Improved fault diagnostics of a dynamic aircraft fuel system using the

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Risk, Reliability and Societal Safety – Aven & Vinnem (eds)
© 2007 Taylor & Francis Group, London, ISBN 978-0-415-44786-7
Improved fault diagnostics of a dynamic aircraft fuel system using the
digraph approach
E.M. Kelly & L.M. Bartlett
Loughborough University, Loughborough, Leicestershire, UK
ABSTRACT: Fault diagnosis has developed into an integral part of engineering applications. Within the increasing safety conscious climate of today’s world, prompt detection, diagnosis and rectification of faults is imperative
to the operation of a system. In the case of commercial aircraft, efficient diagnosis can minimise both the financial cost of downtime and the disruption caused to passenger travel. The diagnostic method described in this
paper is based on the application of the digraph procedure. Digraphs model the information flow, and hence
fault propagation, through a system. A computational method has been successfully developed to conduct the
fault diagnostics process and produce a list of the determined fault combinations. Guidelines are provided for
a mechanism to further identify the most likely cause(s) of a given deviation. This paper looks in detail at the
application of the diagnostic method to a commercial aircraft fuel system with integrated control.
1
INTRODUCTION
The occurrence of failures within a system can cause
disruption to the operational stability. Fault diagnosis has therefore become a primary objective in
engineering applications. It is concerned with the
isolation of underlying causal faults that can lead
to an observable effect in a monitored process.
Effective detection of system faults decreases downtime and consequently enhances operational stability
(Papadopoulos & McDermid 2001).
Traditional approaches employed to identify faults
involved using testing algorithms to detect single failures (Novak et al. 2000, Pattipati & Alexandridis
1990). In using this approach, prospective faults are
highlighted through the running of a series of tests
at a particular point in time. The tests are comprised
from symptoms that are related to specific system
faults. The effectiveness of the method has been proven
when determining single faults in a system with a
known period of inactivity. Difficulties are noted when
considering the complexities of multiple fault combinations. In an effort to address the diagnosis of multiple
faults, extensions to the sequential testing technique
have been developed and implemented (Shakeri et al.
2000).
Some recent approaches have used reliability
assessment tools such as Failure Modes and Effects
Analysis (FMEA) (Price 1997, Price & Taylor 1997)
and fault tree analysis (Hurdle et al. 2005). Attempts
have been made to automate the FMEA process
and increase its effectiveness through decreasing
the time required for analysis. A different method
(Papadopoulos et al. 2004) proposes translating the
information contained in a network of interconnected
fault trees into FMEA style tables. Variability in the
performance of these methods is noted with increased
system complexity.
Digraphs, also known as signed directed graphs
(Vedam & Venkatasubramanian 1997, Palmer &
Chung 2000), illustrate specific fault propagations
through a system. They are a type of causal model,
clearly representing the cause and effect behaviour
within a system. Causal models can be employed
in fault diagnosis to reason about the behaviour
of processes under normal and abnormal conditions
(Maurya et al. 2003).
The characteristics associated with modern day
systems require fault diagnosis to incorporate both
adaptability and identification of multiple faults
(Venkatasubramanian et al. 2003). Modern systems
are normally required to operate in more than one
mode. An ideal diagnostic procedure would therefore
incorporate an adaptable scope.
This paper applies a fault diagnostics strategy based
on using digraphs to the fuel system of a Boeing 777-200 aircraft. A brief insight into digraphs
through considering their representation of fault propagations in a system is considered. The results yielded
through automating the fault diagnostics process
are reviewed along with suggestions for ‘honing-in’
on the most probable fault cause from the complete list of fault causes produced for a specific
situation.
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2 THE DIGRAPH METHOD
2.1
Description
A digraph (Kohda & Henley 1988) is constructed from
a set of nodes and edges. The nodes represent system
process variables and the edges connecting the nodes
illustrate the interrelationships that exist between components in a system. Nodes are also used to represent
component failure modes; whereby a signed edge connecting a failure mode node to a process variable
node indicates the resulting disturbance caused by the
failure mode.
