Takahisa Kobayashi

QSS Group, Inc., Brook Park, Ohio

Donald L. Simon

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

NASA/TM—2001-211088

July 2001

ARL–TR–1266

AIAA–2001–3763 U.S. ARMY

RESEARCH LABORATORY

A Hybrid Neural Network-Genetic

Algorithm Technique for Aircraft

Engine Performance Diagnostics
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cosponsored by the AIAA, ASME, SAE, and ASEE

Salt Lake City, Utah, July 8–11, 2001

U.S. ARMY

RESEARCH LABORATORY

Takahisa Kobayashi

QSS Group, Inc., Brook Park, Ohio

Donald L. Simon

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

NASA/TM—2001-211088 ARL–TR–1266

AIAA–2001–3763

A Hybrid Neural Network-Genetic

Algorithm Technique for Aircraft

Engine Performance Diagnostics
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

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American Institute of Aeronautics and Astronautics 

1 

AIAA-2001-3763 

A HYBRID NEURAL NETWORK-GENETIC ALGORITHM TECHNIQUE 

FOR AIRCRAFT ENGINE PERFORMANCE DIAGNOSTICS

Takahisa Kobayashi*

QSS Group, Inc. 

Brook Park, Ohio 44142

Donald L. Simon†

U.S. Army Research Laboratory 

NASA Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

In this paper, a model-based diagnostic method, which 

utilizes Neural Networks and Genetic Algorithms, is 

investigated. Neural networks are applied to estimate 

the engine internal health, and Genetic Algorithms are 

applied for sensor bias detection and estimation. This 

hybrid approach takes advantage of the nonlinear 

estimation capability provided by neural networks 

while improving the robustness to measurement 

uncertainty through the application of Genetic 

Algorithms. The hybrid diagnostic technique also has 

the ability to rank multiple potential solutions for a 

given set of anomalous sensor measurements in order to 

reduce false alarms and missed detections. The 

performance of the hybrid diagnostic technique is 

evaluated through some case studies derived from a 

turbofan engine simulation. The results show this 

approach is promising for reliable diagnostics of 

aircraft engines. 

Nomenclature

A8 Nozzle area 

A16 Variable bypass duct area 

BST Booster 

CLM Component Level Model 

FAN Fan 

GA Genetic Algorithms 

HPC High-Pressure Compressor 

HPT High-Pressure Turbine 

LPC Low-Pressure Compressor 

LPT Low-Pressure Turbine 

MBD Model Based Diagnostics 

 

* Aerospace Engineer 

†

 Electronics Engineer, Member 

N2 Low pressure spool speed 

N25 High pressure spool speed 

P27D Booster tip pressure 

P42 Inter-turbine pressure 

PS15 Bypass duct static pressure 

PS21 Fan exit static pressure 

PS3 Combustor inlet static pressure 

T27 HPC inlet temperature 

T3 Combustor inlet temperature 

WF36 Fuel Flow 

Introduction

Over the last several decades, significant research 

efforts have been directed at the development of 

performance diagnostic systems for aircraft engines. 

Such systems can provide a variety of benefits to 

aircraft operators including improved safety,1

 improved 

reliability, and reduced operating costs. With the 

significant growth in air traffic projected in the coming 

years, it is expected that the demand for enhanced 

performance diagnostic methods will continue to 

increase. 

In this work, aircraft engine performance diagnostics is 

accomplished by estimating a set of internal engine 

health parameters from available sensor measurements. 

These measurements, which include gas path 

temperatures and pressures, spool speeds, fuel flows, 

and variable geometry, provide information regarding 

the health of the engine. The general approach to 

performance diagnostics can be expressed using the 

following relationship between the engine health 

parameters and the sensed parameters. 

y = f ( p, operating condition ) + w (1) 

Copyright © 2001 by the American Institute of Aeronautics and

Astronautics, Inc. No copyright is asserted in the United States under

Title 17, U.S. Code. The U.S. Government has a royalty-free license to

exercise all rights under the copyright claimed herein for Governmental

Purposes. All other rights are reserved by the copyright owner.

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

2 

where y is an m×1 vector representing sensed 

parameters, p is an n×1 vector of engine health 

parameter deltas (deviations from nominal), f(·) is a 

nonlinear function of p and operating condition such as 

altitude and engine power level, and w is an m×1 vector 

representing measurement inaccuracies including bias 

and white noise. The problem is to estimate the health 

parameter delta vector p given the sensed parameter 

vector y. 

Several issues make this problem highly challenging. 

First, the only information available for health 

parameter estimation is the sensed parameters, and the 

number of health parameters to be estimated is often 

greater than the number of sensors available. For such 

an underdetermined problem, there exists an infinite 

number of solutions for a given set of sensor 

measurements, and some assumptions must be made to 

select the best or most probable solution. One option is 

to assume that the most likely solution has the 

minimum deviation from the condition estimated in the 

previous time frame assuming the health condition is 

expected to degrade gradually rather than rapidly. A 

second issue is that accurate estimation of health 

parameters may not be achieved if sensor locations are 

not appropriate. For instance, assume that a health 

parameter is primarily affecting the flow condition in 

the bypass duct and has a minor influence on the core 

flow. It will be difficult to estimate this health 

parameter from core flow measurements alone even if 

there are an excessive number of sensors. In such a 

case, some heath parameters are unobservable since 

critical measurements are missing. Another issue is 

that the sensor measurements are often distorted by 

noise and bias as described in Equation 1, thereby 

masking the true condition of the engine and leading to 

incorrect estimation results. Moreover, accurate 

statistical information to characterize measurement 

uncertainty may not be available, and filtering 

techniques are ineffective against biases. Sensor biases 

are often treated as part of the engine health parameters 

because of their relatively large magnitude and timeinvariant character. However, this obviously increases 

the number of unknowns in the estimation problem. 

