Figure 3.5 The Checking Error and Training Plot …………...………………………….20
17. Figure 3.6 Testing the Training Data against the FIS Output …………...………………21
18. Figure 3.7 The FIS Editor ………………………………………………..……………...22
19. Figure 3.8 Visibility Membership Functions ………………………………. ….……….23
20. Figure 3.9 Pilot Experience Membership Functions …………………………………….24
21. Figure 3.10 Air Speed Membership Function …………………………………………...25
x
22. Figure 3.11 The Proposed FIS Rule Viewer ………………………………...…………..26
23. Figure 3.12 The Proposed Rule Viewer ……………………………………...………….28
24. Figure 3.13 Visibility VS Pilot Experience ………….……………………….…………29
25. Figure 3.14 Air Speed VS Pilot Experience ………………………………………...…..30
26. Figure 3.15 Air Speed VS Visibility ………………………………………………..…..31
27. Figure 3.16 Out Put Response Comparison of Simulation and FIS Result ……………..34
xi
1
Chapter 1
INTRODUCTION
The purpose of this thesis is to design a fuzzy logic engine to evaluate the success rate
of landing of the airplane on approach to land (final leg) under different visibility and
airspeed.
To train the fuzzy logic system, data were collected by simulation of 100 flight cases
under different visibilities, pilot experience and air speed. Two pilots have done the flight
simulations, One with 500 hours flight experience and another one with 2000 hours flight
experience. In addition to 100 flight simulations applied for training the fuzzy engine, 16
flight simulation data were applied for checking and testing the system and 16 flight
cases were evaluated by the created fuzzy logic engine.
Chapter 2 discusses the description of the proposed fuzzy inference system. There are
some inputs, like visibility and pilot experience and air speed and the output is the
success rate of landing. This chapter shows how the components of the proposed fuzzy
engine work. Based on the nature of fuzzy human thinking, Lofti Zadeh originated the
“fuzzy logic” or “fuzzy set theory”, in 1965 [4]. Fuzzy logic deals with the problems that
have fuzziness or vagueness. In fuzzy set theory based on fuzzy logic a particular object
has a degree of membership in a given set that may be anywhere in the range of 0
(completely not in the set) to 1 (completely in the set) .For this reason fuzzy logic is often
defined as multi-valued logic (0 to 1).
2
Chapter 3 discusses how to train the fuzzy inference system and test the fuzzy
inference system under MATLAB fuzzy logic toolbox and fuzzy logic application. This
toolbox relies heavily on graphical user interface (GUI) tools to help accomplish the
work. After the fuzzy inference system has been fully trained. We start creating the
engine to evaluate the success rate of landing under set conditions.
The objective of this thesis is to build a fuzzy logic engine using to calculate the
success rate of landing under different inputs (visibility, pilot experience and air speed).
The thesis will conclude with the simulation results and evaluation of the proposed fuzzy
inference system.
Figure 1.1 shows a simulated flight done with Microsoft flight simulator under high
visibility,pilt experience with 500 hours and 100knots air speed on final approach.The
visibility range is from 0 to 15 Statute Miles and the air speed range is between 40 knots
to 100 knots.Pilot experience is based on flight hours (A pilot with 500 hours and another
pilot with 2000 hours ).
3
Figure 1.1 Flight Simulation with MS Flight Simulator
When pilot is on the approach and landing phase of flight, there are many factors can
affect the landing. This is the single most demanding phase of flight, and the one that
carries the highest risk. One of the elements in a successful landing is the pilot
experience. It is also necessary to keep up with any changes in the runway status or
destination weather as the flight progresses therefore visibility is a very important
element in a spectacular landing. Another element in making a spectacular landing is to
fly a stabilized approach with the manufacturer’s recommended airspeed on final. In this
4
thesis 3 elements considered (visibility, pilot experience and airspeed) as the inputs for
calculating the success rate of landing. There are some other important parameters which
could significantly influence for successful landing. One of the important parameter is
wind speed and wind direction. In all the flight simulations, wind considered to be calm.
