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Diagnostic Methods for an Aircraft Engine Performance

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 Jestr Journal of Engineering Science and Technology Review 8 (4) (2015) 64-72
JOURNAL OF
Engineering Science and
Technology Review

Research Article www.jestr.org

Diagnostic Methods for an Aircraft Engine Performance

Ε. L. Ntantis* and P. N. Botsaris

Department of Production Engineering & Management, Polytechnic School of Engineering, Democritus University of Thrace,
67100, Xanthi, Greece

Received 24 September 2015; Accepted 19 November 2015

___________________________________________________________________________________________

Abstract

The main gas path components, namely compressor and turbine, are inherently reliable but the operation of the aero
engines under hostile environments, results into engine breakdowns and performance deterioration. Performance
deterioration increases the operating cost, due to the reduction in thrust output and higher fuel consumption, and also
increases the engine maintenance cost. In times when economic considerations dominate airline operators’ strategies,
carrying out unnecessary rectification, can be very costly and time consuming. In an attempt to minimize such
unexpected circumstances, having detailed knowledge prior to any inspection will allow the gas turbine user to take some
of the maintenance action when it is necessary. Advanced engine-fault diagnostics tools offer the possibility of
identifying degradation at the module level, determining the trends of these degradations during the usage of the engine,
and planning the maintenance action ahead.

Keywords: aircraft, gas turbine, diagnostic methods, physical faults, performance deterioration
__________________________________________________________________________________________

1 Introduction is necessary, reducing downtime and increasing the

availability of the engine. Maintenance action is the process,
The performance of an aircraft gas turbine is highly to ensure that the gas turbine systems continually perform
dependent on the aerodynamics and thermodynamics of the intended function, at its designed level of reliability and
every single component due to its complexity as a machine. safety. These condition monitoring systems, examples are
The main gas path components, namely compressor and described in [9,10], gather measurements data periodically
turbine, are inherently reliable but the operation of the aero from the engine instrumentation in service and then process
engines under hostile environments, such as varying information that can optimize both the subsequent operation
conditions of load, temperature and speed, and the cycle of the gas turbine and the maintenance, repair and overhaul
sensitivity to component degradation, results into engine [11]. Advanced engine-fault diagnostics tools offer the
breakdowns and performance deterioration [1-6]. The effect possibility of identifying degradation at the module level,
of component degradation is that the efficiencies and determining the trends of these degradations during the
capacities of these get changed, and in order to determine the usage of the engine, and planning the maintenance action
degradation level, it is required to estimate the level of ahead. Therefore the purpose of monitoring systems is to
changes in efficiency and capacity [1,7,8]. Performance extent to which it can enable the proper deduction of engine
deterioration is inevitable; increases engine maintenance faults and minimize the total life cycle costs [88-96].
cost and ultimately affects the safety of the engine, the
aircraft and the crew. A deteriorated engine also increases
the operating cost, due to the reduction in thrust output and 2 Physical Faults
higher fuel consumption. In order to keep the same thrust
level of a clean engine, the engine reaches higher spool It is useful to examine a number of physical faults that may
speeds and running temperatures that shorten the life span of exist in the gas path of the gas turbine, affecting seriously
various components. the component and therefore the overall performance of the
In times when economic considerations dominate airline engine. The physical faults presented in Table 1 and
operators’ strategies, carrying out unnecessary rectification, discussed in details.
such as replacing a fine or not taking action to a faulty Fouling: Fouling is one of the commonest causes of
component, can be very costly and time consuming. In an performance reduction encountered by users of gas turbines
attempt to minimize such unexpected circumstances, having [4,12] and can count for more than 70% of the performance
detailed knowledge prior to any inspection will allow the gas loss during operation [2]. Particular contaminants (dirt, dust,
turbine user to take some of the maintenance action when it oil, pollen, salt etc.) have the tendency to stick to the airfoil
______________
surface and change the aerofoil inlet angle, aerofoil shape,
* E-mail address: entantis@gmail.com increase surface roughness and narrowing airfoil throat
ISSN: 1791-2377 © 2015 Kavala Institute of Technology. All aperture [2], causing the degradation of gas path
rights reserved. components’ pumping capacity and efficiency [13]. The
decrease in mass flow will result in a decrease in thrust
 Ε. L. Ntantis and P. N. Botsaris/
Journal of Engineering Science and Technology Review 8 (4) (2015) 64- 72
necessitating an increase in the rotational speed to maintain between static and rotating parts that happens in both
a required thrust level, while the decrease in isentropic compressors and turbines.
efficiency will cause an increase in TET [2,3,14] and SFC, Hot end component damage: The very high temperatures
thereby reducing the engine life and increasing the engine in turbines can eventually cause damage at the trailing edges
operating costs. Performance deterioration due to fouling is of the NGVs and rotor blades, because these parts are thin
recoverable by cleaning/washing; when the mass flow and difficult to cool.
decreases by approximately 2.5% [2]. Labyrinth seal damage: The damage to the seals e.g. due
to aging, increases the internal leakage between the
Table 1. Effect of physical faults on components’ discharge and suction side of the compressors and turbines.
performance Increase tip clearance: Typical reason for the increased
tip clearance is the thermal expansion. This effect can be
accentuated by casing and shaft distortion, which is
susceptible to high G loadings during combat flight
maneuvers, as well as to turbulence and heavy landings.
Seal erosion: Any wear in the seals results in localized
heating and an increase in compressor bleed air.