Digraph nodes contain an alphanumeric label which
symbolises a specific process variable or component
failure mode. With regards to process variable nodes,
the numeric section of the label corresponds to a
precise location in the application system. The precursor to the numeric section indicates the type of
process variable the node represents. Examples of
process variables include temperature, mass flow, pressure and signals from sensors. Following the same
order, these would be represented in nodes by the
precursors T, M, P and S. Process variable deviations
(Andrews & Morgan 1986, Andrews & Brennan 1990)
are expressed as one of five discrete values: +10, +1,
0, −1 and −10 corresponding to large high, small high,
normal, small low and large low deviations.
A simple digraph is illustrated in Figure 1. In the
simple digraph illustration it can be noted that P1
and P2, the nodes, are connected by three edges. The
alphanumeric code P1 represents pressure at location
one. The edge with a gain of +1 is considered to be the
normal edge since this represents the relationship that
is normally true; pressure at location one has a positive
effect on pressure at location two. The second and third
edges in the illustration are termed conditional edges
since their relationship is only true whenever the condition represented by ‘:’ exists. It must be noted that
only one edge is true at any one time.
An unexpected process deviation within a system
is represented by ‘highlighting’ the respective node
in the digraph. Subsequent propagation of the deviation through the system is conducted by marking all of
the nodes which were affected by the initial highlighting. This process, termed ‘back-tracing’, is described
further in Section 5.3.
2.2
Figure 1. A simple digraph
relevant component failures of the system are compiled. A failure mode code is then attached to each
fault. The system is also separated into sub-units
and components.
2 Digraph Generation: The unit digraph models for
the sub-units, previously noted in step one, are generated. All process variable deviations which could
have an effect on the variables in the model are taken
into consideration. The extent of the effect any disturbance may have on the system with regards to
the assigning of discrete values is also noted. The
system digraph is formed by connecting common
variables from the sub-unit models.
The fault diagnostics process is conducted using the
system digraph. System behaviour can be monitored
using data retrieved from sensors. In a given mode of
operation the system would have a set of expected sensor readings. These are compared with the actual system readings during the diagnostics procedure (Steps
3 to 5) to identify the presence of any deviations.
3 Determination of System Deviations: The expected
system sensor readings are noted. The actual sensor readings from the system are retrieved and then
compared with those expected to determine the
existence of any deviations.
4 Flagging of Non-Deviations: Non-deviating sensor
nodes in the digraph are ‘flagged’. It is assumed
that a non-deviating reading indicates the absence
of a failure.
5 Back-tracing Process: If a sensor registers a deviation then fault diagnosis involves back-tracing
through the system digraph from the node which
represents the location of the given deviation. The
back-tracing process ceases once either (i) a flagged
section is reached or (ii) no more back-tracing is
possible. For multiple deviating sensors the diagnostic results obtained through back-tracing from
each deviating node are ANDed together. All potential fault causes are listed at the end of the fault
diagnostics procedure.
Procedure
A generalized procedure outlining the main steps
involved in developing a system digraph is provided:
3
1 System Analysis: Firstly the system under investigation is defined. A specific number is allocated
to each component so generating a straightforward
location reference approach for process variables
and component failure modes at a given point. All
The Boeing 777-200 is a twinjet aircraft that entered
into revenue service in the middle of 1995. Fuel is
stored in three tanks; the left main, centre and right
BOEING 777-200 FUEL SYSTEM
3.1 System architecture
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– Phases Three & Four: Fuel can be transferred from
one wing to the other by opening one of the crossfeed valves and shutting off the pumps on the side
to which fuel is being transferred.
– Phase Five: For cases whereby the fuel pumps are
switched off and the cross-feed valves are closed,
engine feed can occur through suction via the
suction bypass valves in the main tanks.