Virtually every pilot has experienced some form of illusion during the approach and
landing phases of a flight. There are a variety of illusions that can create problems during
the approach and landing. Human factors are other parameters affecting the landing. Due
to the vagueness of the flight environment there is no flight parameter limitation. There
are many other factors that can be considered for successful landing. In this thesis
visibility, pilot experience and air speed are the only inputs considered for calculating the
success rate of landing.
Good landings are the result of good approaches with flying at a constant target
airspeed, and constant target descent rate. The touchdown point should be within the first
third of the runway's length. At touchdown and thereafter, the airplane should be
sufficiently well centered that the centerline is between the main wheels. The touchdown
should be gentle enough that the nose wheel stays in the air during touchdown and during
the first 50 feet of the rollout. Other than that it will be considered to be bad or failed
landing.
5
Chapter 2
DESCRIPTION OF THE PROPOSED FUZZY LOGIC
2.1 Introduction
In this research with information about what the visibility, pilot experience and air
speed were on the instrument precision approach and landing, the proposed fuzzy logic
system can evaluate the success rate of landing.
Figure 2.1 shows a graphical map of the input-output. This figure shows the success
rate of landing as the output and visibility as one of the inputs. The black box between the
input and the output is the proposed fuzzy engine which calculates the success rate of
landing.
Figure 2.1 A Graphical Example of an Input-Output Map
6
Figure 2.2 provides a roadmap for the fuzzy inference process. It shows the general
description of a fuzzy system on the left and the proposed fuzzy system on the right.
Based on the set of rules and interpreted inputs (visibility is interpreted as low, medium
and high), the proposed fuzzy engine assigns values to the output (success rate of
landing).
Figure 2.2 Roadmap for the Fuzzy Inference Process
7
Figure 2.3 shows the sharp edged MF for visibility that the degree of membership is
either 0 or 1 and the continuous MF for visibility with the degree of membership range
from 0 to 1.
Figure 2.3 Visibility Membership Function Curve
8
Figure 2.4 shows antecedent and consequent with crisp visibility inputs, pilot
experience and air speed. This figure shows application of AND operator and implication
operator.
Figure 2.4 The Proposed Fuzzy Inference System
9
2.2 The Proposed Fuzzy Inference System
2.2.1 Overview of Fuzzy Inference Process
Fuzzy inference process comprises of five parts: fuzzification of the input variables,
application of the fuzzy operator (AND or OR) in the antecedent, implication from the
antecedent to the consequent, aggregation of the consequents across the rules, and
defuzzification. Figure 2.5 shows the basic structure of the proposed fuzzy logic system.
Figure 2.5 The Basic Structure of the Fuzzy Inference System
10
2.2.2 Step 1. Fuzzify Inputs
Figure 2.6 shows the process of fuzzifying the visibility. The visibility input is a crisp
numerical value from 0 to 15 statue miles and the output of fuzzyfying visibility is a
fuzzy degree of MF between 0 and 1.
Figure 2.6 Visibility Input
2.2.3 Step 2. Apply Fuzzy Operator
Figure 2.7 shows the AND operator. The three different pieces of the antecedent
(visibility is good and pilot experience is high and air speed is normal) yielded the fuzzy
membership values 0.8, 0.9 and 0.8 respectively. The fuzzy AND operator simply selects
the minimum of the three values, 0.8.
11
Figure 2.7 Apply Fuzzy Operator AND
2.2.4 Step 3. Apply Implication Method
Figure 2.8 shows the implication process after proper weighting of the rules.
Figure 2.8 Apply Implication Method
12
2.2.5 Step 4. Aggregate All Outputs
Figure 2.9 shows aggregation process by which the fuzzy sets that represent the
outputs of each rule are combined into a single fuzzy set. Aggregation only occurs once
for each output variable, just prior to the defuzzification.
Figure 2.9 Aggregate All Outputs
13
2.2.6 Step 5. Defuzzify
Figure 2.10 shows the defuzzification process by which the output (success rate of
landing) is a single number.
Figure 2.10 Defuzzify the Aggregated Output
14
Chapter 3
THE FIS MODELING AND SIMULATIONS
3.1 Introduction
This chapter will discuss modeling and simulation of the proposed fuzzy inference
system.