Finally, the combined effect of system non-linearity and 

sensor selection may result in multiple health 

degradation scenarios producing similar measurement 

shifts. This is a difficult problem to deal with because 

estimation techniques, in general, give only one set of 

estimated health parameters for a given set of 

measurements without the capability to indicate the 

level of confidence in the results. One possible 

approach which addresses this issue involves the use of 

a failure data base developed a priori from flight tests 

or simulation; several possible solutions are selected 

from the data base and a confidence level is determined 

using statistical approaches. Incorporation of 

intelligence in the estimation architecture is 

indispensable in determining the most reasonable 

solution in the highly nonlinear and noise-corrupted 

problem environment. A health monitoring system 

without the capability to deal with these issues will 

exhibit unacceptable false alarm or missed detection 

rates. 

Researchers have investigated a number of estimation 

techniques such as Weighted Least-Squares,2,3 Kalman 

Filters,4,5,6 Neural Networks,7,8 and Genetic 

Algorithms.9,10 Each approach has relative strengths, 

however, a technique that is capable of addressing all of 

the above issues has not yet emerged. In this paper, the 

engine diagnostics problem is approached through a 

Model-Based Diagnostic method utilizing Neural 

Networks and Genetic Algorithms. The proposed 

technique takes advantage of the nonlinear estimation 

capability provided by neural networks while 

improving the robustness to measurement uncertainty 

due to bias through the application of Genetic 

Algorithms. The hybrid diagnostic technique also has 

the capability to rank multiple potential solutions for a 

given set of anomalous sensor measurements in order to 

reduce false alarms and missed detections. 

Model-Based Diagnostics

One approach to aircraft engine performance 

diagnostics that has been investigated by a number of 

researchers is called Model-Based Diagnostics 

(MBD).2-6,8-12 As shown in Figure 1, the MBD 

architecture is composed of an engine model and an 

associated parameter estimation algorithm for 

monitoring engine component performance 

deterioration. The engine model can be linear or 

nonlinear. In this architecture, a set of engine model 

Engine

Engine Model

Parameter

Estimator

PLA

Altitude

Mach

y

yˆ

pˆ error y_ ˆ

-

+

Engine

Health

Estimation

Model-Based Diagnostics

Engine

Engine Model

Parameter

Estimator

PLA

Altitude

Mach

y

yˆ

pˆ error y_ ˆ

-

+

Engine

Health

Estimation

Model-Based Diagnostics

Figure 1. Model-Based Diagnostics Architecture. 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

3 

health parameters, pˆ , is tuned such that the model 

outputs match the engine physical sensor 

measurements. It is assumed that the health parameters 

have sufficient authority to describe the actual engine’s 

performance variations due to component degradations. 

In addition to estimated health parameters, an 

accurately tuned engine model provides estimated 

sensor values as well as estimations of unmeasurable 

parameters such as thrust and component stall margins. 

With these estimated parameters, a variety of 

accommodating actions can be performed to prevent the 

progression of damage. Estimated health parameter 

information can be integrated with control system logic 

in the development of a comprehensive engine health 

management system which maintains safe operation of 

the propulsion system by simultaneously considering 

performance and engine operability. 

Engine Model 

In this research, the XTE46 engine model developed by 

General Electric Aircraft Engines (GEAE)12 was used. 

This model is constructed as a Component Level Model 

(CLM), which assembles the major components of an 

aircraft engine. The CLM is a nonlinear simulation that 

represents engine physics and is capable of real-time 

execution. The XTE46 engine model is a scaled, 

unclassified representation of an advanced military 

twin-spool turbofan engine. Engine performance 

deterioration is modeled by adjustments to efficiency 

and/or flow coefficient scalars of the following 

components: Fan (FAN), Booster (BST), High-Pressure 

Compressor (HPC), High-Pressure Turbine (HPT), and 

Low-Pressure Turbine (LPT). A set of nine health 

parameters, shown in Table 1, must be estimated 

correctly in order to diagnose the engine health 

condition. There are 17 sensors and three actuators that 

can potentially be used as sensed parameters. In a 

realistic application, such a large set of sensors would 

not be available. After some investigation, a set of 12 

sensed parameters was selected as shown in Table 1. In 

the current study, the performance of the health 

estimator is evaluated in the simulation environment. 

The XTE46 CLM is used to represent both the physical 

engine and the MBD system engine model. 