3.3 Monitoring system behaviour
Figure 2. Boeing 777-200 fuel system (left side).
main. A surge tank is situated outboard of each main
tank; the function of which is to temporarily hold fuel
that flows due to aircraft turns, thermal expansion or
overfilling. The 777-200 fuel system can hold a total
of 117,400 litres; 35,200 in each main tank and 47,000
in the centre tank.
Figure 2 provides an illustration of the left side of
the Boeing 777-200 fuel system.The right side exhibits
a similar structure. The engine feed operating mode is
the only phase considered in this analysis. The components of interest in the engine feed mode are briefly
described in Section 3.2.
3.2
Engine feed operating mode
The main purpose of the engine feed operating mode
is to supply fuel to the engines from the main and
centre tanks. Six powered fuel pumps supply fuel to the
engines. These pumps have individual control switches
and are controlled manually by the pilot. The centre
tank has two override/jettison pumps that operate at
higher pressures than the main tank pumps. Each main
tank comprises a forward boost and aft boost pump.
Fuel scavenge pumps transfer fuel from the bottom of
the centre tanks to the main tanks once fuel levels in
both of the tanks are low enough. Float operated shut
off valves ensure that the transfer process does not start
whilst the tank levels are considered to be ‘too high’.
Two manually controlled cross-feed valves connect the
left and right sides of the fuel system and so allow
the transfer of fuel from one side to the other. Spar
valves permit the transfer of fuel from the engine feed
manifold to the engines. The spar valves are controlled
by the pilot via the fuel control switch in the cockpit.
The engine feed operating mode is subdivided into
five operational phases. The five phases represent the
manner in which engine feed can be conducted:
– Phase One: Fuel is pumped from the centre tank into
the engine feed manifold by the jettison/override
pumps.
– Phase Two: Once the centre tank is nearly empty,
fuel is pumped from the main tanks into the engine
feed manifold by the main tank boost pumps.
A mixture of sensors and switches are utilised in the
fuel system to provide system information regarding
flow, pressure and tank levels. Data related to component control switches and their respective component
positions is also obtained and compared to highlight
any inconsistencies, if present.
Flow meters are located at the inlet to both engines.
There is therefore a left and right flow meter. The flow
readings are classified into three groups; flow, no flow
and partial flow. Low pressure at the fuel pump outlets is noted by a light on the fuel panel. There is a
low pressure light for the left and right aft boost, forward boost and jettison/override pumps. The lights are
linked to an associated low pressure switch located on
the pumps.
The fuel pumps and valves are controlled via their
respective switches by the pilot. Should an actual valve
position and the position indicated by its respective
switch disagree, a warning is issued to the pilot. The
engine indicating and crew alert system notes the total
fuel quantity. The fuel synoptic display indicates the
individual tank quantities obtained from the tank units.
Tank units are constructed from an ultrasonic transmitter/receiver and still-well. The information retrieved
from the units is utilised to determine the tank height.
For initial research the tank heights are scaled from
0–10 since the exact output is unknown and therefore
an arbitrary scaling system is used. (Note: 0 = empty,
10 full)
3.4 Component failure modes
A total of 59 types of component failure modes are
considered in the analysis. It is assumed that the stated
failure modes may affect the functionality of the aircraft fuel system. Each component failure mode is
allocated a code associated to a related component
identification tag.
Seven failure modes are linked to faults in the crossfeed section whilst the remaining fifty-two can be
found in the left and right sides of the fuel system.
The majority (40) of the failures are associated with
valves and fuel pumps. Pumps are considered to fail
in either ‘run’ or ‘no run’ scenarios. There are three
related valve failure modes; open, closed or stuck in
an intermediate position.
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Figure 3. Left main tank section.
Each tank (centre and main) possesses a single failure mode; tank fractured. There are three possible
manifold and pipe component failures. These relate
to fractures and complete or partial blockages.
4
FUEL SYSTEM DIGRAPH DEVELOPMENT
With the system defined and component failure modes
identified, the next step involves generating the system
digraph (step 2 from Section 2.2). The fuel system is
split into three main sections:
– Cross-feed.
– Left centre tank and left main tank.