This section will discuss the use of the function ANFIS and the ANFIS Editor GUI in the
toolbox. These tools apply fuzzy inference techniques to data modeling. The shape of the
membership functions depends on parameters, and changing these parameters change the
shape of the membership function. Fuzzy Logic Toolbox applications were used to get
the shape of the membership functions [3].
3.2 Modeling
To apply the proposed fuzzy inference to a system for which all the flight
simulations have been done rather than choosing the parameters associated with a given
membership function arbitrarily, Fuzzy Logic Toolbox neuro-adaptive learning
techniques incorporated in the ANFIS command has been used.
Figure 3.1 shows the ANFIS Editor window where training data and check data will be
loaded. It can be seen that ANFIS Editor window consists of 4 major sections (Load data,
Generate FIS, Train FIS and Test FIS).
15
Figure 3.1 The ANFIS Editor GUI Window
16
3.3 Loading Data
The training data set collected from the flight simulations is used to train the proposed
fuzzy system. Figure 3.2 shows the loaded training data and checking data. The training
and checking data are annotated in blue as circles, and pluses respectively.
Figure 3.2 Loading the Training Data Set
17
Figure 3.3 shows the loaded checking data. Checking data appears in the GUI plot as
pluses superimposed on the training data. This data set will be used to train the proposed
fuzzy system.
Figure 3.3 Loading the Checking Data Set
18
Grid partition method is being used to initialize the FIS. The following Number of
membership functions will be considered in this case; [4 2 4],[3 2 3] and [2 2 2]. All these
cased will be evaluated for better performance of the FIS. Membership type will be trimf
and the output membership type is constant. Figure 3.4 shows the model structure after
the FIS was generated. This figure shows that there are 3 inputs (visibility, pilot
experience and air speed), first input (visibility) with 4 membership functions, second
input (pilot experience) with 2 membership functions and the last input (Air speed) with 4
membership functions.
19
Inputs
Membership Functions
Rules
Figure 3.4 The Model FIS Structure
Output
20
Checking Error
Training Error
Figure 3.5 The Checking Error and Training Error Plot
3.4 ANFIS Training
The two ANFIS parameter optimization method options available for FIS training are
hybrid and back propagation. To train the FIS, the back propagation method was used.
Figure 3.6 shows the results of the training data against the FIS output. The training data
are annotated in blue as circles, and the FIS output are annotated in red.
21
Training Data
FIS Output
Figure 3.6 Testing the Training Data against the FIS Output
22
3.5 The FIS Editor
Figure 3.7 shows the information about a fuzzy inference system with the names of
each input variable on the left and the output variable on the right. In the proposed FIS,
Sugeno type inference used, with 3 inputs and 1 output. The three inputs are visibility,
pilot experience and air speed. The one output is success rate of landing.
Figure 3.7 The FIS Editor
23
3.6 The Membership Function Editor
Figure 3.8 shows the visibility membership functions for the proposed fuzzy
inference system. The visibility membership functions are interpreted as very low, low,
medium and high.
Figure 3.8 Visibility Membership Functions
24
Figure 3.9 shows the pilot experience membership functions for the proposed fuzzy
inference system. The pilot experience membership functions are interpreted as low, and
high.
Figure 3.9 Pilot Experience Membership Functions
25
Figure 3.10 shows the air speed membership functions for the proposed fuzzy inference
system. The air speed membership functions are interpreted as low, average, high and
very high.
Figure 3.10 Air Speed Membership Functions
26
3.7 The Rule Editor
Figure 3.11 shows the generated rules for the proposed fuzzy logic engine. At this
point, the fuzzy inference system has been completely defined, in that the variables,
membership functions, and the rules necessary to calculate success rate of landing.
Figure 3.11 The Proposed FIS Rule Editor
27
3.8 The Rule Viewer
Figure 3.12 shows the Rule Viewer of the proposed fuzzy logic system. Each rule is a
row of plots, and first column is the visibility, second column is the pilot experience and
the third column is the air speed. The fourth column of plots shows the membership
functions referenced by the consequent, or the then-part of each rule. This decision will
depend on the input values for the system. The defuzzified output is displayed as a bold
vertical line on this plot. The variables and their current values are displayed on top of the
columns. Each of the characterizations of each of the variables is specified with respect to
the input index line in this manner. The defuzzified output value is shown by the thick
line passing through the aggregate fuzzy set.
