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DRAFT MANUSCRIPT
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Computational Intelligence for Diagnosing Gas path related faults
in Gas Turbine Engines
Suresh Sampath and Riti Singh
School of Engineering,
Cranfield University,
Bedfordshire. MK 43 OAL. UK.
ABSTRACT
The paper attempts to give an overview of the recent developments in engine diagnostics using
advanced techniques like ANN and GA. These techniques have opened new opportunities in the
field of engine fault diagnostics. It also discusses the potential of advanced engine diagnostics using
such advanced features in contributing to the management of availability for gas turbines in industries.
In this technique the issue of engine fault diagnosis is treated as an optimisation problem. The
differences between observed data and synthetic data are minimised as an objective function of some
model parameters. The synthetic data is generated using a known set of faults applied to the engine
performance model and the minimum objective function is indicative of the problem. The application
of genetic algorithm for the search of the global minimum, which represents the solution, has proven to
be an efficient, flexible, robust and a reliable way of solving engine diagnostics problems. Finally, the
paper discuses the benefits of such techniques by an example of an industrial problem and how an
advance warning on the impending problem can help improving the overall safety in engine operation,
reduced overall life cycle cost, optimisation of maintenance interval and prioritisation of tasks to
enhance operational availability and provide engineering justification for scheduling maintenance
while identifying corresponding economic benefits.
The continued escalation in engine purchase price, costs of spare parts, maintenance
operations and soaring fuel costs have made it increasingly desirable for operators to
employ engine diagnostics or engine health monitoring which implies the ability to
accurately assess the relative health and performance of their engines in a reliable
cost effective and technically sound way. The purpose of engine diagnostics or
monitoring is to reduce actions taken on the basis of judgments made from directly
measured or inferentially calculated information with varying degrees of emphasis
dictated by the needs and capabilities of their individual organizations. Operators have
shown interest in both determination of initially installed engine condition and in
condition throughout the operation phase.
Effective maintenance schedules rely upon the ready availability of relevant
information. Deducing trends from engine-performance data, in order to diagnose the
causes of the engine faults, is a standard practice. Such engine-condition monitoring is
an effective, but complex, way to improve safety and reduce operation and
maintenance costs of gas turbines. Increased competition within the civil-airline
industry and diminished military-budget allocations have led to increased emphasis
on reducing engine life-cycle costs (LCCs). The operation and maintenance of the
propulsion system contributes substantially to the overall LCC[1].Engine-health
monitoring systems have become increasingly important in recent years due to the
development of engines with improved power-to -weight ratios: the need for
enhanced reliability at reduced costs requires major advances in controls and
diagnostics. Computer technology and computational tools have led to a shift in the
way in which diagnostics is undertaken. In recent years, there has been growing
interest in the machinery prognostics, which is considered as the successor to
diagnostics capability. The benefits of accurate engine diagnostics are related not only
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to the manufacturer, but also every user or maintainer throughout an engine’s life-
cycle. Increased competition within the civil airline industry has led to further efforts
towards reducing operating costs in order to increase profit margins. In the light of the
above a great deal of research efforts have been directed towards the development of
cost effective , reliable and technically sound fault diagnostics system.
NOTATIONS
h Measurement vector from engine performance model
K,S Biased Measurement
L Number of operating points
M Number of measurements
N Number of performance parameters
OP Number of operating points
R Relative Redundancy Index
w Vector of environment and power setting
z Value of measurement
z Measurement vector
∆ Percentage Deviation from the baseline
η Component Efficiency
σ Noise level
Γ Component Flow Capacity
ABBREVIATIONS
EKF Extended Kalman Filters
EP Environment Parameters
GA Genetic Algorithm
GPA Gas-Path Analysis
HPC High-Pressure Compressor
HOT Higher Order Terms
KF Kalman Filters
LCC Life-Cycle Cost
LPC Low-Pressure Compressor
NN Neural Network
OF Objective Function
RMS Root Mean Square
SLS Sea Level Static
TET Turbine Entry Temperature
WLS Weighted Least Squares
SFDIA Sensor Fault Detection, Isolation and Accomodation
GLOSSARY
Bias A fixed error in the measuring instrument
Crossover A method of generating a new solution by using parts of earlier solutions
Fitness A positive value defining the accuracy of solution and it determines the progress
of the solution to the next generation
Generation A cycle of operation which involves selection, crossover and mutation.
Mutation A method of generating new solutions by making random changes to the existing
solutions
Noise A random measurement error which causes disagreement in repeated measurement.
Objective-
Function Summation of the percentages deviation of measurements from their baseline values
used for comparing measurements.
Observability The ability of the instrument to perceive the change in performance.
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Pareto A method for choosing a particular string from a group of strings
Population A group of solutions to the problem
Search Space A collection of all possible solutions to the problem from which the best solution is
chosen
Selection A method of separating the good solutions from a pool of solutions
Smearing Distribution of fault value to other components other than the one under
consideration.