– Right centre tank and right main tank.
In total, the system digraph for the engine feed
phase is constructed from 282 nodes; of which 88
are process variable nodes and 194 are component
failure mode nodes. The unit digraphs for the centre
and main tanks (left and right wings) are developed
through a process of building up from the tank levels
nodes to the fuel pumps, engine feed manifold and spar
valves at the inlet to the engines. The cross-feed section
digraph encompasses the pipe-work and related valves
that connect the left and right engine feed manifolds.
As a means of illustrating the development of the
fuel system digraph, Figure 3 depicts a section of
the pipe-work incorporating a spar valve and suction
bypass valve in the left wing. Fuel enters the left engine
via the spar valve from the engine feed manifold. The
numbered locations noted in Figure 3 (40, 48, 49 &
50) form a reference approach, utilised when generating the fuel system digraph for the engine feed
operating mode.
A section of the respective left main tank digraph is
presented in Figure 4. Mass flow along the left engine
feed manifold is represented by the process flow structure exhibited by nodes M48 → M50. The direction
of flow in the manifold, and hence the direction of the
edges connecting the mass flow nodes, is towards the
spar valve which allows fuel to pass to the left engine.
There are three identical failure modes associated with
the mass flow nodes that represent the left engine feed
manifold. Two failure modes, left engine feed manifold fractured and partially blocked (LMF, LMPB),
Figure 4. Left main tank digraph section.
result in a small negative disturbance and the mode,
left engine feed manifold blocked (LMB), results in
a large negative disturbance. These disturbances are
indicated by signing the edges, connecting the failure
mode nodes to the process variable nodes, ‘−1’ and
‘−10’.
The left spar valve is denoted by the relationship
between nodes M49 and M50. If the spar valve is
closed then this normally positive relationship is nullified, as indicated by the conditional edge signing
‘0: SPVL Closed’. There are three spar valve failure modes which may result in a disturbance on mass
flow entering the left engine: spar valve open (SVLO),
spar valve closed (SVLC) and spar valve intermediate
position (SVLI). The failure modes would generate a
large positive, large negative and small negative disturbance respectively. These deviations are indicated
by the signs, ‘+10’, ‘−10’ and ‘−1’ on the edges
connecting the failure mode nodes to M50.
The branch encompassing the suction bypass valve
(LMTL → M49) extends from the main tank level
node (LMTL). The relationship between the level node
LMTL and the mass flow node M40 represents the
suction bypass valve. The tank level normally has no
effect on mass flow at location 40. Should the circumstances change, as defined by the conditional edge
connecting LMTL and M40, then mass flow would be
drawn from the main tank into the engine feed manifold. For mass flow to pass through to the manifold
it is required that the left fuel pumps do not run and
for the cross-feed section not to be engaged. There are
three pipe failure modes associated with node M40;
pipe blocked (P40B), partially blocked (P40PB) and
fractured (P40F). A further failure mode considered
is suction bypass valve failed closed (BVLC), thus
causing a large negative disturbance.
The signal flow structure exhibited by nodes
SFCSW → M50 illustrates the control relationships
that are assumed from the possible pilot inputs for
the spar valve. The pilot input is represented using
the fuel control switch node, SFCSW. The fuel control
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switch controls the mass flow entering the engine via
the left spar valve. If the pilot sets the switch in the
‘run’ position then the denoted relationship is positive. Conversely, if the switch is set in the ‘cut-off’
position then a negative relationship is exhibited.
5
SYSTEM FAULT DIAGNOSTICS
The method for performing system diagnostics using
digraphs is based on comparing system sensor readings with those which would be expected whilst the
system is in a known operating mode. The first step
therefore involves determining if any system variable deviations exist. The presence of a deviation
is considered indicative of a fault having occurred.
Non-deviating nodes in the digraph are ‘flagged’. It
is assumed that a non-deviating transmitter reading
indicates the absence of failure in its respective section. Back-tracing commences from the location of
any noted deviations to determine the possible fault
causes.