Nonlinear Effects of Health Degradation

One of the challenges often encountered in the health 

estimation problem is the highly nonlinear relation 

between health parameters and sensed parameters. It is 

possible that small degradations in health parameters, 

which are considered insignificant from an operability 

perspective, can cause large shifts in the sensor 

measurements. Likewise, significant degradation in a 

single health parameter can result in small measurement 

shifts relative to the standard noise level. Furthermore, 

there is a chance that distinct health degradations will 

result in indistinguishable shifts in sensor 

measurements.11 An example of this is shown in Figure 

2 which compares the measurement shifts for two 

health degradation scenarios at cruise condition: Case A 

for 2% degradations in Fan and LPT efficiencies, and 

Case B for a 3% degradation in Fan efficiency. The 

two cases are distinct, however, the differences in all 

sensor measurements between these two cases are 

within the range of noise. One approach to address this 

problem is to incorporate some intelligence logic which 

can provide a list of possible degradation scenarios for 

given measurement shifts. Even if a diagnostic system 

cannot give a clear answer, such a list can provide very 

useful information to maintenance personnel attempting 

to troubleshoot anomalous engine behavior. Another 

Table 1. XTE46 Engine Variables 

Health Parameter Sensed Parameter 

1 FAN efficiency 1 N2 

2 FAN flow 2 N25 

3 BST flow 3 T27 

4 HPC efficiency 4 T3 

5 HPC flow 5 PS15 

6 HPT efficiency 6 PS21 

7 HPT flow 7 P27D 

8 LPT efficiency 8 PS3 

9 LPT flow 9 P42 

 10 WF36 

 11 A8 

 12 A16 

1 2 3 4 5 6 7 8 9 10 11 12 −2

−1

0

1

2

Measurement Change

from Nominal (%)

Sensor Number

1 2 3 4 5 6 7 8 9 −4

−3

−2

−1

0

1

Health Deterioration (%)

Health Parameter Number

Case A: 2% Reduction in FAN and LPT Efficiencies

Case B: 3% Reduction in FAN Efficiency

Figure 2. Comparison of Two Degradation Cases 

at Cruise Condition. 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

4 

approach is to use sensor measurements from more than 

one operating point so that a unique set of measurement 

shifts can be assigned for each degradation scenario. 

This approach takes advantage of the non-linearity in 

the system. Diagnostics based on multiple operating 

points10,13 has been investigated by several researchers, 

but it has some limitations. First, it must be assumed 

that a given health degradation does not progress as 

multiple operating points are traversed. Second, it takes 

additional time to reach a diagnosis. Third, additional 

restrictions may be imposed on the selection of 

diagnostic sensors. In the current research, feedback 

parameters regulated by a control system must be 

excluded from the diagnostic sensor suite since bias in a 

feedback parameter causes other sensor measurements 

to shift. In such a case where a bias has a healthdegradation-like effect on multiple sensors, the 

nonlinear function in Equation 1 becomes a function of 

that bias in addition to health parameters and operating 

condition. This obviously increases the number of 

unknown parameters in the problem. Since different 

parameters may be regulated at different operating 

points due to control mode changes, the number of 

diagnostic sensors which can be used across multiple 

operating points is limited. As the number of operating 

points increases, the impact of the above three issues 

increases, and a multi-point diagnostic approach 

becomes less practical. 

Hybrid Neural Network-Genetic Algorithm 

Estimation Architecture

Accurately estimating the health parameters is a critical 

issue for the development of a MBD system. Any 

estimation architecture must be able to handle nonlinearity as well as be robust to sensor noise and bias as 

discussed earlier. 

The estimation architecture in this paper combines 

neural networks and Genetic Algorithms (GA) for 

aircraft engine performance diagnostics at steady-state 

conditions. It is assumed that the sensor measurements 

are time averaged; however, they still contain some 

uncertainty due to sensor noise and modeling errors. 

Neural networks exhibit excellent nonlinear estimation 

capabilities, but the training set required to fully 

represent all possible permutations of health parameters 

and sensor bias is prohibitively large. It would take 

excessive time to train such neural networks, and their 

performance might not reach a satisfactory level. In 

order to avoid this problem, the approach taken by the 

hybrid estimator designates neural networks for the 

health estimation task while designating GA for the 

sensor bias detection task. This approach reduces the 

size of the training set significantly. 

The problem setup is shown in Figure 3. The vector p

represents a set of health parameter deltas to be 

estimated. In the simulation environment, the 

measurement uncertainty vector in Equation 1 is 

decomposed as 

w = b + v (2) 

where b and v represent a bias vector and a white noise 

vector, respectively. In this paper, it is assumed that at 

most one sensor can be biased at a time to make the 

problem manageable. Thus, the bias vector contains 

one non-zero value at most, and its magnitude must be 

large relative to the expected noise magnitude. This 

vector will be estimated; however, the estimated value 

of the non-zero element will be under the influence of 

noise to some degree since bias and noise contained in 

measurements are indistinguishable. Therefore, an 

estimated bias vector will have only one non-zero 

value, just as the actual bias vector b does, but the 

estimated value will be an approximation of the largest 

normalized value contained in the uncertainty vector w. 

The unknown vectors p and b must be estimated based 

on the available physical sensor measurements y. 

As shown in the figure, the hybrid estimator 

architecture is composed of the bias data set, the neural 

network estimator, the engine model, and the GA 

optimization technique. The bias data set, which is 

composed of a large number of bias vectors, is defined 

a priori and is used by the GA in the search for a bias 

vector that matches well with an actual bias contained 

in the measurement vector. The neural network 

estimator is trained off-line with noise-corrupted but 

bias-free sensor measurements, and it will perform 

sufficiently well in estimating health parameters as long 

as the sensor measurements do not contain any bias. 

For a given set of estimated health parameters and 

sensor bias, the engine model is executed and its 

outputs are evaluated against the physical sensor 

measurements. The bias data set, the neural network 

estimator, and the engine model are coordinated by the 

GA in the search for an optimal solution. 

