Multi-mode diagnosis of a gas turbine engine using an adaptive neuro-fuzzy system

Houman HANACHI,Jie LIU,Christopher MECHEFSKE

aNational Research Base of Intelligent Manufacturing Service,Chongqing Technology and Business University,Chongqing 400067,China

bDepartment of Mechanical and Materials Engineering,Queen’s University,Kingston,ON K7L 3N6,Canada

cDepartment of Mechanical and Aerospace Engineering,Carleton University,Ottawa,ON K1S 5B6,Canada

1.Introduction

Components of Gas Turbine Engines(GTEs)operate in harsh environments that create different degradation mechanisms in the parts.The degradation mechanisms lead to growth of faults in various modes and result in deviation of the performance from that of the brand-new condition.In the compressor section,erosion of the blades and vanes and the fouling phenomena lead to loss of the isentropic efficiency and decrease of the massflow capacity,given the shaft speed and the pressure ratio.1In the turbine section,however,the massflow capacity would increase,while the isentropic efficiency declines with degradation for a given pressure ratio and shaft speed.2,3It is a common practice to utilize the symptoms of the isentropic efficiency’s decline and the mass flow capacity’s change to quantify the degradation level in both compressors and turbines.4,5Degradation of the parts moves the operating match point of GTE subsystems away from the optimal criteria and results in deviation of gas path parameters from those of a healthy condition.At the same time,it leads to loss of the thermal efficiency and extra fuel consumption at the system level.6Deterioration of the GTE performance is not necessarily rooted in part degradation.When the ambient condition changes or the GTE is operated at off-design control settings,e.g.,partial load,the performance of the GTE will deteriorate.Such deteriorations automatically reverse when the operating conditions return to on-design conditions.7It is critical for a GTE diagnosis system to separate the deterioration causes and to isolate those attributable to degradation of the components but not off-design control settings.

Condition-based health management strategies tend to extract real-time health-related information from systems so that the required maintenance actions can be taken at the right time for the right part(s).GTE measurements of gas-path parameters contain valuable information on the health conditions of the parts;however,the number of operating parameters recorded with a GTE performance monitoring system is limited by the cost,maintenance,and other technical reasons.In many conventional GTEs used for power generation,measurements are limited to a few parameters such as power,shaft speed,EGT,and fuelflow.As a result,extraction of information from data analysis becomes challenging.At the same time,small variations of the measurements due to component faults can be masked by signal noise,if the measurement noise is relatively high.This calls for competent health monitoring and diagnostic techniques that manage to extract health information from limited measurements contaminated with noise.

Nomenclature Symbols ANFIS adaptive neuro-fuzzy inference system ANN artificial neural network APU auxiliary power unit D(·) diagnostic model e diagnostic error EGT exhaust gas temperature GTE gas turbine engine G(˙s)measurement model N shaft speed NRMSE normalized root mean squared error P pressure PW power R linear fuzzy rules s measurement signal SNR signal to noise ratio T temperature u control input v ambient condition W massflow w weight of fuzzy rules x health state y performance parameter η isentropic efficiency ρ degradation symptom σ standard deviation of noise φ relative humidity Subscripts A actual value am ambient C compressor F fuel i inlet M measured parameter o outlet T turbine