3 Diagnostic Methods

3.1 Gas Path Analysis (GPA)

Corrosion: The chemical reaction between flow path Gas Path Analysis (GPA) pioneered by Urban
components and contaminants that enters the gas turbine [18,19,52,53], is used to assess the condition of individual
with the inlet air, fuel or injected water/stream, causes engine components based, on the aero-thermodynamic
corrosion that is the loss of material from those gas path relationships that exist between the component and direct
components [2]. Turbine blades are more susceptible to measurements of gas path parameters [49]. The theory
corrosion due to the presence of combustion products and behind this relationship is shown in the conceptual
elevated temperatures. The effect of corrosion is quite framework in Fig.1 which can be summarised by: The
similar to the effect of erosion, since there is a loss of presence of a primary gas-path physical fault induces
material, increase of surface roughness that leads to change in the component characteristic that shows up a
reduction of the component performance and isentropic deviation of the measurable parameters from the baseline
efficiency. An effective protection from corrosion attack and conditions [12]. Therefore, the purpose of the GPA is to
subsequent loss of performance for both compressor and detect, isolate and quantify the gas path components faults
turbine is through coating. that have observable impacts on the measurable variables
Erosion: Operators flying in sandy or dusty with the hope that will facilitate the subsequent isolation of
environments suffer from the phenomenon of erosion. Most the underlying physical fault [83-87].
of the ingested dust particles in a desert environment are
found to have sizes of 0-1000 µm [15]. Erosion is caused by,
the abrasive removal of material from the gas path
components by hard particles suspended in the air stream.
Erosion leads to increased blade surface roughness, blade
tip, seal clearance and changes in the inlet metal angle,
airfoil profile, throat opening and blade surface pressure
distribution. In compressors due to pressure loss, there is
drop of mass flow capacity and component efficiency [3,16].
In turbines there is a drop in efficiency but due to larger
passing area, flow capacity increases and less back pressure Fig. 1. GPA Principle Engine
produced on the compressor [17]. In contrast to the case of
fouling erosion is non-recoverable by washing or cleaning. In an arbitrary gas-turbine configuration, the
FOD: FOD is the result of a body striking the internal mathematical relationship between dependent and
surfaces of the gas path components of the gas turbine. The independent parameters is expressed analytically in Eq.1
origin of such particles can be via fan section, with air or [12]:
broken particles from the engine inside being carried
downstream [12]. A small dent or nick to the leading edge of
(1)
attacked blades can cause a stress concentration that may
develop into a fatigue crack and threaten the integrity of the
blades and therefore the whole engine. The impact of larger Linear GPA
object damage increases the throat area, altering the surface To simplify the non-linear relationship between components
roughness and resulting reduction in both flow capacity and and measurable performance parameters, a linear
efficiency. approximation is introduced and can be expressed in matrix
Air leakage: Air leakage on gas turbines refers to the form, based on the assumption that the changes in the health
leak of a duct or other mechanical containment of the engine parameters are very small and an operation point (e.g.
(e.g. compressor), to the outer environment. maximum power or cruise) is selected. Given a steady state
Rubbing wear: Rubbing wear is the removal of material operating point, there is no deviation from standard ambient
from the rotor blade tips and knife edges seal, due to contact and nominal operating conditions, and so the measurement

65
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Journal of Engineering Science and Technology Review 8 (4) (2015) 64- 72
values depends only on the health condition of engine In particular, the convergence process is completed when
(neglecting any effect of measurement noise and bias). Root-Mean-Square (RMS) is equal or lower to the
convergence criteria δ [27]. The convergence criterion δ is a
very small number, around 0.01 or less, and is being used
through all the non-linear GPA calculations. However, this
The health parameters deviation can be calculated by the advantage comes at the expense of an increased
inversion of the ICM matrix, named as “Fault Coefficient computational time, due to the number of iterations required
Matrix” (FCM) by using Eq.2: in order to get satisfactory result.