String A potential solution of the GA
ENGINEERING PROBLEM & THE NEED FOR FAULT DIAGNOSIS
Industrial gas turbine development has followed aero gas turbine technology and has
emphasised high thermal efficiency and high specific power. A consequence of this is
that modern high efficiency gas turbines are high temperature, high pressure ratio
machines, with highly stressed rotating components. In spite of this, when used in the
simple open cycle form, the efficiency of the gas turbine is typically less than that of
the steam turbine or diesel engine. Nonetheless, gas turbines are used for a wide range
of applications. Possible advantages to users are: short start times and time to accept
load; limited on-site maintenance; low weight; limited cooling requirements; low
pollution and good efficiency if used with exhaust heat recovery for either combined
heat and power or combined cycle.
Current gas-turbines offered for base load operation have high levels of availability.
However, when a forced outage is experienced, the down-time incurred depends on
the period required to complete the necessary repair or maintenance action. The
largest contributors to forced outage rates are often engine support systems such as
control and fuel systems. The down-times associated with these systems can be
managed to acceptable levels by design redundancy and the holding of appropriate
spares. Advances in instrumentation and microprocessor-based controllers can be
expected to contribute to further improvements in the availability of engine support
systems. In contrast, the major gas-path components such as compressors and turbines
have a high reliabilities. However, when a forced outage is caused by deteriorations of
these components, the down-time experienced can be large. Both the high cost of
such components and the low likelihood that they will be required means that they are
often not held as spares. For large base-load combined-cycle gas-turbines, the
manufacture of such spare components can take many weeks for maintenance action,
and the appropriate maintenance and repair work package and team can be assembled
to ensure that the down-time is kept low and hence a high level of availability
becomes possible.
FORCED OUTAGE RATE
COMBUS TION
8%
POWER DISTRIBUTION
3%
CONTROL SY STEM
24%
ATOMIZING AIR
4%
FUEL OIL
11%
GENERA TOR
5%
OTHERS
37%
LUBE OIL
5%
COMPRE SSOR
2%
TURBI NE
1%
PERCENTAGE FORCED OUTAGE TOTAL DOWNTIME
GENERATOR
17%
TURBINE
14%
COMPRESSOR
12%
LUBE OIL
9%
COMBUSTION
8%
POWER DISTRIBUTION
8%
CONTROL SYSTEM
6%
ATOMIZING AIR
6%
FUEL OIL
4%
OTHERS
16%
Figure
-
1: Forced outage and dowtimes
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0.00
0.25
0.50
0.75
1.00
0 0.2 0.4 0.6 0.8 1
Time
Failure Probability
0.00
0.25
0.50
0.75
1.00
0 0.2 0.4 0.6 0.8 1
Time
Failure Probability
The importance of a timely fault diagnostics and the need for an appropriate remedial
action and the influence it can have on the maintenance can be explained by briefly
dwelling upon the concepts of Maintability, Availability and Reliability.
Maintenance costs and availability are two of the most important concerns to the
equipment owner. A maintenance program that optimises the owner's costs and
maximizes equipment availability must be instituted. For a maintenance program to
be effective, the owner must develop a general understanding of the relationship
between his operating plans and priorities for the plant, the skill level of operating and
maintenance personnel, and the manufacturer's recommendations regarding the
number and types of inspections, spare parts planning, and the major factors affecting
component life and proper operation of the equipment. A well-planned maintenance
program will result in maximum equipment availability and optimal maintenance
costs.
The failure rate/time relationship for most of the equipment has traditionally been
represented by the bath-tub curve.
The first stage of the curve represents the running in period characterised by falling
failure rate. During this period, manufacturing and minor design mistakes are
corrected. The next stage is one of constant failure rate, the level of which depends on
the intensity and efficiency of maintenance assuming that after repair the equipment is
restored to as good as new conditions. The third part of the curve represents the wear
out stage, which is characterised by sharp increase in the overall failure rate of the
system. Gas turbines have a progressively increasing probability of failure with time.
Figure-2 (b) shows the failure probability for a gas turbine. It is clear from the figure
that the failure probability remains more or less same with time and therefore the
additional need for good techniques for engine fault diagnostics and Engine Health
Monitoring(EHM).
(a) (b)
Figure-2: Failure Rate relationship
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Reliability is basically a design feature and even with the best of the maintenance
techniques it can only be restored to the designed level. Design influences reliability
via such considerations as stress margins used, margins to critical speeds, margins to
blade and vane vibration frequencies for both "flap" and "torsion" modes, and
environmental conditions including fuel, air and oil specifications. The simplicity of
the design, the design maturity and established design and development procedures
along with redundancy make an important contribution to engine reliability.
Manufacture, quality control and experience also make a major input. Often a reliable
gas turbine can be let down because of inadequate installation and/or auxiliaries.
An increase in reliability requires high developmental costs and then in order to
maintain this reliability with time, good maintenance techniques are required.