There are two main approaches for fault diagnostics:system identification and pattern recognition.8In system identifi-cation where a measurement model for a system is required,the objective is to update internal fault-related parameters of the system model so that model outputs become consistent with measurements.It requires a reliable measurement model for the system that establishes functional relationships between internal health parameters and measurements.9Pattern recognition is a practical computational approach that can be applied effectively if an accurate measurement model is not available.Variations of the internal health parameters of gas turbines create distinct clusters in the multi-dimensional space of measurable operating data.The task of pattern recognition is to classify those clusters and attribute them to the corresponding faults.10Fig.1 shows the process of GTE fault detection through pattern recognition in a multi-dimensional measurement data space,wherexrepresents the health condition of the system andy,uandvrefer to the performance parameters,control inputs and ambient conditions respectively.The dimensions are limited in this case to three for improved visualization.This is an effective approach for fault detection and isolation in GTEs with a limited number of measurable parameters.Mathematically,pattern recognition algorithms are mapping functions,which need a training process to set their internal parameters.After the training process,upon receiving a new set of measurements,the classification function maps the inputs to the corresponding classes of faults.Various classification techniques including fuzzy-logic,11–13probabilistic networks,14,15artificial neural networks,16,17support vector machines,18stochastic neuro-fuzzy inference systems,19and statistical-based approaches20have been utilized for GTE diagnosis by pattern recognition.In a comparative study,Bettocchi et al.showed that under measurement uncertainty,an ANFIS structure could lead to superior diagnostic results compared to those obtainable from Artificial Neural Networks(ANNs).21Despite significant research work,for most conven-tional GTEs where the number of GTE measurements is limited,it is a challenge to extract accurate diagnostic results,and it is critical to identify parameters that can improve diagnostic results if measured and utilized in the diagnostic algorithm.

To address the stated problem,in this work,an Adaptive Neuro-Fuzzy Inference System(ANFIS)-based diagnostic scheme is structured to receive GTE measurement signals and map the results to a degradation symptom space per the following procedure.An ANFIS framework for pattern recognition on GTE degradation is developed in Section 2.In Section 3,gas-path parameters of a single-shaft GTE are generated under different ambient conditions,control settings,and signal to noise ratios using a high-fidelity GTE model for training and testing the framework.The performance of the diagnostic framework with diverse combinations of measurable parameters and noise levels is verified in Section 4,and a conclusive discussion on the results is presented at the end.

Fig.1 Classification of measurement sets ［y，u，v］linto clusters of different health states xj.

2.A data-driven model for GTE degradation estimation

For a GTE,the set of real-time performance parametersyis dependent on the control inputu,the ambient conditionv,and the health state of the partsxas follows:

whereGis the measurement model of the GTE.A fault detection algorithm shouldfind the health statex,so that the observed performance parametersyMbecome consistent with prediction;x|G（x，u，v）=yM,which is the answer to the inverse measurement model with respect toxas

Accurate measurement models require complete information about properties and performances of GTE parts,yet creating inverse models adds to the complexity of the problem.If sufficient data,from a GTE experiencing degradation with a known health state,are available,a trainable data-driven model can be utilized for mapping the measured data into the known health state.With high-dimensionality of the input data,numerical models such as multi-variate polynomial regression,artificial neural networks,and ANFIS frameworks have been practiced by researchers.22–24For this mapping problem,an ANFIS framework is employed for two main reasons:the degree of functionfitting can be controlled within the membership functions with respect to sensitivity to each input,and it shows a high repeatability for parameter setting when trained on a set of training data,as opposed to an ANN.25,26

ANFIS frameworks were introduced by Jang in the 1990s.27Unlike the conventional fuzzy systems that require expert knowledge in a design process,an ANFIS makes use of adaptive capability of the neural network to adjust the parameters of a fuzzy model to optimallyfit the training data.

Given that sufficient data become available on GTE performance at ambient conditionvand control settinguunder a known state of healthxj,an ANFIS framework can be developed with the following procedure,as shown in Fig.2.

(1)Afirst-order Sugeno model is employed for the fuzzy inference process.

(2)In thefirst layer,the set of inputs comprises the available measurements on （y，u，v）at a given instance.

(3)The last layer includes the magnitude of the jthdegradation symptom as the health state xj,associated with the measurement data in thefirst layer.

(4)Generalized bell-shaped membership functions are utilized in the second layer.The number of membership functions is a design parameter for the ANFIS structure,and the optimum number can be evaluated when practicing the model.Fig.1 shows two membership functions for each input.

Fig.2 ANFIS framework to estimate the j th degradation symptom,given measurements on performance,control,and ambient condition.