28
Figure 3.12 The Proposed Rule Viewer
29
3.9 The Surface Viewer
Figure 3.13 shows the surface view of the proposed FIS for visibility and pilot
experience. This curve represents the mapping from visibility and pilot experience to
success rate of landing. This figure represents the success rate of landing based on the
visibility and pilot experience. It shows the success rate of landing remains slightly
steady high after the visibility is high enough.
Figure 3.13 Visibility VS Pilot Experience
30
Figure 3.14 shows the surface view of the proposed FIS for air speed and pilot
experience. This curve represents the mapping from air speed and pilot experience to
success rate of landing. This symmetrical surface shows that success rate of landing is
more sensitive to the air speed.
Figure 3.14 Air Speed VS Pilot Experience
31
Figure 3.15 shows the surface view of the proposed FIS for air speed and visibility.
This curve represents the mapping from air speed and visibility to success rate of landing.
This symmetrical surface also shows that the success rate of landing is more sensitive to
the air speed.
Figure 3.15 Air Speed VS Visibility
32
3.10 The FIS Evaluation
In order to validate the proposed approach for the fuzzy inside instrument approach
and landing several cased had been conducted based on simulated experimental data.
Three inputs (visibility, pilot experience and airspeed) were used to provide the
measurable inputs to the fuzzy system through the simulations. To evaluate the output of
the proposed fuzzy logic system for a given input, 16 cases were evaluated. The
following table shows the results from fuzzy logic system were compared with the
simulated results. The presented simulation results have confirmed the ability of the
proposed fuzzy logic system to calculate the success rate of landing. By comparing the
FIS results and the simulated results, it can be noticed that the proposed fuzzy engine is
able to accurately calculate the success rate of landing under different cases.
33
Table 1 The FIS and Simulation Results
CASE # VISIBILITY
PILOT
AIRSPEED
EXPEREINCE
FIS
SIMULATED
RESULTS
RESULTS
1
0
500
100
0.0035
0
2
1
500
90
0.0099
0
3
2
500
80
0.0121
0
4
3
500
77
0.0170
0
5
4
500
65
0.9588
1
6
5
500
62
0.9523
1
7
6
500
59
0.9347
1
8
7
500
48
0.0044
0
9
8
2000
66
0.9995
1
10
9
2000
59
09654
1
11
10
2000
56
0.9540
1
12
11
2000
53
0.8995
1
13
12
2000
49
0.0215
0
14
13
2000
46
0.0133
0
15
14
2000
43
0.0098
0
16
15
2000
40
0.0059
0
34
Output response comparison
1.2
Success rate of landing
1
0.8
0.6
FIS results
0.4
Simulated results
0.2
0
0
5
10
15
20
-0.2
Flight case
Figure 3.16 Output Response Comparison of Simulated and FIS Results
35
Chapter 4
CONCLUSION AND FURTHER STUDY
The current research has been carried out for developing a fuzzy logic engine to
estimate the success rate of landing under the set conditions.
By using a fuzzy inference system in the framework of an adaptive neuro-fuzzy
inference System (ANFIS), it provides a tool which makes the success rate of landing
more accurate because by ANFIS fuzzy logic, it would be possible to estimate the fuzzy
inference system parameters. This method could be applied extensively to solve the
engineering problems in which most of them are in some specify fuzzy conditions. The
performance of the model with respect to the estimation made by evaluation and test data
has been satisfactory.
It was also illustrated that the fuzzy logic engine is able to calculate the success rate
of landing under the assigned inputs. It is also concluded the ANFIS technique could be
used as a very accurate, reliable and fast method for calculation of the success rate of
landing.
The methodology presented in this thesis explored and combined two concepts:
Fuzzy Logic and airplane instrument approach and landing where the uncertainty is very
frequent. The proposed fuzzy engine can successfully calculate the success rate of
landing based on different visibility, pilot experience and air speed. This work can be
further developed in the following areas:
36
By doing more flight simulations for better and more accurate results and apply
human factors as an input to the fuzzy logic system which human factors are a broad field
that examines the interaction between people, machines, and the environment for the
purpose of improving performance and reducing errors. As aircraft became more reliable
and less prone to mechanical failure, the percentage of accidents related to human factors
increased. Some aspect of human factors now accounts for over 80 percent of all
accidents. Pilots who have a good understanding of human factors are better equipped to
plan and execute a safe and uneventful flight [1].