Bias Data Set

The bias data set defines the solution space over which 

the GA searches for an optimal sensor bias solution. It 

is composed of a set of bias vectors, each of which has 

a non-zero value only in the kth entry, defining the bias 

value and also identifying the k

th sensor as biased. A 

vector with zeros in all entries is also included in the 

data set to account for the case where no bias is present. 

The bias values for each sensor are equally spaced, 

based on the noise standard deviation σ over a range of 

possible values. The minimum bias value is defined by 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

5 

the detection threshold while the maximum value is set 

in accordance with a bound that would typically 

disqualify the sensor for being out of range, as shown in 

Figure 4. The detection threshold is set large enough so 

that noise is unlikely to be interpreted as a bias. In this 

paper, the threshold is set to 4σ while the upper bound 

is set to 20σ. 

Neural Network Estimator Design

The neural network estimator is the key element of the 

hybrid architecture. As mentioned earlier, the neural 

network estimator does not need to account for sensor 

bias, but it still has to tolerate the effects of 

measurement uncertainty due to noise. The robustness 

of the estimator can be improved by using noisecorrupted sensor measurements during training so that 

neural networks will learn to distinguish the range of 

measurement shifts due to noise and those due to health 

degradations. However, since the number of health 

degradation scenarios that an engine may encounter is 

virtually infinite, it is still a challenging problem to 

develop an estimator that performs adequately well. It 

was found that sensor measurements from at least two 

operating points were needed in order to achieve the 

desired estimation performance level. This problem 

may be due to sensor location, sensor noise, highly 

nonlinear engine dynamics, or a combination of these 

as discussed earlier. Table 2 compares the performance 

of two estimators; one designed at cruise condition and 

another designed using data from cruise and takeoff 

conditions. For the two-point design, the estimation 

process is initiated after the steady-state data at the 

second operating point are collected. Both of them are 

composed from nine multiple-input, single-output subestimators, each of which was developed using a 

feedforward neural network. They were trained by 

backpropagation using about 3000 degraded engines. 

The single-point design has 12 inputs while the twopoint design has 24 inputs. The table shows the 

standard deviation and mean value of estimation errors. 

The result was obtained using the sensor measurements 

p

Engine

Neural

Network

Estimator

Bias 

Data Set

Engine

Model

y_ref

(Baseline)

y

∆ y

- +

Genetic Algorithm

b

pi ˆ bi

ˆ i yˆ

b

ˆ

errori y _ ˆ

error y_ˆ

+

-

Optimization: Find which minimize 

v

[ ] optoptopt , ybp ˆ ˆ ˆ ,

+

-

+

+

Operating Condition

• Altitude

• Mach

• PLA

p

Engine

Neural

Network

Estimator

Bias 

Data Set

Engine

Model

y_ref

(Baseline)

y

∆ y

- +

Genetic Algorithm

b

pi ˆ bi

ˆ i yˆ

b

ˆ

errori y _ ˆ

error y_ˆ

+

-

Optimization: Find which minimize 

v

[ ] optoptopt , ybp ˆ ˆ ˆ ,

+

-

+

+

Operating Condition

• Altitude

• Mach

• PLA

Figure 3. Hybrid Engine Health Estimation Architecture. 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

6 

of 500 degraded engines without noise. These 500 

engines were not used in the neural network training. 

Although a single-point diagnostic approach is desired 

as discussed earlier, it was found to provide 

unsatisfactory estimation accuracy. Thus a muti-point 

estimator is utilized. It should be noted that some of the 

health parameters are more difficult to accurately 

estimate than others. 

Genetic Algorithm Optimization Process

To find an optimal solution in the bias data set, the GA 

search sequence shown in Figure 3 proceeds as follows. 

First, a bias vector bi

ˆ selected from the bias data set is 

subtracted from physical sensor measurement deltas 

(the deviations from nominal condition) ∆y, and the 

resultant vector is fed into the neural network estimator. 

If the selected bias vector is identical or close to the 

true bias b, then the bias in the measurements is 

cancelled out. This allows the neural network estimator 

to generate an accurate estimation of the health 

parameter vector pi ˆ from the bias-free measurements. 

The engine model is run with inputs of bi

ˆ and pi ˆ to 

synthesize engine sensor outputs i yˆ for comparison 

with the sensor measurements. 

For each selected bias vector bi

ˆ , the following cost 

function, which accounts for the multi-point estimator, 

is computed. 

2

1

1

2

1

2

( ˆ () ˆ )



































 − +















 − = ∑∑ == Takeoff

m

j j

jji

Cruise

m

j j

jji

i W

yy

W

yy J (3) 

where m is the number of sensors and 





 = = otherwise

when kj W

j

j

j σ

σ

3 (4) 

where σj is a standard deviation of noise in sensor j, and 

k indicates the non-zero entry of a selected bias vector. 

The parameter Wj normalizes the estimation error while 

imposing a larger penalty for discrepancies in the k

th



 



 

Measurement Uncertainty

Distribution

Bias

Detection

Range

Detection

Threshold

Upper

Bound













Bias

Detection

Range

Upper

Bound

Detection

Threshold

Sensor Out

of Range

Sensor Out

of Range



 



 

Measurement Uncertainty

Distribution

Bias

Detection

Range

Detection

Threshold

Upper

Bound













Bias

Detection

Range

Upper

Bound

Detection

Threshold

Sensor Out

of Range

Sensor Out

of Range

Figure 4. Measurement Uncertainty Distribution with Bias Detection Thresholds. 