Figure-3 shows the reliability/cost relationship. It is seen that though the resultant cost
of achieving a high reliability reduces with an increase in reliability, but the cost of
achieving and maintaining this rises rapidly. There is thus a compromise between
reliability and cost and equipment cannot be designed for 100% reliability. It should
also be borne in mind that as ageing occurs reliability of various equipment would
reduce. Thus there would be failures. Therefore, in order to prevent these unscheduled
failures, there is a requirement to have knowledge of the engine condition at most of
the operating time.
Since reliability decreases with age , there is a requirement to restore it to the
designed value, which can only be achieved through proper maintenance techniques.
It is not only desirable to have a good maintenance technique but this should be
achieved at a minimum possible cost.
In order to meet the requirement of reducing the life cycle costs one would have to
concentrate on reducing the maintenance costs, which depends on a knowledge of the
engine condition and also the maintenance philosophy. The main benefit of this would
be an increase in savings and more profit margins for the user.
Though one could say that the operation and maintenance costs could be reduced as
the machine/plant is used, by adopting better maintenance philosophies, but
0.00
0.25
0.50
0.75
1.00
0 0.2 0.4 0.6 0.8 1
Reliability
Cost
Figure-3: Failure Rate relationship
Total Cost
Resultant Cost Cost of
Maintainin
g
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modifying an existing system in order to adopt a different technique is more
expensive than incorporating such a technique in the design stages. This is made
amply clear form the figure-3.
In an ideal world we could measure the parameters of the deteriorated engine and
compare with that of the clean engine and could arrive at a conclusion about the
possible problems, however in the real world we have to overcome the problems due
to noise in the measured values and also the sensor bias. We have to take into account
the various possibilities of sensor error and try and isolate the faulty sensors.
Errors can have serious effects on any analysis, because they result in incorrect
component performance calculations, which lead to misleading hardware fault
diagnosis. Failure to detect measurement errors can have serious financial
consequences, as time and effort are spent searching ( on the basis of flawed
calculations ) for non-existent faults in one part of the gas turbine while genuine faults
go undetected . Any analyst who ignores the possibility of corruption of his
calculations by erroneous measurements is treading on dangerous ground, and is
certain to run into problems
Advanced engine-fault diagnostics techniques offer the possibility of identifying
degradations at the module level, determining the trends of these degradations during
the usage of the engine, and planning the maintenance action based on this
information parts can be ordered ahead of an engine removal. To achieve effective
monitoring and diagnostics, it is necessary to gather and analyze both the mechanical
and aero-thermal operating data from machines. The instrumentation and diagnostics
must also be custom tailored to suit the individual machines in the system and also to
meet the requirements of the end users. The reasons for this are that there can be
significant differences in machines for the same type or manufacturer because of
difference in installation and operation. The various issues discussed above pose
major challenge to the manufacturer, operator and research community alike. This has
been a major motivating factor in directing a lot of effort towards the development of
comprehensive engine diagnostics and prognostics system that can predict within
certain confidence bound, time to failure of critical engine components. These
systems can provide many benefits including
• Improved safety associated with operating and maintaining gas turbines.
• Reduced overall life cycle costs of engines from installation to retirement.
• Ability to optimise maintenance intervals for specific engines and
prioritisation of tasks to be performed during the planned maintenance events.
• Increased up/time availability of all engines within a fleet.
• Provides engineering justification for scheduling maintenance actions with
corresponding economic benefits clearly identifiable.
GAS TURBINE ANALYSIS – MATHEMATICAL MODELLING APPROACH
The gas turbine as such is a complex machine and its performance is dependent on the
aerodynamics and thermodynamics of the components and the performance is highly
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non-linear. The performance of components usually deteriorates over a period of time
but ascertaining the deterioration quantitatively is a challenging task. Performance
monitoring, locating and determining the effects of faults involves processing engine
measurements. In all cases, a comparison of some parameter values of the engine,
under examination to the corresponding values for an otherwise nominally similar
engine, which is considered “healthy”, is performed in order to answer the relevant
questions. The parameters used and the way of deriving them characterizes each
different diagnostic approach. The objective of the mathematical modelling process is
clear: use component characteristics and thermodynamic relation ships to build a
mathematical model of a gas turbine from its parts.
GAS PATH ANALYSIS (GPA)
GPA was introduced in the early seventies and since then has been popular form of
diagnostics tool. Despite development of newer techniques the underpinning
principle has been the same The fundamental premise of this technique is that, the
deterioration in an engine can cause changes in performance. These changes in
performance will cause the components to rematch the engine to a new operating
point and therefore will lead to shift in measurable parameters. (Figure -3.1).