(2)

ICM inversion to FCM is dependent on the number of

performance parameters that should be less than or equal to
the number of measurements, otherwise estimation Fig.3 illustrates the improvement on the accuracy of
techniques should be used. The whole basis of this linear predicted deviation of component parameters on using non-
GPA method is the assumption that the ICM is invertible linear over linear. For the non-linear technique, the exact
and the measurements are noise-free. Investigation of the solution is found much higher than the solution obtained by
newer techniques, each with an ability to take into account linear GPA.
the noise and possible sensor bias, while preserving the non-
linearity of the behaviour, led to the development of engine
diagnostics based on optimisation techniques [80].

Non-linear GPA
The assumption of linearity becomes increasingly false,
when deteriorations cause the engine to operate further away
from the condition for which the matrix was calculated [20].
The development of non-linear GPA addresses the non-
linear nature of Eq.1 and provides a significant advantage on
the severe limitations of linear GPA models. The non-
Fig.3. Prediction of component parameter with linear and non-linear
linearity of the engine thermodynamic behaviour is taken GPA [21]
into account, by using the Newton-Raphson iterative
technique, where linear prediction process is applied 3.2 Kalman Filters
iteratively, until a converged solution is obtained [11]. In 1960, Kalman published a recursive solution to the
discrete data linear filtering problem [22] and in 1961,
Kalman and Bucy followed up a paper on the continuous-
time version [23]. The filter was finally called the Kalman
Filter, although Shet and Rao argued that it is an algorithm
rather than a filter [24]. Kalman Filter (KF) is an optimal
recursive data processing algorithm, used in order to provide
an estimation of the health of the engine components in
presence of measurement noise and sensor bias [22,25,26].
A KF processes all available measurement data regardless of
their precision, plus prior knowledge about the system and
measuring devices, to produce an estimate of the desired
Fig. 2. Non-linear diagnostic model [47] variables in such a manner that the error is minimized
statistically [81]. After a run of a number of candidate filters
many times for the same application, the average results of
Fig.2 demonstrates the idea of the non-linear model based the KF would be better than the average results of any other
method. The real engine component parameter vector x [54-58].
determines engine performance represented by the
measurement vector z. With an initial guessed parameter
vector the model engine provides a predicted performance
measurement vector . An optimisation approach is applied Fig. 4. Typical application of the Kalman Filter
to minimise an objective function, which describes the
relative difference between the predicted measurement
vector and the actual measurement vector z. A The linear algorithm of KF based on two mechanisms:
minimisation of the objective function is carried out
iteratively until diagnostic error e from the iteration process § Prediction: This step is used to propagate the
is very small and thus the best predicted engine component internal state of the system. At time step k, the
parameter vector is obtained. filter predicts the value of the internal state vector
at the next time step k+1.
§ Correction: This step is responsible for fine-tuning
the prediction step under the influence of external
observations. At time k+1 when an actual
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Journal of Engineering Science and Technology Review 8 (4) (2015) 64- 72
measurement is available, the filter corrects itself decided upper and lower thresholds to produce new
based on the prediction error. This correction is individuals.
done by minimizing the error covariance.
The number of GA generations and the size of
Although, the Kalman Filter is a successful method for population determine the accuracy of searched results and
tracking and estimation, its application to non-linear systems the speed of search, thus the selection of these GA
can be difficult. Bearing in mind that, most of applications parameters should be a compromise between the accuracy
of interest the system dynamics and observation equations and speed [27].
are non-linear, a suitable extension to the KF has to be
sought. The most common approach to non-linear systems is
the Extended Kalman Filters (EKF) and the Iterated
Extended Kalman Filters (IEKF) [59-61]. The EKF and
IEKF apply to non-linear systems by simply linearising all
the non-linear models so that the traditional linear KF
equation can be applied. However both produce biased and
sub-optimal estimates, due to the linearization of the
functions which leads to a low accuracy estimation.