Table 2. Performance Comparison of Estimators 

Single-Point Design 

at Cruise 

Two-Point Design 

at Cruise & Takeoff 

Mean 

Absolute 

Error 

(%) 

Standard 

Deviation 

of 

% Error 

Mean 

Absolute 

Error 

(%) 

Standard 

Deviation 

of 

% Error 

FAN 

Eff 

9.00 13.01 5.55 9.15 

FAN 

Flow 

5.42 9.28 2.92 4.77 

BST 

Flow 

6.08 9.90 5.03 8.55 

HPC 

Eff 

9.64 15.22 4.19 7.79 

HPC 

Flow 

9.39 15.69 5.52 9.30 

HPT 

Eff 

8.86 14.66 4.91 8.50 

HPT 

Flow 

2.94 4.92 1.51 2.65 

LPT 

Eff 

10.33 15.16 6.38 10.09 

LPT 

Flow 

5.63 9.11 2.79 4.70 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

7 

sensor. If a selected bias vector contains a bias 

estimation value in the wrong sensor, the estimation 

error in the k

th entry is magnified. The noise standard 

deviation for the sensors changes with operating point. 

Therefore, in the above equation, Wj and noise 

contained in yj are based on the corresponding sensor σ

values at the specific operating point. However, the σ

value used to create bias intervals in the bias data set is 

based on the σ value at the cruise condition. 

A value indicating the estimation accuracy, or fitness 

value, for each selected bias vector is defined as 

i i J Fitness = K (5) 

where K is a constant for normalization. In this paper, a 

fitness value larger than 1 indicates good agreement 

between model outputs and actual measurements. The 

fitness value becomes larger as the output error between 

i yˆ and y diminishes. 

A unique aspect of the GA search process is that a set 

of multiple points in the solution space is evaluated at 

each iteration, and the content of this set is updated 

from iteration to iteration. In the GA problem setup, 

each bias vector in the data set is referred to as an 

“individual,” and a number of individuals are selected 

from the data set to construct a “population.” At each 

iteration, or “generation,” the entire population is 

evaluated, and a fitness value is assigned to each 

individual. The higher the fitness value, the higher the 

probability that the corresponding individual will 

survive into the next generation. The population of the 

next generation is constructed from individuals of the 

previous generation and individuals newly introduced 

from the data set. As the population is updated from 

generation to generation, those individuals with high 

fitness values will occupy the major portion of the 

population. The objective of the GA optimization is to 

find the best individual among the data set through this 

search process. Unlike gradient search methods, the 

GA search process starts from multiple points set by the 

initial population; this helps to avoid convergence to a 

local peak in the highly nonlinear environment. 

Moreover, the fitness values indicate the level of 

confidence in the estimation. If an appropriate 

estimation set is not found in the search process, the 

fitness value will remain small. This indicates the best 

estimation set should not be relied upon for accurate 

diagnosis of engine health although an anomalous 

condition may exist. 

A GA is generally run for many generations until the 

set of individuals constructing the population converges 

to a single individual. In the current study, the GA is 

run for relatively few generations. In this highly 

nonlinear and noisy environment, it is possible to have 

dissimilar faults producing similar sensor signatures, as 

was illustrated in Figure 2. Running the GA until 

convergence to a single individual can lead to erroneous 

conclusions regarding engine health. After the search 

process, the searched bias vectors are ranked based on 

their corresponding fitness values. A list of several 

fault candidates can help to avoid false alarms or 

missed detections. Moreover, running the GA for fewer 

generations can save a significant amount of computing 

time. 

Results of Hybrid Estimator Performance

This section shows some of the results obtained from an 

extensive assessment of the hybrid estimator. Table 3 

shows the estimation of health parameters from sensor 

measurements which contain no bias. The set of actual 

health parameters shown in Table 3 was not a part of 

the neural network estimator training set. There are no 

clear guidelines to define the adequate performance 

Table 3. Health Parameter Estimation Without 

Sensor Bias 

Health 

Parameter 

Actual 

Condition 

(%) 

Estimated 

Condition 

(%) 

% Error 

*100 ( ˆ )

p − pp

FAN Eff -2.900 -2.793 -3.682 

FAN Flow -1.800 -1.819 1.029 

BST Flow 0.000 0.000 ------- 

HPC Eff -2.300 -2.177 -5.367 

HPC Flow -1.900 -2.016 6.078 

HPT Eff -1.400 -1.612 15.138 

HPT Flow 1.000 0.883 -11.750 

LPT Eff -2.000 -2.199 9.930 

LPT Flow 2.100 2.093 -0.320 

Normalized Estimation Error ( )

3σ

ˆ − yy

Sensor Cruise Takeoff 

 N2 0.750 -0.069 

 N25 -0.155 0.755 

 T27 -0.378 0.007 

 T3 0.482 0.028 

 PS15 0.146 0.029 

 PS21 -0.059 0.163 

 P27D 0.281 0.600 

 PS3 0.155 1.095 

 P42 -0.235 0.467 

 WF36 -0.222 0.412 

 A8 0.198 0.121 

 A16 -0.263 -0.062 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

8 

level in the highly nonlinear environment of the current 

study. In this paper, the performance of the estimator is 

considered satisfactory if the maximum health 

estimation error is less than 30%. Table 3 shows both 

good sensor matching and good health estimation 

accuracy, meeting with the performance requirements. 