(5)In the third layer,the linear fuzzy rules corresponding to all possible combinations of the membership functions are situated.

(6)The fourth layer includes weights of the rules,found from multiplication of the results of the membership functions.

(7)In thefifth layer,the summation of layer three,weighted with layer four,is calculated.

Once the framework is structured,the training data set is introduced to the model,so that the parameters of the membership functions and the fuzzy rules in the second and third layers are adjusted.After the training process,the model can be used for degradation estimation by feeding measurement data as inputs.

3.Performance data for a GTE experiencing degradation

The performance of a GTE deteriorates with degradation of the components.As explained in the Introduction,degradation of GTE components in the compressor and turbine sections are quantitatively represented by two metrics corresponding to their dominant symptoms,i.e.,decline of the isentropic effi-ciency ρηand change of the flow capacity ρW,4,5as follows:

whereWCAand ηCAare the actual mass flow and isentropic efficiency of the compressor,respectively,whereasWCand ηCare the expected values at the same operating condition for the healthy compressor.Considering the increase of the massflow capacity for turbines experiencing degradation,turbine degradation symptoms are defined as:

Loss of the isentropic efficiency in the compressor has been reported between 0.5%to 0.8%against a 1%decrease in the massflow capacity.28,29In the turbine section,however,loss of the isentropic efficiency and change of the massflow capacity depend on the dominant fault mode in the parts,i.e.,increase of the tip clearance,surface roughness,and profile loss.2,30A ratio between the two symptoms is not definite in either case,and a competent diagnostic system should be able to detect them independently.

To acquire performance data under diverse operating conditions from a GTE with multiple fault modes,a high-fidelity GTE model is utilized to simulate performance data for a single-shaft GTE.The GTE model was developed and verified as a reliable virtual tool through past research work by the authors.31Table 1 includes the input and output parameters of the GTE model,as formulated in Eq.(1).

Design information on the single-shaft GTE,including numerical tables for the compressor and turbine maps,are utilized for performance simulation.For the health state,degradation with three intensity levels of 0%(healthy),2%(mild),and 4%(severe)are considered at each degradation symptom.GTE performance is simulated at six power levels and three ambient temperatures for each health state,as shown in Table 2.As a result,performance parameters are available at 1458 operating scenarios,i.e.,combinations of health state,ambient conditions,and control settings.Fig.3 shows the resulting performance parameters with different operating scenarios forTam=15°C.

GTE measurable parameters,i.e.,ambient condition,control setting,and performance parameters,include measurement noise.The noise level depends on various factors within the GTE system and the surrounding environment.To verify the developed diagnostic framework,zero mean Gaussian noise ε～N（0，σ2）from a 30 dB to 80 dB Signal to Noise Ratio(SNR)is introduced to the GTE measurements,where σ is the standard deviation of the noise for a measurement signalsover the operating scenariosjas follows:

Table 1 Measurable parameters and health state.

Table 2 Assumptions for GTE operating scenarios.

Fig.3 GTE performance parameters at different health states and power levels.

4.Diagnostic results of the framework

The developed framework should estimate the health state of the GTE based on Eq.(2).Considering the variable parameters of the system as inputs for diagnosis,i.e.,v= ［Tam］,u= ［PW］,andy= ［WF，EGT，TCo，PCo，TTi，WT，...］,the diagnostic modelDtakes the following functional form:

Under a known health state,the GTE model solves for gaspath parameters,once the ambient condition,shaft speed,and power are determined.32From the mathematical prospective,if any of the degradation symptoms is unknown,then many gaspath parameters are required,so that an enough number of equations become available to determine the system.As a result,at least four performance parameters are needed in Eq.(6)to determine the severity level of four degradation symptoms.In practice,the number of parameters measured in conventional GTEs is limited due to economic and technical reasons,and diagnostic techniques are expected to work using the limited readings from a GTE.Among the performance parameters,WFand EGT are always measured by the GTE operating system.The compressor discharge temperatureTCoand pressurePCoare also available in most of modern GTEs.