By changing weather conditions as another input. The safety of the flight depends
upon the pilot’s ability to manage this variable. In addition to the weather conditions that
might affect a VFR flight, an IFR, it is being recommended to consider the effects of
other weather phenomena such as thunderstorms, turbulence, icing, fog and wind shear
[1].
37
APPENDIX A
The Matlab Structure Syntax
[System]
Name='THE PROPOSED FIS'
Type='sugeno'
Version=2.0
NumInputs=3
NumOutputs=1
NumRules=32
AndMethod='prod'
OrMethod='probor'
ImpMethod='prod'
AggMethod='max'
DefuzzMethod='wtaver'
[Input1]
Name='VISIBILITY'
Range=[0 15]
NumMFs=4
MF1='VERY_LOW':'trimf',[-5 -0.0866953195682162 4.99977536353742]
MF2='LOW':'trimf',[-0.00247475523808451 4.89582230292664 9.9510965722722]
MF3='MEDIUM':'trimf',[5.01857521769034 9.90447138015018 14.8681033531786]
MF4='HIGH':'trimf',[9.99951155119642 14.9198722966028 20]
[Input2]
Name='PILOT_EXPERIENCE'
Range=[500 2000]
38
NumMFs=2
MF1='in2mf1':'trimf',[-1000 500 1999.99999999277]
MF2='in2mf2':'trimf',[500.000000001233 2000 3500]
[Input3]
Name='AIR_SPEED'
Range=[40 100]
NumMFs=4
MF1='in3mf1':'trimf',[20 40.0822855887941 59.8978408262497]
MF2='in3mf2':'trimf',[40.2203650852729 60.1983524621982 79.998830690857]
MF3='in3mf3':'trimf',[60.1510956994258 80.0917240621206 99.9752927916075]
MF4='in3mf4':'trimf',[79.9472637715754 99.9756462725235 120]
[Output1]
Name='SUCCESS_RATE_OF_LANDING'
Range=[0 1]
NumMFs=32
MF1='out1mf1':'constant',[0.0082081939390241]
MF2='out1mf2':'constant',[0.569701574525364]
MF3='out1mf3':'constant',[0.0400047904307698]
MF4='out1mf4':'constant',[0.0165440923348753]
MF5='out1mf5':'constant',[-0.264906080378969]
MF6='out1mf6':'constant',[0.512033081547978]
MF7='out1mf7':'constant',[-0.244285271708471]
MF8='out1mf8':'constant',[0.0793180922669434]
MF9='out1mf9':'constant',[-0.438131938839094]
MF10='out1mf10':'constant',[1.18104476635337]
MF11='out1mf11':'constant',[0.167113520979754]
39
MF12='out1mf12':'constant',[-0.0803868979781637]
MF13='out1mf13':'constant',[-0.0478079763911111]
MF14='out1mf14':'constant',[1.38817384556867]
MF15='out1mf15':'constant',[0.160606314987157]
MF16='out1mf16':'constant',[-0.035215328374081]
MF17='out1mf17':'constant',[-0.0392689626147112]
MF18='out1mf18':'constant',[1.32098913325736]
MF19='out1mf19':'constant',[-0.126975761506084]
MF20='out1mf20':'constant',[0.107398937311983]
MF21='out1mf21':'constant',[-0.351857337467939]
MF22='out1mf22':'constant',[1.27922619878734]
MF23='out1mf23':'constant',[0.167575483585494]
MF24='out1mf24':'constant',[-0.235623827741807]
MF25='out1mf25':'constant',[-0.141197825918983]
MF26='out1mf26':'constant',[0.604231529198334]