5.1
Fault diagnostics program
The process of back-tracing within the Boeing 777200 fuel system digraph model, from a deviating node
to determine possible component failure mode combinations, is automated through running scripted code
in Matlab. The diagnostic program can be sub-divided
into four main sections. Namely; input, comparison,
fault diagnostics and output.
During the ‘input’ stage the individual fuel system
transmitter readings, switch positions and assumed
engine feed operating mode phase are ‘read into’ the
program by way of three text files. The program then
determines the expected system readings from the
noted operating mode phase.
Two deviation matrices, [D] and [DI], are formed
during the ‘comparison’ phase by comparing the
retrieved data with those readings which would be
expected under the assumed engine feed operating
mode phase. If the readings are identical then a corresponding element in the deviation matrix is allocated
the value ‘0’. This indicates the presence of nondeviating data and so it is assumed no failures are
present in the associated specific section of the fuel
system. Should a reading deviate then the respective
element in the matrix is assigned a value which is consistent with the deviation (e.g. +10). The matrix [D]
considers deviations associated with the switch positions that have previously been determined by the pilot
whilst [DI] contains deviations noted by the indication
system, such as low pressure at a specific pump outlet
or no flow at the inlet to one of the engines.
On generating the deviation matrices the next phase
is the ‘flagging’ process. Firstly, values are allocated
to flags representing the cross-feed, left wing and right
wing sections. Each section has two associated flags,
related to the two deviation matrices. If deviations are
outlined in [D] or [DI] for a specific section then its
corresponding flag is assigned the value ‘1’. The value
‘0’ is used for situations where no deviations are registered. The next stage involves allocating values to
the flags used to represent the individual transmitter
elements noted in the deviation matrices.
The fault diagnostics process involves re-enacting
the procedure of back-tracing through using matrices
which contain the individual component failure mode
results for a registered deviation. The number of flags
signed ‘1’, representing system deviations for given
tank sections and transmitters, dictates which backtracing results should be ANDed.
Diagnostics of the fuel system during the engine
feed operating mode is split into two sections: (i) no
deviations registered by the flow meter at the engine
inlet and (ii) deviations registered by the flow meter
at the engine inlet. This sectioning was decided upon
due to the fact that the main purpose of the engine feed
operating mode is to provide fuel to the engines.
The tank level data is used to calculate the rate of
change in the fuel system tank levels. These calculations are performed after data has been retrieved from
the second sampling interval. The tank level rate of
change data is utilised when performing fault diagnostics of the fuel scavenge section. Once the operating
mode has switched from phase one to phase two the
fuel scavenge pumps are switched on. As the main tank
level decreases, the remaining fuel in the centre tank
is transferred to the main tank.
The diagnostic results are displayed whilst the program runs. Initial display features involve noting the
status of the fuel system sections with regards to the
presence or absence of any noted deviations. If deviations are noted, the determined fault diagnostic results
are displayed on screen for each section.
5.2 Diagnostic considerations
As an initial means of ‘honing-in’on the most probable
fault cause for a given set of deviations, the following ‘logic’ statements were applied to the diagnostic
strategy:
805
– Should a pump switch deviation be present then it
is assumed that a pump ‘no run’ or ‘run’ failure has
occurred. For scenarios containing a ‘−10’ pump
switch deviation and noted low pressure by the indication system, the failure leading to the disturbance
is documented as pump ‘no run’. When considering
only a pump low pressure deviation a list of failures
associated with both the pump and associated pump
pipe-work are recorded.
– When taking into account the situation ‘no flow’ at
the engine inlet, other component data is utilised
to determine the possible system failures that may
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have led to the variation in flow. The ‘spar valve
closed’ failure is only considered on its own when
either the valve switch or valve position notes a
deviation of ‘−10’. Should no deviation be noted
in the switch and valve positions, all failures determined through back-tracing from the location of the
flow meter are considered. For cases where both
a flow meter and pump deviation are noted, it is
assumed a single failure associated with the pump
is the most likely cause. However, multiple failure
combinations associated with both of the deviations
are also recorded. The same logic is employed for
registered ‘partial flow’ at the engine inlet.