4.1.Diagnosis with determined and undetermined faulty sections

When studying the short-term degradation of a GTE,the dominant growing fault modes correspond to the compressor section.The long-term degradation of the GTE can be observed by monitoring the performance,right after the compressor wash,when the effects of compressor fouling are removed.As a general case,both short-term and long-term degradations do occur concurrently.To verify the performance of the diagnostic framework in each condition,the following three degradation conditions are considered for running.

(1)Compressor degradation,i.e.,ρWTand ρηTare constant.

(2)Turbine degradation,i.e., ρWCand ρηCare constant.

(3)A combination of compressor and turbine degradations.

With performance parametersWF，EGT，TCoandPCoas input signals of the diagnostic framework,Fig.4 shows the diagnostic results for a combination of compressor and turbine degradations trained and run with non-noisy signals.The results are shown for 81 health states at constant power and constant ambient temperature.It can be seen that the diagnostic framework successfully detects and estimates the degradation level for all degradation symptoms.

To compare the diagnostic performances in three degradation conditions,i.e.,compressor,turbine,and combined degradations,we obtain the normalized root mean square error(NRMSE)of the results as metrics of the errors33as follows:

whereeijis the estimation error for the degradation symptomxi∈ ｛ρWC，ρηC，ρWT，ρηT｝ on a particular scenarioj,ranging onnpopulation.

Fig.4 Diagnostic results of combined degradation at Tam=15°C and PW=2.0 MW.

Fig.5 compares the diagnostic errors in the three aforementioned degradation conditions.When the degradation is exclusive to one section,i.e.,the compressor or the turbine,diagnostic errors are tangibly smaller than that of the combined degradation.Taking ρWCsymptom for instance,the diagnostic error is 0.013 when the degradations are limited to the compressor,whereas the error reaches 0.081 if the degradations are to be estimated in both the compressor and the turbine,which is still fairly acceptable.

Fig.5 Diagnostic errors with exclusive compressor degradation,exclusive turbine degradation,and combined degradation.

4.2.Enhancement of the measurement data set

Gas path parameters are highly correlated and measurement signals are noisy.It is expected that more measurements on gas-path parameters would lead to better diagnostic results due to redundancy.34To investigate the effects of additional performance parameters on diagnostic accuracy,measurements of the exhaust massflowWTand the turbine inlet temperatureTTiare added to the sets of input parameters respectively,and diagnostic frameworks are structured and trained with three different sets of performance parameters:

Diagnostic results for Cases 2 and 3 for selected operating scenarios are shown in Fig.6,comparable with the results of Case 1 in Fig.4.A slight improvement in the results of Cases 2 and 3 is visually observable.

Diagnostic errors of the three cases based on Eq.(7)are presented in Fig.7.For Cases 2 and 3,whereWTandTTiare respectively added to the input parameters,the diagnostic errors decrease,with respect to Case 1.We can generally conclude that estimation accuracy increases when further measurementsfrom GTE performanceparametersbecome available.Further discussion on the effects of measured parameters on degradation estimation accuracy is provided in Section 4.3.

4.3.Effect of the measurement noise

Despite the advancements in electronics and signal processing,measurement noise cannot be entirely eliminated from a signal.When training a diagnostics classifier on noisy data,the parameters of the fuzzy model typically will not adjust optimally,and after training,using noisy test data would result in further errors in the results.In this section,we investigate the robustness of the developed framework to significant measurement noise.

From Section 3,GTE operating data are available at different noise levels.By training and running the diagnostic framework on operating data with different SNR levels,i.e.,from 30 dB to 80 dB,diagnostic errors are calculated with Eq.(7)as plotted in Fig.8.As expected,diagnostic errors decline with improvement of the SNR in all three cases.To fully investigate the effect of measurement redundancy on improving the diagnostic performance,the differences of errors for Cases 2 and 3 with respect to Case 1 are calculated and shown in Fig.9.