Mathematics of GPA
Theoretically there exists a relationship between the measured parameters and the
independent parameter. Let us consider an arbitrary condition where z is dependent
on 2 independent variable x &y. If the baseline value of z0 is known for a given
values of
x = x0 and y = y0, then the function z can be expanded using Taylor series
PHYSICAL PROBLEMS
EROSION
CORROSION
FOULING
F.O.D
BUILT-UP DIRT
WORN SEALS OR
EXCESS CLEARANCE
BURNED, BOWED OR
MISSING BLADES
PLUGGED NOZZLES
DEGRADATION OF
COMPONENTS
PERFORMANCE
• PUMPING
CAPACITY
• EFFICIENCIES
• PRESSURE
LOSSES
• TEMPERATURE
PROFILE
• EXHAUST NOZZLE
AREA
CHANGE IN
MEASURABLE
PARAMETERS
• SPOOL SPEEDS
• TEMPERATURES
• PRESSURES
• POWER OUTPUT
DEPENDENT PARAMETER
INDEPENDENT PARAMETER
COMPONENT MAP
SHIFTS
CORRECTIVE
ACTION
ICM
FCM
Figure-4: Aero-Thermo relationship for GPA
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)()( 000 00 yy
y
z
xx
x
z
zz yyxx −×+−×+= ==
δ
δ
δ
δ
+……..(HOT) (1)
as magnitude of changes in independent parameters are likely to be small, higher
order terms(HOT) can be neglected and equation 3.1 can be rewritten as
0
0
0
0
0
0
0
0
0
0
00
)(
y
yy
y
z
z
y
x
xx
x
z
z
x
z
zz
yyxx
−
××+
−
××=
−
==
δ
δ
δ
δ
(2)
It is customary to define performance shifts in terms of percentage deviation from
baseline therefore defining
100
0
0×
−
=∆ z
zz
z (3)
Substituting equation -3 in equation-2 we get
y
y
z
z
y
x
x
z
z
x
zyyxx ∆×
×+∆×
×=∆ == 00 0
0
0
0
δ
δ
δ
δ
(4)
all terms inside curly brackets are constants, in mathematical terms called coefficients
and equation-3.4 can be written as
yCxCz ∆×+∆×=∆ 21 (5)
the above equation defines a relationship between change in dependent parameter z to
change in independent parameter x & y. However in reality we are likely to measure a
set of dependent parameters to detect a set obtain the independent parameters, the
general form of the equation can be written as:
eee XHZ ×= (6)
Ze : Set of engine parameter measurements
Xe : Set of engine module deviations
He : Set of influence coefficients determining relationship between dependent
and independent parameters.
Where, He is called the Influence Coefficient Matrix (ICM). In our study we would
be interested in obtaining Xe , therefore, mathematically
eee ZHX ×= −1 (7)
The matrix H-1 which is inverse of the ICM is called the diagnostics or the Fault
Coefficient Matrix(FCM). Thus, knowing the dependent parameters, calculating the
ICM and hence the FCM, it is possible to estimate magnitude, nature and location of
the degradation.
The technique described above relies on simple matrix multiplication and has several
advantages like a) ability to isolate fault at component levels b) identification of
multiple faults capability, fault Quantification. However, the assumption that the
relationship between the independent and the dependent parameters is linear becomes
a serious limitation when the degraded point shifts further away from the original
operating point (where the matrix was created). It was found that when the deviation
increases beyond 1% the linear GPA become unreliable. This led to the development
of Non-Linear GPA. The solution to this problem is to run the linear GPA with in a
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iterative process by creating new ICM and FCM with the degradation values obtained
in the previous step until the algorithm converges to a pre-decided error bound. In
addition ,An effective diagnosis will require a large number of monitored parameters,
but in actuality, the number of sensors is always less than the numbers of
components. Additional sensors leads to increased cost. Less sensor leads to the
phenomenon of smearing, which is nothing but under-assignment of a fault and
distribution of remainder faults to other components. A comprehensive assessment of
health of various gas path components calls for a large number of performance
parameters to be evaluated and therefore a large number of sensors to be installed on
the engine .
The conventional GPA poses certain problems when accounting for measurement
uncertainties. To overcome certain drawbacks of GPA, estimation techniques like
Weighted Least Square(WLS) analysis , Kalman Filters(KF) and its variants have
been used. The technique based on WLS has shown to underestimate the actual fault
and assigning the remaining deviation in performance parameters to other components
and the size of error is typically proportional to the size of the actual performance
fault[12]. Even the use of KF ,though very popular has not been able to deal with the
non-linear nature of the operation and inaccurate diagnosis can result in “smearing
effect”[62].
ENGINE FAULT DIAGNOSIS USING ARTIFICIAL INTELLIGENCE
Artificial intelligence techniques have been quite popular with researchers and have
made effective use it in recent past for engine fault diagnosis and engine health
monitoring (EHM). Several researchers have used concept of expert systems, fuzzy
logic, Bayesian belief network etc.. however the use of ANN has been by far the
most popular technique. Due to the wealth of knowledge available in this field in the
public domain it would not be possible to present a detailed description of the
technique and therefore a brief review of the use of ANN for engine and sensor fault
diagnosis is presented in the succeeding paragraphs.