It should be noted that estimation accuracy is 

influenced by sensor noise. 

When one of the sensors is biased, the neural network 

estimator alone can no longer accurately estimate health 

parameters. The following example shows a case 

where the fuel flow sensor has a 9.5σ bias with the 

same health degradation as shown in Table 3. This bias 

magnitude is in the medium range of the current 

problem setup. After the GA search process, the hybrid 

estimator provides the rank of bias estimations as 

shown in Table 4 and the corresponding plots shown in 

Figure 5. Table 4 shows the identification numbers of 

biased sensors, bias values, and corresponding fitness 

values. Sensor matching is considered adequate if the 

fitness value is larger than 0.75 and is considered very 

good if the fitness value is larger than 1. Therefore, the 

top four bias estimations are good candidates for 

representing the actual bias. Figure 5 shows the fitness 

values of individuals (bias vectors) selected by the GA 

during the search process. The horizontal axis varies 

from -20σ to 20σ with a 1σ increment. The bias vector 

representing the no-bias case is shown at the center of 

all plots, providing a baseline for comparison between 

estimations with and without bias detection. As 

mentioned earlier, the detection threshold is set to 4σ. 

The bias data set contains 409 individuals and the 

population size is set to 50. The initial population 

included four individuals from each sensor, two 

individuals for each bias direction. 

Table 5 shows the health parameter estimation and 

sensor matching of the estimator with and without bias 

detection. The estimation result of the individual 

ranked first in Table 4 is shown. For the estimator with 

bias detection, the performance requirement is met. 

Although the estimation errors of HPT efficiency and 

HPT flow coefficient are relatively high among the 

health parameters, a similar trend was noticed in the 

previous example where no bias was present, as was 

shown in Table 3. This illustrates the highly effective 

performance of the hybrid estimator in isolating a 

sensor bias. 

The task of bias detection and estimation becomes 

easier for larger biases. With a large bias in the 

measurements, the cost function value of Equation 3 

ideally remains large unless the bias is canceled out by 

an accurate estimate. This task becomes more difficult 

for small biases which are less distinguishable from 

noise. Table 6, Figure 6, and Table 7 show a case 

where the fuel flow sensor has a 4.5σ bias with the 

same health degradation as shown in Table 3. Table 6 

and Figure 6 show that the individuals representing the 

bias in the correct sensor (WF36) no longer dominate 

the GA population as they did in the previous case with 

a larger bias value. Depending on the sensor noise 

profile, this ranking can change, and the correct sensor 

may not be ranked highest. The performance goal of 

the hybrid estimator is to at least capture the correct 

sensor in the ranking of plausible solutions in order to 

avoid missed detection. For smaller bias magnitudes, 

the robustness of the neural network estimator is 

demonstrated. The bias vector representing the no-bias 

case (Sensor ID 0) is ranked 4th overall, and the 

corresponding health estimations and sensor matching 

shown in Table 7 are well within the acceptable range. 

Table 4. Rank of Sensor Bias Estimation After the 

GA Search (Case 1: 9.5σ Bias in WF36) 

Rank Sensor ID Bias Value 

(σ) 

Fitness 

1 10 (WF36) 10 1.036 

2 10 (WF36) 9 1.020 

3 10 (WF36) 11 0.878 

4 10 (WF36) 8 0.852 

5 10 (WF36) 7 0.723 

6 10 (WF36) 12 0.594 

7 10 (WF36) 6 0.554 

8 10 (WF36) 13 0.512 

9 10 (WF36) 5 0.458 

10 10 (WF36) 14 0.402 

−20 0 20 0

0.5

1 N2

Fitness Value

−20 0 20 0

0.5

1 N25

−20 0 20 0

0.5

1 T27

−20 0 20 0

0.5

1 T3

Fitness Value

−20 0 20 0

0.5

1 PS15

−20 0 20 0

0.5

1 PS21

−20 0 20 0

0.5

1 P27D

Fitness Value

−20 0 20 0

0.5

1 PS3

−20 0 20 0

0.5

1 P42

−20 0 20 0

0.5

1 WF36

Fitness Value

−20 0 20 0

0.5

1 A8

−20 0 20 0

0.5

1 A16

Figure 5. Fitness Values of Individuals Selected by 

GA Search. (Case 1: 9.5σ Bias in WF36) 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

9 

Table 5. Health Parameter Estimation With and Without Bias Detection 

(Case 1: 9.5σ Bias in WF36)

 With Bias Detection Without Bias Detection 

Health Parameter Actual 

Condition (%) 

Estimated 

Condition (%) 

% Error Estimated 

Condition (%) 

% Error 

 FAN Efficiency -2.900 -2.788 -3.876 -2.950 1.722 

 FAN Flow -1.800 -1.811 0.596 -1.819 1.076 

 BST Flow 0.000 0.000 ------- -0.134 ------- 

 HPC Efficiency -2.300 -2.172 -5.578 -2.305 0.234 

 HPC Flow -1.900 -2.027 6.658 -1.497 -21.213 

 HPT Efficiency -1.400 -1.614 15.254 -1.715 22.516 

 HPT Flow 1.000 0.875 -12.484 2.201 120.045 

 LPT Efficiency -2.000 -2.197 9.857 -2.303 15.146 

 LPT Flow 2.100 2.083 -0.819 2.393 13.942 

 With Bias Detection Without Bias Detection 

 Error ( )