With regard to the obtained results in Figs.8 and 9,the following conclusions can be suggested:

(1)Diagnostic errors decline with improvement of the SNR in all three cases on four degradation symptoms,as observed in Fig.8.

(2)When signals are highly noisy,i.e.,SNR=30 dB,additional measurements on either WTor TTido not improve the diagnostic performance.It should be noted that performance parameters are highly dependent on degradation symptoms.When themeasured parameters include high levels of noise,the classifier finds the corresponding degradation symptoms matching the noisy signals,and that naturally leads to erroneous results.

Fig.6 Diagnostic results with different sets of performance parameters at Tam=15°C and PW=2.0 MW.

(3)Degradation symptoms of ρηCand ρηTcan be effectively identified by the four parameters WF，EGT，TCoand PCo,as in Case 1.As shown in Fig.9,diagnostic accuracy for the mentioned symptoms does not practically improve when additional measurements on WTand TTiare added to the inputs in Cases 2 and 3.

(4)Using the turbine massflow WTin Case 2 improves the diagnostic results on the massflow variation symptoms in both the compressor and turbine sections,especially from 35 to 60 SNR dB,where the diagnostic error improves over 10%for ρWCand 5%for ρWT,as shown in Fig.9.

(5)Using the turbine inlet temperature TTiresults in a small improvement on diagnosis of the massflow variation symptoms ρWCand ρWT,but barely reaches 5%,as shown in Fig.9,in Case 3.

Fig.7 Diagnostic errors with different sets of performance parameters.

Fig.8 Effect of measurement noise on diagnostic error.

5.Conclusions

In this work,a fault diagnostic framework has been proposed and developed for GTEs based on an adaptive neuro-fuzzy inference system.The framework receives operating parameters available from a GTE to estimate degradation symptoms in the compressor and turbine sections.The dominant degradation symptoms,i.e.,variation of the massflow capacity and isentropic efficiency decline in both sections,are quantitatively defined and utilized for this purpose.To verify the performance of the diagnostic framework on GTE data,gaspath parameters were generated by a high-fidelity GTE model under various operating scenarios,i.e.,diverse combinations of degradation symptoms （ρWC，ρηC，ρWT，ρηT）at healthy,mild,and sever levels,ambient conditions （Tam，Pam，φam）,and controlsettings （PW，N）.Four gas-path parameters,i.e.,WF，EGT，TCoandPCoavailable with most of GTEs,were separated for training the diagnostic framework.

Atfirst,to verify the diagnostic performance of the framework using the aforementioned gas-path parameters,three degradation conditions,i.e.,exclusive compressor degradation,exclusive turbine degradation,and a combination of both degradations,were considered.By training and running the diagnostic framework,the results show that it can effectively detect and estimate the degradation symptoms in all conditions;however,the estimation accuracy would be higher if the faulty section is known beforehand.

To improve diagnostic accuracy for the combined degradation condition,redundant information from gas-path parameters,i.e.,WTandTTi,were added to the diagnostic framework inputs respectively.The preliminary results show that additional gas-path data improve the diagnostic performance and result in a more accurate degradation estimation when mea-surement signals are virtually noiseless.For fault diagnostics with noisy gas-path signals,the results show that usingWTmeasurements improves the results on massflow capacity variation symptoms in both the compressor and the turbine,whereasTTimeasurements have a smaller effect for improving the diagnostic results.

Fig.9 Improvement of diagnostic errors in Cases 2 and 3,compared to error of Case 1.

The study clearly supports the concept of the developed ANFIS-based diagnostic framework for real-time fault detection and degradation estimation for GTE faults using limited gas-path data.The study also provides metrics for diagnostic uncertainty when measurement signals are noisy at different SNR levels.The strength of the developed framework is in separating and estimating multi-mode faults while degradation symptoms are randomly combined.In real conditions,degradation symptoms in GTE subsystems grow gradually with a slow pace and they are interdependent,e.g.,a massflow capacity decrease and an isentropic efficiency decline of the compressor are correlated.In the next step of the research,knowledge of the dependency and the growth rates of fault symptoms will be utilized on real GTE operating data with gradual degradation,to extend and verify the performance of the developed diagnosticframework on pseudo-continuousdegradation conditions.