Artificial Neural Network For Engine Fault Diagnosis
Early applications of neural network to aircraft engine diagnostics were carried out by
Denny (1965) and Dietz et al. (1989), and to the Space Main Engine by Whitehead et
al. (1990a, 1990b). Different neural networks have been used in gas turbine engine
fault detection, diagnosis and accommodation since then. The most popularly used
artificial neural network in gas turbine diagnostics is the Feed-Forward Back-
Propagation Networks (FFBPN). Application of Feed-Forward Back-Propagation
neural networks to gas turbine diagnosis have been performed by many researchers,
such as Eustace (1993), Torella and Lombardo (1995, 1996), Kanelopoulos et al.
(1997), Torella (1997), Roemer (1998), Tang et al. (1998), Cifaldi and Chokani
(1998), Zedda and Singh (1999b), Volponi et al. (2000), Sun et al. (2000), Lu et al.
(2000), Kobayashi and Simon (2001) and so on. Torella and Lombardo (1996)
described a calculation for learning rate factor (LRF) for improving the learning rate
BPNN. Kanelopoulos et al. (1997) presented a partial network architecture to perform
sensor and component fault diagnosis step by step. Zedda and Singh (1998)
introduced a modular neural network system to tackle large-scale diagnostic problem
and applied it to Garrett TFE 1042 engine. The first type is a Probabilistic Neural
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Network (PNN), a derivative of the Radial Basis Function neural network, used by
Eustace and Merrington (1995), Patel et al. (1996), Sun et al. (2000), and Eustace and
Frith (2001). The training of the networks is a supervised learning procedure, where
PNN classify the training patterns to classes. PNN is a network implementation of
Bayesian statistics where the previous case studies are directly stored in the network
as mathematical coefficients while no training is required. When an unknown pattern
is input to the network, the Euclidean distances between the input pattern and stored
case centers are calculated. The distances are then converted to probabilities via a
density function; the smaller distance has the higher probability and vice verse. The fit
for each case is compared and the case with highest probability indicates the most
possibility. Application of the method to a fleet of engines (Eustace and Merrington,
1995) showed that it is capable of diagnosing faults even when the parameter changes
due to faults are less than the no- fault engine-to-engine variation. A real-time engine
health monitoring (EHM) and diagnostic system were described by Roemer (1998),
where both self organizing neural network maps and trained network classifiers were
utilized in diagnostic module. The self organizing neural network map (Kononen
network , Kohonen, 1987) was used for initial pattern clustering to identify similar
patterns and a trained back-propagation network classified the coordinate location on
the map into a specific diagnosis.
Adaptive Resonance Theory networks (ART) introduced by Grossbery (1976) are
capable of stable categorization of an arbitrary sequence of unlabeled input patterns in
real time. It was applied by Torella and Lombardo (1995) and Torella (1997) to gas
turbine trouble shooting and diagnostics. Such architecture has the capability of stable
categorization of an arbitrary sequence of unlabeled input patterns in real time. Three
different groups of neurons usually form the networks and are arranged in two layers
where the nodes on each layer are fully interconnected to the nodes of the other layer.
The first layer manages the input information and the second layer clusters the
information by grouping similar information. Opposite to fixed architecture neural
networks are the Resource Allocating Networks (RAN) (Pratt, 1991;
Kadirkamanathan and Niranjan, 1993) which have the capability to allocate new
neurons, as needed, as more patterns are learned. One of RANs is a self-learning
Radial Basis function (RBF) network and was applied to gas turbine diagnostics by
Patel et al. (1995), Patel et al. (1996a, 1996b), Patel and Kadirkamanathan (1996),
Patel et al. (1996), Arkov et al. (1997) and was further investigated by Romessis et al.
(2001). The network can grow by itself by adding new hidden neurons and output
neurons when new fault patterns are presented to it and also can improve its
generalising qualities by adapting itself when presented with similar faults to those
previously encountered. The novelty of a pattern is determined by comparison
between the response of each hidden node and a pre-defined threshold. Another
Resource Allocating Network applied to gas turbine diagnostics is the Recurrent
Cascade Correlation (RCC) Neural Network (Figure 5), a supervised neural network,
developed by Fahlman and Lebiere (1990). It was introduced and compared with
Back-Propagation Neural Network by Tang et al. (1998, 1999) for jet engine fault
diagnosis.
Advantages and Limitations:
The features which make them amenable to application in engine diagnostics task are,
the ability to cope with noise affecting the measurements, take care of the non-linear
relation between measurements and performance parameters. In addition it could also
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be used to perform data fusion to develop a comprehensive diagnostics which could
include vibrations analysis, oil analysis, gas path analysis etc...However, it has certain
limitations and the commonly reported one is requirement of a large number of data
for training and also the long training times involved. Zedda & Singh[] have reported
the drawbacks of the requirement of a large number of networks.
Comparison between the Feed-Forward Back-Propagation Neural Network and the
model based Kalman Filter method for gas turbine engine single fault linear
diagnostic problems (Volponi et al., 2000) shows that such a network has slightly
poorer performance than Kalman Filter approach in terms of accuracy. Volponi et al.