3.3 Genetic Algorithms

First pioneered by H.J Holland in the 1960 at University of
Michigan, Genetic Algorithms (GA) has been widely
studied, experimented and applied in many engineering
fields. The basic concept of GA is designed to simulate
processes in natural system necessary for evolution,
specifically those that follow the principles first laid down
by Charles Darwin of survival of the fittest. The GAs is
Fig.6. GA re-production cycle [46]
applied as an effective optimization tool to obtain a set of
components parameters that produce a set of predicted
dependent parameters, through a non-linear gas turbine
3.4 Artificial Neural Network
model that leads to predictions which best match the
Artificial Neural Network (ANN) or Neural Network (NN)
measurements [20,48]. The solution is obtained when an
began in 1943 [28] and showed that it was possible to
objective function which is a measure of difference between
construct a network using only mathematics and algorithms.
predicted and measured parameters, achieves its minimum
Neural Network found application in aircraft engine
value [78,79].
diagnostics by Dietz [27], space main engine by Whitehead
A diagnostic algorithm based on GA is
[30,31] and an increasing number of other fields [32]. The
implemented as a computer simulation in which a
Neural Network approach is a non-linear estimator that
population of abstract representations (called as genome or
attempts to simulate the learning process performed by the
the genotype or chromosomes) to an optimisation problem
brain, making it effective at pattern recognition [62-65].
fitness is associated to the value of one.
According to [33], the NN is a mathematical structure that
distributes input data into several interconnected simple
(3) units (the artificial neurons), separating the fault diagnosis
into two phases: identifying the faulty component(s) and
proceeding to quantify the fault. For example, Fig. 7 pictures
the inputs of the NN which are the changes in the
measurable parameters, whereas the outputs are the resulted
shifts in some gas turbine components characteristics [66-
69].

Fig. 5. The objective function [48]

The GA is operating over a wide number of iterations, each

one of them consists, the following fundamental [20,47,48]:
§ A selection is a process where stings are assessed
according to a ‘survival of the fittest’ criterion and Fig. 7. A neural network for fault quantification [95]
selectively copied to be used in the next
generation. The NN structure in Fig.7 demonstrates that the data within
§ A crossover is a process that permits information neurons processed in parallel system and its functionality is
exchange between strings in the form of swapping determined by the network structure and connection
of parts of the parameter vector, so as to produce strengths [32]. Because of their high connectivity and
fitter strings from the current population. parallelism, NN is able to link, in a non-linear way, a multi-
§ The mutation operation randomly alters part of dimensional input space with a multi-dimensional output
existing individuals without exceeding the pre- space, allowing very high computational speed [33]. This
technique is capable of simulating the functional relationship
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 Ε. L. Ntantis and P. N. Botsaris/
Journal of Engineering Science and Technology Review 8 (4) (2015) 64- 72
between dependent and independent variables by adapting
and storing experimental knowledge in the network (which § The inference engine which deals with all the
is the training phase) and can be configured to be tolerant of reasoning operations of the system.
noise in the measured or training-data sets. The stopping § The knowledge base which contains the inference
criterion for the NN training phase is the minimization of a rules and facts that the expert system has been
performance function or the mean-square error on the whole taught about the problem by the human tutor.
training set between the target and the corresponding NN
computed outputs [32].

3.5 Bayesian-Belief Network

Bayesian-Belief Network (BBN) is a powerful tool for fault
identification in gas turbines and based upon formal
probability theory [74-76]. It is a system that integrates test
measurements and gas path analysis program results with
information regarding operational history and direct physical
observation, helping for a cost effective diagnosis and using Fig. 9. Typical Expert System layout
value of information calculations [36]. More generally, BBN
is a graphical representation of a probability distribution
which encodes the cause and effect relationships between
3.7 Fuzzy Logic Systems
particular variables represented as nodes and arches. Each
Fuzzy logic systems (FLS) were introduced by L.Zedah at
node represents an observation or a fault that contains the
University of Berkeley in 1960 as means to model the
conditional probability that describes the relationship
uncertainty of natural language. Historically, FLS has been
between the node (effects) and the parents (causes) of that
used to identify and isolate the faulty components rather
node. Kedamb at [37], designated the health parameters as
than the degree of deterioration [51,77,82], however, they
the parent nodes and the measurements as the child nodes. If
were used to determine when to service the T700 engine
a particular child node is affected by the fault the link
[36]. FLs are defined as a method to formalise the human
between parent and child node is established as the
ability to reason approximately and judge under uncertain
illustrated example in Fig.8.
conditions [39]. The primary benefit of FL is to approximate
system behaviour, where analytical functions or numerical
relations do not exist [40]. Therefore, they have the potential
to understand complex systems that have not been tested or
that do not have a vast array of data available on them, such
as the gas path diagnostics of gas turbines [41]. A typical
FLS design may consists of:

§ Fuzzifiation; the process of converting crisp

ordinary values into degrees of membership to
predefined fuzzy input set [38,39].
§ Rule evaluation or fuzzy inference engine; maps
fuzzy input sets to fuzzy output sets.
§ Defuzzification; a scalar quantity is delivered from
the fuzzy outputs when crisp numbers are needed
as an output of the fuzzy logic system.
§ A knowledge base includes fuzzy rules and
functions that play a key role in the fuzzy inference
process.
Fig. 8. Typical BBN layout [35]

3.6 Expert Systems

Expert systems have been in use for medical diagnosis for
over 30 years so far, and since there are direct comparisons
between medical and technical diagnosis, it was decided to
build an expert system to diagnose engine faults [70-73].
Expert systems are defined as a computer program designed
specifically to simulate a specialist human engineer’s ability
to problem-solve or giving advice(s). Expert systems use
sophisticated problem-solving techniques and vast stores of
organised knowledge, concerning a definite area of expertise
to solve problems justify its own line of reasoning, and to act
on deductions just as human would. Instead of being
programmed to follow step-by-step procedures, expert
systems uses facts about the problem supplied by a user,
plus its knowledge base and general problem solving Fig. 10. Typical FLS layout
procedures to find and apply a specific solution. The main
components of an expert system, as illustrated in Fig.9, are:
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Journal of Engineering Science and Technology Review 8 (4) (2015) 64- 72
3.8 Weighted-Least-Squares Advantages
Weighted-Least-Squares (WLS) algorithms are linear but - The inductive nature of the GA means that it
often employ non-linear extensions to identify large- doesn't have to know any rules of the problem,
magnitude faults. WLS emphasize correct determination of since it works by its own internal rules. This
the faulted component, while placing less emphasis on characteristic is very useful for complex or loosely
getting the magnitude right [38]. They do not seek to find a defined problems.
single true solution but instead a solution with the highest - It can quickly scan a vast solution set.
probability of being near to the one, true solution. Therefore, - Bad proposals do not affect the end solution
WLS tries to find a function that closely approximates the negatively as they are simply discarded.
data for a best fit and is weighted such that points with a Disadvantages
greater weight contribute more to the fit. In order to account - Evolution is inductive; in nature life does not
for the fact that some measurements are more accurate than evolve towards a good solution, it evolves away
others, it may be necessary to place more weight on the more from bad circumstances and therefore GAs risk
accurate readings and less on the accurate measurements. finding a suboptimal solution.
- As population and generation number grows,
longer computation time required.
4 Discussion
Neural Network
An overview of the most common GPA techniques is Advantages
presented, with the intention of highlighting some of the - Able to deal with large non-linearity degradations
most important advantages and disadvantages for each and instrumentation faults.
diagnostic tool according to [20, 42-46]. - Using the information of data for training, makes
the network suited for solution to the problems
Linear/Non-Linear GPA where no exact algorithmic solutions exist but
Advantages: large number of examples.
- Faults can be isolated at component level by means - Very good data fusion technique; different kind of
of calculations of the corresponding performance data such as vibrational, thermodynamic and
parameters variations. electrostatic, are allowed to be used to produce an
- Diagnosis can be performed in more than a single answer.
engine component. - Can be trained to recognise noisy measurements to
- Calculations of the performance allow interpret them accordingly.
quantification of the fault(s). Disadvantages
Disadvantages: - The period of the system training is highly timing
- Accurate assessment is complicated by only having consuming.
relatively few measurements available and errors in - Difficulties when diagnosing faults with noisy
the measurements. data.
- Linearization and iterative approaches can only - Requires good quality data for the training phase.
handle the non–linearity. - Needs time to be retrained if model engine
- Larger number of sensors - for better predictions - hardware changes.
leads to higher costs.
Kalman Filter Bayesian-Belief Network
Advantages: Advantages
- Is recursive method; the memory requirements are - Different types of data (qualitative, continuous
minimised and thus the filter can deal with real- numbers or discrete numbers) are accepted.
time data processing. - Diagnosis can be performed in more than a single
- It provides after each measurement an estimate of engine component.