– The fuel scavenge system is considered once the
first interval data has been retrieved, due to the fact
that both tank levels and the rate of change in tank
levels are utilised to determine if any deviations are
present. A failure is assumed to have occurred in the
fuel scavenge section if:
(i) Centre tank (CT) level ≤ 2, CTdhdt = 0,
(ii) Main tank (MT) level < 6, MTdhdt < 0.
– Actual cross-feed valve faults are taken into account
when either a deviation is noted with the cross-feed
valve switch or cross-feed valve position.
The back-tracing conducted by the program is
dependant on the specific engine feed operating mode
phase, as determined by the pilot. Consequently,
sections of the digraph can be ‘turned on or off’
accordingly.
All control aspects of the engine feed phase
come about through the pilot – switch interface. The
pilot conducts informed decisions based on the data
retrieved from the flow meters and tanks levels, as
well as the indication lights. Consequently, when backtracing along the routes between the switches and
controlled components there is no need to consider the
paths separately. Loop operators (Andrews & Brennan
1990) need not be employed since they do not form
‘complete’ control loops.
5.3
Example
A single faulty fuel system scenario is used to illustrate
the diagnostic capability of the fuel system digraph.
The system is assumed to be in phase five of the engine
feed operating mode. The retrieved readings, displayed
in Table 1 note a single deviation (highlighted in bold)
from those expected; ‘no flow’ is registered by the left
flow meter instead of ‘flow’. The readings are retrieved
at 30s intervals, with the deviation being noted at
t = 90s.
When reading the retrieved data into the program,
results are output for each interval. For the first three
intervals it is noted that no deviations exist.A deviation
is recorded in the left wing during interval four (t = 90
seconds).
During the fault diagnostics process for interval
four, the right wing and cross-feed section flags are
signed ‘0’ whilst the left wing flag is signed ‘1’,
thus indicating the presence of a transmitter deviation. Back-tracing commences from node M50(−10),
and given the stated operating mode phase considers
the process flow structure in the digraph that represents the left engine feed manifold and suction bypass
valve. Node M50 marks the location of the transmitter
deviation at the inlet to the left engine and ‘−10’ takes
into account the magnitude of the registered deviation. The back-tracing procedure ceases at the main
tank level node. The fault propagation can be followed
by referencing Figure 4:
1 M50(−10) → LMB
2 M50(−10) → M49(−10) → M40(−10) →P40B,
BVLC.
Three diagnostic results are output by the program;
left engine feed manifold blocked (LMB), pipe 40
blocked (P40B) and left suction bypass valve closed
(BVLC). A fourth failure mode (SVLC) illustrated as
causing a large negative disturbance on flow at location 50 (M50) in Figure 4 is not listed. The spar valve
is not considered to have failed closed given that the
spar switch is in the ‘RUN’ position and no warnings
have been issued to the pilot regarding a disagreement between the spar valve and spar valve switch
positions.
Results for single and multiple deviating transmitter
readings have been obtained for other example scenarios covering the entire range of the engine feed
operating mode. In some cases the diagnostic results
yield numerous fault options, both single and multiple.
A ‘honing-in’ mechanism, as described in the following section, is therefore utilised to identify the cause
considered most apt.
5.3.1 Determining the most probable fault cause
Three minimal cut sets of the order one are output for
the given deviation in the example discussed in the
previous section. Reliability theory (Andrews & Moss
2002) regarding unavailability functions and importance measures is utilised in order to rank the cut sets
yielded accordingly.
It is assumed that the repair process would be initiated once a failure is revealed and therefore the
unavailability is given by Equation 1:
Where λ = failure rate; ν = repair rate; and t = time.
Generic failure rate data (Moss 2005) is employed
in Equation 1 as a means of defining the fuel system
component’s unavailability. For the given example, the
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Expected and retrieved readings.