(2000) introduced a hybrid neural network where part of the network model was
replaced by influence coefficients and the accuracy of such a network was favorable
compared to back-propagation net and Kalman. This has necessitated the use of other
AI techniques to offset the limitations of ANN.
Evolution Strategy for Fault Diagnosis
One possible method of finding the problem with an engine is to run the engine model
with every possible combination of error and compare the synthetic measurements
from the engine model with that of the one obtained from the actual engine . The and
compare this to the actual engine data to get the closest one. This idea sounds quite
logical till we consider the number of permutations possible. Let us consider an
example of an engine with a total of 8 components (C=8) , i.e 2 compressors, 3
turbines, combustor, intercooler and recuperator. If each component has 2
performance parameters i.e efficiency(η) and flow capacity( Γ) (P=2). If we estimate
a changes to be +/- 5% of the base line, at an accuracy of +/- 0.1% then this would
give 100 different options( E=100). If there are 2 instruments with each component
and at the inlet and exit of the gas turbine then I=14. If we keep the instrumentation
error to +/- 2% and with an accuracy of +/- 0.1 % then A=40.
The number of times the performance model will have to run in 896000 times.
Assuming that each model takes 1 second to run then total time taken
= C*P*O*E*I*A*(1/3600)
= 8*2*100*14*40*(1/3600)
= 249 Hrs or appx 10 days.
Though it can be argued that the processing power of the processor can reduce the
time required but the example considered is a very simple. In reality we would want
to examine the data from a more complicated instrumentation set or transient data and
also include the variation in environment and power setting parameters. The search
space shown in figure-5, shows the variation in objective function (i.e a way of
representing the deviation in parameters from the baseline) for a HPC on a two spool
engine. The plot shows the values of all objective function obtained by varying the
component efficiency from 0 to –3%(η) and varying the flow capacity(Γ) from –3 %
to +3%. This implies that every point on the plot is a potential solution , but the best
solution would be one having the lowest objective function. However, it would be
prudent to generate a few random solutions and use some method to steer the search
towards some meaningful direction.
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The vast search space necessitates the use of some robust search techniques which
are capable of overcoming the problems of local minima. After investigating the
possibility of using various conventional optimisation technique like the downhill
method, simplex method etc.. it emerged that the use of Genetic Algorithm would be
the most suitable form of search technique for the problem in hand.
A technique based of genetic algorithm was developed purpose of the engine fault
diagnostics. The approach has been effective at exploring a large and complex space
in an adaptive way guided by the equivalent biological evolution mechanisms of
reproduction, crossover and mutation.
ARCHITECTURE AND ITS IMPLEMENTATION
Figure-6 (Sampath et al ,2002) shows the basic architecture of the diagnostic system.
The engine performance model is simulated at various fault condition and noise and
sensor bias are added to the measured parameter. The synthetic measurements are
then compared with the actual measurements for optimisation.
1
6
11
-3 S6 S11
0
10
20
30
40
50
60
Objective Function
Efficiency
Mass Flow
0.00
10.00
20.00
30.00
40.00
50.00
60.00
0 50 100 150 200 250
Engine
Performance
Power Setting
Parameters
Measurement
Noise
Instrum ent Bias
Model based
Measurements Real Engine
Measurements
Objective Function
to be Minimised
Figure- 6: Schematic Diagram of the Diagnostic Strategy
Figure-5: A Typical Search Space for HPC
(a) (b)
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Mathematical explanation -
A function, which defines a relationship between the dependent and independent
parameters noises or biases, is given as-
z = h(x) (8)
where,
• z
∈
RM is the measurement vector and M is the number of measurements
• x
∈
R
N is the performance parameter vector and N is the number of
parameters
• h(.) is the vector valued function.
h(.) is provided by the simulation program and is non linear. If we consider the noise
to be present then the model has to appropriately modified as follows
z = h(x)+v (9)
where, v is the measurement noise vector.
In the presence of sensor biases, the equation (4.2) is further modified to
z = h(x)+b+v (10)
where b is the measurement bias vector,
equation(4.3) defines the relationship for a certain operating point. If dependence on
the operating point is written explicitly:
z = h(x,w)+b+v (11)
where w
∈
RP is the vector of the environment and power setting parameters(e.g inlet
conditions and fuel flow) and P is the number of parameters. Usually v is assumed to
have gaussian probability density function(Pdf) and moreover to have independent
components. Therefore, the joint pdf is the product of independent pdfs.
()
2
1
2
1
1
1
2
1
)( ∑
==
−
=
∏
M
jj
j
v
M
jj
Mevp
σ
σ
π
(12)
where
σ
j is the standard deviation of the j th measurement. It should also be noted
that w is affected by noise as well as biases like the other measurements
u = w + bw+ vw (13)
where: • u is the vector of measured values
• w is the vector of actual values
• bw is the vector of biases
• vw is the vector of noise
Having defined the problem in equations (11) & (13), we need to find a solution to it.