Acknowledgements

Thisprojectwasfinanciallyco-supported by Fond de Recherche Nature et Technologies(FRQNT)from the Quebec government in Canada,the Natural Sciences and Engineering Research Council(NSERC)of Canada,and Life Prediction Technologies Inc.(LPTi)in Ottawa,Canada.

1.Diakunchak IS.Performance deterioration in industrial gas turbines.J Eng Gas Turbines Power1992;114(2):161–8.

2.Granovskiy A,Kostege M,Lomakin N.Parametrical investigation of turbine stages with open tip clearance for the purpose of stage efficiency increase.Proceedings of ASME turbo expo 2010 conference;2010 June 14–18.Glasgow,UK.New York:ASME;2010.p.1425–32.

3.Matsuda H,Otomo F,Kawagishi H,Inomata A,Niizeki Y,Sasaki T.Influence of surface roughness on turbine nozzle profile loss and secondary loss.Proceedings of ASME turbo expo 2006 conference;2006 May 8–11.Barcelona,Spain.New York:ASME;2006.p.781–8.

4.Panov V.Auto-tuning of real-time dynamic gas turbine models.Proceedings of ASME turbo expo 2014 conference;2014 June 16–20;Du¨sseldorf,Germany.New York:ASME;2014.

5.Hanachi H,Liu J,Banerjee A,Chen Y.Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbinedegradation estimation.MechSystSignalProcess2016;72–73:32–45.

6.Kurz R,Brun K,Wollie M.Degradation effects on industrial gas turbines.J Eng Gas Turbines Power2009;131(6):62401.

7.Petek J,Hamilton P.Performance monitoring for gas turbines.J Orbit2005;25(1):65–8.

8.Loboda I.Gas turbine diagnostics,performance and robustness of gas turbines.[Internet].[cited 2017 Nov.9];Available from:https://www.intechopen.com/books/efficiency-performance-androbustness-of-gas-turbines/gas-turbine-diagnostics.

9.Loboda I.Gas turbine condition monitoring and diagnostics,gas turbines.[Internet].[cited 2017 Nov.9];Available from:https://www.intechopen.com/books/gas-turbines/gas-turbine-conditionmonitoring-and-diagnostics.

10.Mohri M,Rostamizadeh A,Talwalkar A.Foundations of machine learning.Cambridge:MIT Press;2012.

11.Ganguli R,Verma R,Roy N.Soft computing application for gas path fault isolation.Proceedings of ASME turbo expo 2004 conference;2004 June 14–17;Vienna,Austria.New York:ASME;2004.p.499–508.

12.Marinai L,Singh R.A fuzzy logic approach to gas path diagnostics in aero-engines.Computational intelligence in fault diagnosis.London:Springer;2006.p.37–79.

13.Mohammadi E,Montazeri-Gh M.A fuzzy-based gas turbine fault detection and identification system for full and part-load performance deterioration.Aerosp Sci Technol2015;46:82–93.

14.Aretakis N,Roumeliotis I,Alexiou A,Romesis C,Mathioudakis K.Turbofan engine health assessment fromflight data.J Eng Gas Turbines Power2014;137(4):41203.

15.Mathioudakis K,Romessis C.Probabilistic neural networks for validation of on-board jet engine data.Proc Inst Mech Eng Part G J Aerosp Eng2004;218(1):59–72.

16.Joly R,Ogaji S,Singh R,Probert S.Gas-turbine diagnostics using artificial neural-networks for a high bypass ratio military turbofan engine.Appl Energy2004;78(4):397–418.

17.Loboda I,Feldshteyn Y,Ponomaryov V.Neural networks for gas turbine fault identification:multilayer perceptron or radial basis network?Int J Turbo Jet-Engines2012;29(1):37–48.