Expected
Retrieved (after 90s)
Variable
Left
Right
Left
Right
Centre tank level
Main tank level
Jettison pump switch
Jettison pressure light
Aft boost pump switch
Aft pressure light
Forward boost pump switch
Forward pressure light
Engine flow meter
Spar valve switch
Spar valve & relay position
Cross-feed valve 1 switch
Cross-feed valve 1 light
Cross-feed valve 2 switch
Cross-feed valve 2 light
≤2 & >0
≥2
OFF
OFF
OFF
OFF
OFF
OFF
FLOW
RUN
AGREE
OFF
OFF
OFF
OFF
≤2 & >0
≥2
OFF
OFF
OFF
OFF
OFF
OFF
FLOW
RUN
AGREE
---------
≤2 & >0
≥2
OFF
OFF
OFF
OFF
OFF
OFF
NO FLOW
RUN
AGREE
OFF
OFF
OFF
OFF
≤2 & >0
≥2
OFF
OFF
OFF
OFF
OFF
OFF
FLOW
RUN
AGREE
---------
unavailability of the relevant components were found
to be:
6
– LMB: 1.69999982 × 10−7
– BVLC: 5 × 10−8
– P40B: 3 × 10−10
The fuel system digraph noticeably reflects the physical structure of the system under investigation. Thus
providing a clear representation of the relationships
that exist between the system variables. The complete
digraph for the fuel system is relatively large in terms
of the number of nodes from which the digraph is constructed. The development process is, however, greatly
aided by dividing the system into sub-units and generating the system digraph through combining the unit
digraphs at shared common nodes.
The potential for the presence of anomalies between
failure mode results is eradicated through incorporating ‘flagging’ into the diagnostics process. ‘Flagging’ is considered a consistency check and therefore
removes the possibility of conflicting results arising between non-deviating transmitter nodes and the
failure results achieved through back-tracing from
nodes noting specific deviations.This process has been
adapted further when considering the five defined
phases of the engine feed operating mode. Depending on the specific phase, sections of the system
digraph are effectively turned ‘on’or ‘off’accordingly.
This therefore dictates the route to be followed when
back-tracing from a deviating node, as exemplified in
Section 5.3.
The use of reliability theory permits the presentation of a numerical solution to determine the most
likely fault cause for a given deviation. In this manner it is possible to provide a complete list of the
fault causes yielded though back-tracing, whilst also
highlighting the actual fault that is considered to
have occurred. This development builds on previous
research were a ‘honing-in’ mechanism was cited as
The Fusell-Vesely measure of minimal cut set
importance provides a means of ranking the cut sets
obtained from the system digraph. The expression for
the Fusell-Vesely measure is illustrated in Equation 2:
The importance measure is defined as the probability of occurrence of cut set i [P(Ci )] given that the
system has failed. QSYS is calculated using the rare
event approximation as opposed to calculating an exact
value. For the given example, no difference was noted
in the ranking of the cut sets when considering either
the rare event or exact values for QSYS . For cases
whereby many cut sets are produced, it would be computationally demanding to determine an exact value
for QSYS.
For the example, the cut set importance measures
were found to be (QSYS = 2.2030 × 10−7 ):
– LMB: 0.7717
– BVLC: 0.2463
– P40B: 1.478 × 10−3
From the results the most likely cause for the given
deviation at the inlet to the left engine flow meter is
noted as a blockage in the left engine feed manifold.
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CONCLUSION
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necessary when considering faulty scenarios that yield
numerous diagnostic results.
Current research considers a range of phases for
the engine feed operating mode and deals with multiple faults. Furthermore, real-time diagnosis is allowed
for through computer analysis. Hence, it is proposed
that future research consider the inclusion of further
operating modes with regards to the Boeing 777-200
fuel system. In this manner loop operators could be
employed during the fault diagnostics process when
taking into account the control loop associated with
the refuel mode.
Initial results from the application of the automated
diagnostics process, based on the digraph method, to
a section of a complex real system have been proven
to be credible.
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