The aim would be generate a certain number of random solutions and compare it
with the actual solution obtained. An objective function is to be decided which is a
measure of the consistency between the actual the predicted measurements. Various
factors concerning measurement noise and biases should be accounted for and the
objective function should not be computationally intensive.
A classic choice for the objective function at a given operating point would be-
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[]
()
∑
=
−
=M
jjodj
jj
z
xhz
xJ
12
2
)(
)(
σ
(14)
zodj is the value of the jth measurement in the off-design un-deteriorated condition.
The minimization of the above objective function provides the maximum likelihood
solution for the non-linear problem at hand. Another suitable function is the absolute
deviation.
∑
=
−
=M
jjodj
jj
z
xhz
xJ
1
)(
)(
σ
(15)
Measurement noise is accounted for using the standard deviation
σ
j
The uncertainty affecting the environment and power setting parameter can be
considered by modifying the objective function to
[]
()
∑
=
−
=M
jjodj
jj
wz
wxhz
xJ
12
2
).(
),(
)(
σ
(16)
and equation (4.8) becomes
∑
=
−
=M
jjodj
jj
wz
wxhz
xJ
1).(
),(
)(
σ
(17)
SALIENT FEATURES
Real coded GA - After extensive trial with binary coded GA and real coded GA it
was realised that the real coded GA worked for solving this kind of problem. The
following advantages where observed. The ease of implementation as the
chromosomes where directly made of real vectors. The spread of estimation errors
from run to run was lower with respect to the one provided be the binary GA. higher
speed of convergence observed to be faster leading to lesser number of generations.
Constrained optimisation – one of the ways to reducing the effect of smearing is to
apply constraints on the number of components which are faulty simultaneously and
also the maximum and minimum levels of fault in the performance parameters of the
engine components . for the purpose of experimentation the maximum change is
component efficiency has been restricted to –3.5% and the change in component
flow capacity in the range of -3.5 % to +3.5 %.
ANALYSIS OF THE TECHNIQUE
The use of a GA based optimization technique for gas turbine diagnostics has been
shown to be very accurate even in the presence of a large amount of noise , bias and
model inaccuracies. The lack of information from less number of measurements for
poorly instrumented engines can be overcome by use of the technique based on
multiple operating point analysis using GA’s and using the concept of pareto
optimality[Gulati et al,2000].
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The problem of smearing as experienced with other current day methods has been
effectively dealt with by dividing the engine into a number of fault classes and
aiming to identify only one class that is faulty. Results have shown that this way only
components of the faulty fault class are identified as having changes in efficiency and
capacity whereas the others are left at zero.
The issue concerning non-linearity of the gas turbine operation has been addressed by
the development of an objective function which can also deal with measurement noise
and bias adequately.
Results obtained from GA based technique have been very encouraging but there are
still a number of drawbacks with this that need to be addressed before it can truly
become a widely accepted technique. The main drawbacks together with what needs
to be done are now discussed:
(a) The main drawback of a GA based optimization technique is that these require a
very long time to converge. A GA requires an initial population and the members of
this population produce offspring and as generations progress these members get
better and fitter. The larger the number of generations the better for the convergence.
Even under best circumstances the GA based optimizer requires a minimum of 100
members of population per fault class which then have to run for about 100
generations. For an engine of the type of RB 199 that has 36 likely fault classes (for a
maximum of 2 components being faulty), this would require the performance model
to run at least 720000210010036 =××× times. This requires at least 12 hours for
convergence. In case the performance model is slower than this then the time
increases. This is especially true for the Trent 500 in which case there are 45 fault
classes and the model runs for 900000 times, but the model being slower it takes at
least 36 hours for convergence, which can be reduced by half if the model is speeded
up. Though 12 hours for getting an accurate result may be acceptable but for most
manufacturers and users 36 hours would be totally unacceptable
(b) Dividing the engine into a number of fault classes and then trying to identify one
of these as faulty solves the problem of smearing. However, this has an effect on the
maximum number of components that can be identified. For the purpose of this
research it has been assumed that a maximum of two components are faulty. It is
possible to look at more components, but this would lead to more fault classes and
hence more time for convergence.
(c) During the search process it is also possible that the algorithm identifies more
than one fault class which have very close values of objective function and such a
situation would be termed as competing fault classes condition. Such situations need
a careful assessment of the final results and a prior knowledge of the system would
be beneficial.
IMPACT ON BUSINESS
The recent developments of diagnostics using advanced techniques have considerable
potential to replace traditional diagnostics techniques. The new techniques have been
extensively tested on aero-engines with test-bed instrumentation and in-service
instrumentation. Mathematical modelling of the performance of engines suffering
deterioration and diagnostics, albeit complex, are now sufficiently mature for
consideration by industrial gas-turbine users and manufacturers. These techniques
allow the detection of component degradations at the module level with greater
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certainty and accuracy than the earlier linear GPA methods and other traditional
techniques. While the GPA methods have been discussed earlier in this report,
serious limitations of the technique being its dependence on the number and type of
instrumentation being used and the inability to preserve non-linearity of the system.