3σ

ˆ − yy Error ( )

3σ

ˆ − yy

Sensor Actual Bias Estimated 

Bias 

Cruise Takeoff Cruise Takeoff 

N2 0 0 0.751 -0.070 3.432 -0.109 

N25 0 0 -0.154 0.754 -1.896 -0.352 

T27 0 0 -0.377 0.006 0.453 0.078 

T3 0 0 0.482 0.027 0.204 -0.275 

PS15 0 0 0.146 0.030 -1.439 -0.369 

PS21 0 0 -0.058 0.163 0.767 0.100 

P27D 0 0 0.281 0.600 1.217 0.543 

PS3 0 0 0.157 1.091 -3.064 -10.008 

P42 0 0 -0.234 0.466 -0.561 0.194 

WF36 9.5σ 10σ -0.055 0.490 -2.906 -0.645 

A8 0 0 0.198 0.120 2.313 0.397 

A16 0 0 -0.263 -0.063 0.159 -0.488 

Table 6. Rank of Sensor Bias Estimation for Small 

Bias (Case 2: 4.5σ Bias in WF36) 

Rank Sensor ID Bias Value 

(σ) 

Fitness 

1 10 (WF36) 5 1.035 

2 10 (WF36) 4 1.022 

3 10 (WF36) 6 0.878 

4 0 (No bias) 0 0.863 

5 9 (P42) 4 0.828 

6 12 (A16) 4 0.813 

7 12 (A16) 5 0.776 

8 11 (A8) -4 0.776 

9 9 (P42) 5 0.765 

10 12 (A16) 6 0.757 

−20 0 20 0

0.5

1 N2

Fitness Value

−20 0 20 0

0.5

1 N25

−20 0 20 0

0.5

1 T27

−20 0 20 0

0.5

1 T3

Fitness Value

−20 0 20 0

0.5

1 PS15

−20 0 20 0

0.5

1 PS21

−20 0 20 0

0.5

1 P27D

Fitness Value

−20 0 20 0

0.5

1 PS3

−20 0 20 0

0.5

1 P42

−20 0 20 0

0.5

1 WF36

Fitness Value

−20 0 20 0

0.5

1 A8

−20 0 20 0

0.5

1 A16

Figure 6. Fitness Values of Individuals Selected by 

GA Search. (Case 2: 4.5σ Bias in WF36)

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

10 

Concluding Remarks

A hybrid estimation technique for aircraft engine 

performance diagnostics was presented in this paper. 

The hybrid architecture consists of Neural Networks 

and Genetic Algorithms, which function synergistically 

for estimating health parameters from biased sensor 

measurements. Neural networks are well suited for 

estimating health parameters in a highly nonlinear 

environment. However, a major problem arises when 

the size of training data set becomes prohibitively large. 

In order to avoid this problem while improving the 

robustness to measurement uncertainty, Genetic 

Algorithms were applied for sensor bias detection. The 

hybrid estimator exhibited excellent performance when 

at most one sensor was biased. The task of health 

parameter estimation became more difficult when the 

bias was of smaller magnitude and was thus less 

distinguishable from the standard noise level. Since 

measurement shifts due to health degradations are often 

small compared to sensor noise, and distinctive health 

degradations do not necessarily result in distinctive 

measurement shifts, it is difficult to obtain one solution 

with a high level of confidence. This problem was 

handled by ranking individuals in the GA population set 

based on their corresponding fitness values. This 

approach reveals a potential method of reducing the rate 

of false alarms and missed detections. 

There are, however, areas for further improvement. A 

systematic way of selecting and/or locating sensors for 

health estimation is desired. Simply increasing the 

number of sensors for health diagnostics does not 

guarantee improved estimation performance. 

Moreover, as the number of sensors increases, the 

chance of having biases in multiple measurements 

increases. Another desired improvement is a reduction 

of the required computing time. A real-time, on-board 

diagnostic system which can be integrated with a 

control system is desirable, but difficult to achieve with 

the proposed architecture. In future work, new 

approaches that allow improved computing speed 

without sacrificing reliability will be investigated. 

Table 7. Health Parameter Estimation With and Without Bias Detection 

(Case 2: 4.5σ Bias in WF36)

 With Bias Detection Without Bias Detection 

Health Parameter Actual 

Condition (%) 

Estimated 

Condition (%) 

% Error Estimated 

Condition (%) 

% Error 

 FAN Efficiency -2.900 -2.787 -3.887 -2.865 -1.224 

 FAN Flow -1.800 -1.810 0.538 -1.864 3.557 

 BST Flow 0.000 0.000 ------- 0.000 ------- 

 HPC Efficiency -2.300 -2.175 -5.456 -2.228 -3.137 

 HPC Flow -1.900 -2.026 6.624 -1.881 -1.018 

 HPT Efficiency -1.400 -1.608 14.876 -1.642 17.259 

 HPT Flow 1.000 0.877 -12.310 1.235 23.506 

 LPT Efficiency -2.000 -2.197 9.824 -2.227 11.330 

 LPT Flow 2.100 2.085 -0.706 2.220 5.723 

 With Bias Detection Without Bias Detection 

 Error ( )

3σ

ˆ − yy Error ( )