18.Vieira FM,de Oliveira BC,Nascimento CL,Fitzgibbon KT.Health monitoring using support vector classification on an auxiliary power unit.IEEE aerospace conference;2009 March 7–14;Big Sky,MT,USA.Piscataway(NJ):IEEE Press;2009.p.1–7.

19.Ghiocel D,Altmann J.Critical modeling issues for prediction of turbine performance degradation:use of a stochastic-neuro-fuzzy inference system.Proceedings of 42th AIAA/ASME/ASCE/AHS/ASC structures,structural dynamics and materials conference and exhibit;2001 April 16–19;Seattle,WA,USA.Reston:AIAA;2001.

20.Panov V.Gas turbine performance diagnostics and fault isolation based on multidimensional complex health vector space.Proceedings of 11th European conference on turbomachineryfluid dynamics&thermodynamics;2015 March 23–27;Madrid,Spain.

21.Bettocchi R,Pinelli M,Spina PR,Venturini M.Artificial Intelligence for the diagnostics of gas turbines-part II:neurofuzzy approach.J Eng Gas Turbines Power2007;129(3):720–9.

22.Loboda I,Feldshteyn Y.Polynomials and neural networks for gas turbine monitoring:a comparative study.Proceedings of ASME turbo expo 2010 conference;2010 June 14–18;Glasgow,UK.New York:ASME;2010.p.417–27.

23.Salahshoor K,Khoshro MS,Kordestani M.Fault detection and diagnosis of an industrial steam turbine using a distributed configuration of adaptive neuro-fuzzy inference systems.Simul Model Pract Theory2011;19(5):1280–93.

24.Cavarzere A,Venturini M.Application of forecasting methodologies to predict gas turbine behavior over time.J Eng Gas Turbines Power2012;134(1):12401.

25.Cohen ME,Hudson DL.Comparative approaches to medical reasoning.In:Comparative approaches to medical research,vol.3.Singapore:World Scientific;1995.

26.Hanachi H,Liu J,Banerjee A,Chen Y.Effects of humidity condensation on the trend of gas turbine performance deterioration.J Eng Gas Turbines Power2015;137(12):122605.

27.Jang JSR.ANFIS:adaptive-network-based fuzzy inference system.IEEE Trans Syst Man Cybern1993;23(3):665–85.

28.Tarabrin AP,Schurovsky VA,Bodrov AI,Stalder J-P.Influence of axial compressor fouling on gas turbine unit performance based on different schemes and with different initial parameters.Proceedings of ASME international gas turbine and aeroengine congress and exhibition;1998 June 2–5;Stockholm,Sweden.New York:ASME;1998.p.V004T11A006.

29.Melino F,Morini M,Peretto A,Pinelli M,Ruggero SP.Compressor fouling modeling:relationship between computational roughness and gas turbine operation time.J Eng Gas Turbines Power2012;134(5):52401.

30.Montis M,Niehuis R,Fiala A.Aerodynamic measurements on a low pressure turbine cascade with different levels of distributed roughness.Proceedings of ASME turbo expo 2011 conference;2011 June 6–10;Vancouver,BC,Canada.New York:ASME;2011.p.457–67.

31.Hanachi H,Liu J,Banerjee A,Chen Y.Effects of the intake air humidity on the gas turbine performance monitoring.Proceedingsof the ASME turbo expo 2015 conference;2015 June 15–19;Montreal,QC,Canada,New York:ASME;2015.p.V006T05A018.

32.Hanachi H,Liu J,Banerjee A,Chen Y,Koul A.A physics-based modeling approach for performance monitoring in gas turbine engines.IEEE Trans Reliab2015;64(1):197–205.

33.Hyndman RJ,Koehler AB.Another look at measures of forecast accuracy.Int J Forecast2006;22(4):679–88.

34.Zedda M,Singh R.Gas turbine engine and sensor fault diagnosis using optimization techniques.JPropulsPower2002;18(5):1019–25.