An advance warning on the impending problem can help in managing the
maintenance aspects more efficiently by organising logistics support and the
appropriate skills required to rectify the problem and avert surprise failures. Such
techniques would be highly beneficial in increasing the availability and in reducing
the operating and maintenance costs.
CASE STUDY
A simple LCC model based on percentage power shortfall and percentage increase in
s.f.c has been studied[Deshmukh,1996] and applied to an industrial power generating
installation. The result of implanting fouling in an engine which is thermodynamically
similar to the LM2500 with a base load of 29500 HP at SLS and operating 8000
hrs/year has been presented.
Base load s.f.c = 0.385 lb/hp hr
Cost of electricity = £40 /MW hr = £0.030 /Hp hr
Cost of diesel fuel = £0.55/litre = £0.286/lb
A typical fouling case would cause reduction in power output by 6% and increase in
s.f.c by 2.5%
Assuming due to incorrect maintenance the average yearly shortfall is half of a typical
case i.e. decrease in power is 3% and increase in s.f.c is 1.25%
Yearly power shortfall = % short fall x HP Hr /year
= 3/100 x 29500 x 8000
7.08 million Hp Hr/year
yearly cost of power shortfall = £ 7.08 x 0.030 million
= £ 0.2124 Million
yearly excess fuel = % increase in s.f.c x s.f.c base load x Hp-hr yearly base load
= 1.25/100 x 0.385 x (1.03) x 29500 x 8000
= 1.10167 Million lb.
Yearly cost due to excess fuel = yearly excess fuel x fuel cost
=£ 1.10167 x 0.286
= 0.32 million
total costs as a result of engine performance deterioration due to fouling = yearly cost
of power shortfall + yearly cost of excess fuel
= 0.2124 = 0.32
= £ 0.53
this simple case study shows the losses suffered due to running the engine under
faulty condition . In addition the reduction in the overall service life due to operating
the engine with increased temperature. A timely detection of the fouling and remedial
action would have helped the restoration of performance of the engine to its original
condition or very near to its original condition.
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DISCUSSION
The importance of instrument accuracy needs no emphasis: a faulty instrument could
lead to the diagnosis of the wrong component or an existing fault to go undetected.
The measurement uncertainty issues have been tackled in three ways: improvement in
sensor design, use of more comprehensive instrumentation sets and the development
of a statistical technique able to cope with measurements errors. Improvements in
engine diagnostics can in theory be achieved simply by adding more and more
reliable instrumentation to monitor the engine’s health. However, the instrumentation
itself has its own mean-time to failure. Additionally, inappropriate or badly
maintained instrumentation can lead to the detection of spurious faults, leading to
unnecessary expensive maintenance actions. This will occur particularly if the
diagnostic technique employed is not robust. The instrumentation has substantial costs
associated with its installation and use, which rise as the amount of instrumentation
included is increased.
However, cost savings are limited by the capability of the technique employed, the
design and the maturity of the engine in use, the fuel utilised, the operating
environment and the operating profile. Figure-7 illustrates how an excessive use of
instrumentation results in a loss rather than a gain in terms of return on investment.
Computer simulations of the engine performance, the instrumentation behaviour and
operating profile allow the user to optimise the instrumentation set for a particular
duty.
ENGINE MONITORING SYSTEM (EMS) COMPLEXITY
MONEY
Investment in EMS Life Cycle Costs
Life Cycle Cost Savings
Net Savings (+ROI)
Loss (- ROI)
Loss (- ROI)
Conventional technique likes Kalman Filters could be used to estimate the system’s
state and perform SFDIA. Nonetheless, the inherent limitations of those technique
suggest that a different approach could be pursued. The proposed advanced
techniques represent a suitable tool for the SFDIA. The proposed method using a GA
is inherently robust to measurement bias. It relies on a fully non-linear model and
requires minimal statistical information.
Figure- 7: Returns on Investment
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The techniques can assist in assessing the consequences of deteriorations on
components of gas turbines, and hence identifying appropriate instrumentation sets
for monitoring. Performance simulation of a degraded engine can form a useful basis
for component life usage studies and such studies give an insight into the engine
operation and reduce overall life-cycle costs. These techniques can be used to
optimise maintenance intervals and prioritise tasks to enhance the operational
availability and improve safety in operating gas-turbine engines. In addition, it can
provide engineering justification for scheduling maintenance while identifying
corresponding economic benefits. These techniques can be used to identify faults, and
to create appropriate information for the generation of rules and inferential algorithms
for knowledge-based systems. This is particularly of interest when the complete or
desired set of instrumentation is not available.
However, the proposed methods are complex and need to be applied with
considerable care. The choice of measurements, the establishment of a baseline and
the appropriate handling of measurement non-repeatability are especially important.
However, the use of these relatively recent techniques is gradually winning over the
initial scepticism and gaining the confidence of the users
REFERENCES
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