3σ

ˆ − yy

Sensor Actual Bias Estimated 

Bias 

Cruise Takeoff Cruise Takeoff 

N2 0 0 0.759 -0.070 1.237 -0.021 

N25 0 0 -0.149 0.754 -0.365 0.674 

T27 0 0 -0.376 0.006 -0.256 -0.002 

T3 0 0 0.483 0.027 0.409 -0.044 

PS15 0 0 0.144 0.029 -0.075 0.057 

PS21 0 0 -0.057 0.162 -0.014 -0.115 

P27D 0 0 0.283 0.600 0.316 0.278 

PS3 0 0 0.161 1.093 -0.593 -1.506 

P42 0 0 -0.232 0.466 -0.362 0.260 

WF36 4.5σ 5σ -0.052 0.489 -1.617 -0.198 

A8 0 0 0.203 0.120 0.497 0.117 

A16 0 0 -0.260 -0.063 -0.269 -0.201 

NASA/TM—2001-211088
 

American Institute of Aeronautics and Astronautics 

11 

References

1

 Simon, D. L., “An Overview of the NASA Aviation 

Safety Program Propulsion Health Monitoring 

Element,” Paper AIAA-2000-3624, AIAA 36th Joint 

Propulsion Conference, Huntsville, AL, 2000. 

2

 Doel, D. L., “TEMPER - A Gas Path Analysis Tool 

for Commercial Jet Engines,” ASME Journal of 

Engineering for Gas Turbines and Power, Vol. 116, pp. 

82-89, 1994. 

3

 Doel, D. L., “An Assessment of Weighted-LeastSquares-Based Gas Path Analysis,” ASME Journal of 

Engineering for Gas Turbines and Power, Vol. 116, pp. 

336-373, 1994. 

4

 Volponi, A. J., “Sensor Error Compensation in Engine 

Performance Diagnostics,” ASME Paper 94-GT-58, 

International Gas Turbine and Aeroengine Congress 

and Exposition, The Hague, Netherlands, 1994. 

5

 Kerr, L. J., Nemec, T. S., and Gallops, G. W., “RealTime Estimation of Gas Turbine Engine Damage Using 

a Control Based Kalman Filter Algorithm,” ASME 

Paper 91-GT-216, International Gas Turbine and 

Aeroengine Congress and Exposition, Orlando, FL, 

1991. 

6

 Luppold, R. H., Roman, J. R., Gallops, G. W., and 

Kerr, L. J., “Estimating In-Flight Engine Performance 

Variations Using Kalman Filter Concepts,” Paper 

AIAA-89-2584, AIAA 25th Joint Propulsion 

Conference, Monterey, CA, 1989. 

7

 DePold, H. R., and Gass, F. D., “The Application of 

Expert Systems and Neural Networks to Gas Turbine 

Prognostics and Diagnostics,” ASME Journal of 

Engineering for Gas Turbines and Power, Vol. 121, pp. 

607-612, 1999. 

8

 Zedda M., and Singh, R., “Fault Diagnosis of a 

Turbofan Engine Using Neural Networks: A 

Quantitative Approach,” Paper AIAA 98-3602, AIAA 

34th Joint Propulsion Conference, Cleveland, Oh, 1998. 

9

 Zedda, M., and Singh, R., “Gas Turbine Engine and 

Sensor Fault Diagnosis Using Optimisation 

Techniques,” Paper AIAA 99-2530, AIAA 35th Joint 

Propulsion Conference, Los Angeles, CA, 1999. 

10 Gulati, A., Zedda, M., and Singh, R., “Gas Turbine 

Engine and Sensor Multiple Operating Point Analysis 

Using Optimization Techniques,” Paper AIAA 2000-

3716, AIAA 36th Joint Propulsion Conference, 

Huntsville, AL, 2000. 

11 Urban, L. A., “Gas Path Analysis Applied to Turbine 

Engine Condition Monitoring,” Paper AIAA 72-1082, 

AIAA 8th Joint Propulsion Specialist Conference, New 

Orleans, LA, 1972. 

12 Adibhatla, S., and Lewis, T. J., “Model-Based 

Intelligent Digital Engine Control (MoBIDEC),” Paper 

AIAA-97-3192, AIAA 33rd Joint Propulsion 

Conference, Seattle, WA, 1997. 

13 Stamatis, A., Mathioudakis, K., Berios, G., and 

Papailiou, K., “Jet Engine Fault Detection with 

Differential Gas Path Analysis at Discrete Operating 

Points,” ISABE 89-7133. 

NASA/TM—2001-211088
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Takahisa Kobayashi and Donald L. Simon

A Hybrid Neural Network-Genetic Algorithm Technique

for Aircraft Engine Performance Diagnostics

In this paper, a model-based diagnostic method, which utilizes Neural Networks and Genetic Algorithms, is investigated.

Neural networks are applied to estimate the engine internal health, and Genetic Algorithms are applied for sensor bias

detection and estimation. This hybrid approach takes advantage of the nonlinear estimation capability provided by neural

networks while improving the robustness to measurement uncertainty through the application of Genetic Algorithms. The

hybrid diagnostic technique also has the ability to rank multiple potential solutions for a given set of anomalous sensor

measurements in order to reduce false alarms and missed detections. The performance of the hybrid diagnostic technique

is evaluated through some case studies derived from a turbofan engine simulation. The results show this approach is

promising for reliable diagnostics of aircraft engines.