the errors in the parameter characterising the state - No mathematical relationships are required to build
of the system. a BBN, but only the way variables affect to each
- The filter responds well to discontinuous changes other.
(steps) in the measurements, without erratic - Changes of the model engine hardware can be
transients occurring. easily entered in the network because any addition
Disadvantages: or removal of a node can be made, without the
- If a systematic error is present as part of the need to rebuild the whole network as BBN are
measured signal then no amount of filtering will local distributions.
reduce this fixed error. Disadvantages
- KF may become unstable because either it contains - Needs substantial time and big effort to gather
too many small values or because the computer information needed for setting up a data base.
calculations have not been sufficiently accurate. - Requires an expert or someone familiar with this
- The apriori estimate is a reasonable guess and has network to make any change in a timely manner.
to be close to the true value for the residuals to be - Bayesian belief network is combined with the
small and hence higher degree of accuracy. results of GPA hence some of the drawbacks of
- The smearing effect is present and the GPA would be inherently present in such a system.
concentration on the faulty components may be - Cannot deal with sensor bias.
difficult.
Expert Systems
Generic Algorithms Advantages
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Journal of Engineering Science and Technology Review 8 (4) (2015) 64- 72
- Constant availability of expert advice eliminates 5 Conclusion
any waiting for the expert’s time even in a remote
or harsh environment. Apparently, every technique has its own advantages and
- They represent the knowledge of a group as a limitations but it would be interesting to list the
whole and thus there is a elimination of individual characteristics of a theoretically ideal technique that may
bias, prejudice and errors due to oversight or exist in the future. These characteristics of the hypothetical
fatigue. diagnostic tool introduced in 2004 by L. Marinai et al. [20]
Disadvantages and presented as it follows:
- The human experts are often in short supply and as
such are often expensive to maintain reflecting the § Based on a non-linear model.
large investment in time and money required to § Capable of detecting even small changes in
establish this high level of expertise. performance with reasonable accuracy.
§ Able to deal with measurement noise and sensor
Fuzzy Logic Systems bias.
Advantages § Diagnose with high accuracy, by using
- Supports the generation of a fast prototype and measurements less than the number of health
incremental optimization. parameters (N>M).
- The intelligence of the system is not involved with § Designed specifically for single or multiple fault
differential equations or source code and thus isolation.
remains simple to understand. § Avoid any smearing effect and possess a
- The feature of the model-free allows data-fusion concentration capability on the actual fault.
and reductions in computational time. § No need for any training and tuning uncertainties,
Disadvantages difficulties and dependencies for the setting-up
- Unable to approximate faults that occur outside parameters.
range of data that they have already been set up to § It is model-free that allows data-fusion and
tackle. reductions in computational time.
- The achieved accuracy is a compromise between § Competent to incorporate expert knowledge.
the computational speed in producing the required
output and the effort expended by the designer in
formulating the rules. Nomenclature
- The number of rules increases according to the
complexity of the process that is being Acronyms
approximated. DMI - Direct Matrix Inverse
FCM - Fault Coefficient Matrix
Weighted-Least-Squares FOD - Foreign Object Damage
Advantages GPA - Gas Path Analysis
- Constant availability of expert advice eliminates ICM - Influence Coefficient Matrix
any waiting for the expert’s time even in a remote RMS - Root Mean Square
or harsh environment. SFC - Specific Fuel Consumption
- They represent the knowledge of a group as a TET -Turbine Entry Temperature
whole and thus there is a elimination of individual
bias, prejudice and errors due to oversight or Notations
fatigue. Δz - Performance Parameters Deviation
- It uses fewer equations than it has values to find. Δx - Engine Module Parameters Deviation
Disadvantages
- Prior knowledge and tuning is needed. Subscripts
!
- The WLS algorithm tends to smear the fault over z! - Dependent parameter vector
many components; thereby the isolation of the x - Independent (component) parameter vector
faulty component becomes difficult. !
- The assumed approximation to the linear model w - Environmental variables vector (i.e. ambient
may reveal a larger error than anticipated. pressure, temperature)

______________________________
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