MF27='out1mf27':'constant',[0.558989552061019]
MF28='out1mf28':'constant',[1.23753418149047]
MF29='out1mf29':'constant',[-0.155055741776899]
MF30='out1mf30':'constant',[1.0919144580996]
MF31='out1mf31':'constant',[0.323444348254456]
MF32='out1mf32':'constant',[-0.042384497776231]
[Rules]
1 1 1, 1 (1) : 1
1 1 2, 2 (1) : 1
1 1 3, 3 (1) : 1
1 1 4, 4 (1) : 1
1 2 1, 5 (1) : 1
40
1 2 2, 6 (1) : 1
1 2 3, 7 (1) : 1
1 2 4, 8 (1) : 1
2 1 1, 9 (1) : 1
2 1 2, 10 (1) : 1
2 1 3, 11 (1) : 1
2 1 4, 12 (1) : 1
2 2 1, 13 (1) : 1
2 2 2, 14 (1) : 1
2 2 3, 15 (1) : 1
2 2 4, 16 (1) : 1
3 1 1, 17 (1) : 1
3 1 2, 18 (1) : 1
3 1 3, 19 (1) : 1
3 1 4, 20 (1) : 1
3 2 1, 21 (1) : 1
3 2 2, 22 (1) : 1
3 2 3, 23 (1) : 1
3 2 4, 24 (1) : 1
4 1 1, 25 (1) : 1
4 1 2, 26 (1) : 1
4 1 3, 27 (1) : 1
4 1 4, 28 (1) : 1
4 2 1, 29 (1) : 1
4 2 2, 30 (1) : 1
4 2 3, 31 (1) : 1
4 2 4, 32 (1) : 1
41
APPENDIX B
Membership Function Plots and Surface Plot
42
43
44
45
APPENDIX C
Flight Simulation Results
Visibility
Pilot Experience
Airspeed
Result
15
2000
100
0
14
2000
95
0
13
2000
90
0
12
2000
85
0
11
2000
80
0
10
2000
75
1
9
2000
70
1
8
2000
65
1
7
2000
60
1
6
2000
55
1
5
2000
50
0
4
2000
45
0
3
2000
40
0
2
2000
100
0
1
2000
95
0
0
2000
90
0
15
500
100
0
14
500
95
0
13
500
90
0
12
500
85
0
11
500
80
0
10
500
75
0
9
500
70
1
8
500
65
1
46
7
500
60
1
6
500
55
1
5
500
50
0
4
500
45
0
3
500
40
0
2
500
100
0
1
500
95
0
0
500
90
0
15
2000
40
0
14
2000
45
0
13
2000
50
0
12
2000
55
1
11
2000
60
1
10
2000
65
1
9
2000
70
1
8
2000
75
1
7
2000
80
0
6
2000
85
0
5
2000
90
0
4
2000
95
0
3
2000
100
0
2
2000
40
0
1
2000
45
0
0
2000
50
0
15
500
40
0
14
500
45
0
13
500
50
0
12
500
55
1
47
11
500
60
1
10
500
65
1
9
500
70
1
8
500
75
0
7
500
80
0
6
500
85
0
5
500
90
0
4
500
95
0
3
500
100
0
2
500
40
0
1
500
45
0
0
500
50
0
15
2000
55
1
14
2000
60
1
13
2000
65
1
12
2000
70
1
11
2000
75
1
10
2000
80
0
9
2000
85
0
8
2000
90
0
7
2000
95
0
6
2000
100
0
5
2000
40
0
4
2000
45
0
3
2000
50
0
2
2000
55
1
1
2000
60
1
0
2000
65
0
48
15
500
70
1
14
500
75
0
13
500
80
0
12
500
85
0
11
500
90
0
10
500
95
0
9
500
100
0
8
500
40
0
7
500
45
0
6
500
50
0
5
500
55
1
4
500
60
1
3
500
65
1
2
500
70
1
1
500
75
0
0
500
80
0
49
REFERENCES
[1] Federal Aviation Administration Flight Standards Service “Instrument Flying
Handbook 2008” FAA-H-8081-15A, Instrument Flying Handbook, dated 2007
[2] Federal Aviation Administration Flight Procedure Standards Branch” Instrument
Procedures Handbook 2007” FAA-H-8261-1A
[3] The MathWorks, Inc “Fuzzy Logic Toolbox™ User’s Guide R2011b” September
2011 Version 2.2.14 (Release 2011b)
[4] Zadeh, L.A., “Fuzzy sets,” Information and Control, Vol. 8, pp. 338-353, 1965.