Data-Driven Multimode Fault Detection for Wind Energy Conversion Systems

9th IFAC Symposium on Fault Detection, Supervision and 9th IFAC on Fault Detection, Supervision and Safety of Symposium Technical Processes 9th IFAC Symposium on Fault Detection, Supervision and Safety Processes September 2-4, 2015. Arts et Métiers ParisTech, Paris, France Available online at www.sciencedirect.com Safety of of Technical Technical Processes September 2-4, 2015. Arts et Métiers ParisTech, Paris, France September 2-4, 2015. Arts et Métiers ParisTech, Paris, France

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Data-Driven Multimode Fault Data-Driven Multimode Fault Data-Driven Multimode Fault for Wind Energy Conversion for Wind Energy Conversion for Wind Energy Conversion

Detection Detection Detection Systems Systems Systems

Adel Haghani ∗∗ Minjia Krueger ∗∗ Torsten Jeinsch ∗∗ ∗∗ ∗∗ ∗∗∗ Jeinsch ∗ ∗ ∗∗ ∗ Adel Haghani Minjia Krueger Torsten ∗ ∗∗ StevenMinjia X. Ding Peter Engel Krueger Adel Haghani Torsten ∗∗ ∗∗∗ Jeinsch Steven ∗∗ Peter ∗∗∗ Steven X. X. Ding Ding ∗∗ Peter Engel Engel ∗∗∗ ∗ Institute of Automation, University of Rostock, Richard-Wagner str. ∗ ∗ University of Rostock, ∗ Institute of Automation, 31 , 18119 Rostock, Institute of Automation, University of Germany Rostock, Richard-Wagner Richard-Wagner str. str. ∗∗ 31 , 18119 Rostock, Germany Institute of Automatic control and Complex Systems, University of 31 , 18119 Rostock, Germany ∗∗ ∗∗ Institute of control Systems, University ∗∗ Duisburg-Essen, Bismarckstr. 81,Complex 47057 Duisburg, Institute of Automatic Automatic control and and Complex Systems,Germany University of of ∗∗∗ Duisburg-Essen, Bismarckstr. 81, PC-Soft GmbH, Senftenberg, GermanyGermany Duisburg-Essen, Bismarckstr. 81, 47057 47057 Duisburg, Duisburg, Germany ∗∗∗ ∗∗∗ PC-Soft GmbH, Senftenberg, Germany ∗∗∗ PC-Soft GmbH, Senftenberg, Germany Abstract: In this paper a data-driven fault detection scheme for wind energy conversion system Abstract: this paper fault detection for is proposed.In uses the offline of the wind energy turbineconversion in a widesystem range Abstract: InThe this method paper a a data-driven data-driven faultmeasurements detection scheme scheme for wind wind energy conversion system is proposed. The method uses the offline measurements of the wind turbine wide range of operating points and builds a monitoring system which is able to detect faults is proposed. The method uses the offline measurements of the wind turbine in in aa with wide higher range of and a system which detect with detection ratepoints compared to the classical data-driven Theto characteristics of of operating operating points and builds builds a monitoring monitoring systemtechniques. which is is able able tononlinear detect faults faults with higher higher detection rate compared to data-driven techniques. The of wind turbine approximated by multiple piece-wise linear systems and hencecharacteristics the monitoring detection rateare compared to the the classical classical data-driven techniques. The nonlinear nonlinear characteristics of wind turbine are approximated by multiple piece-wise linear systems and hence the monitoring scheme is robust model uncertainties which maylinear arisesystems due to nonlinearity of the system. wind turbine are against approximated by multiple piece-wise and hence the monitoring scheme against uncertainties may to the Moreover, the proposed method is able to which discriminate thedue faults which are of the scheme is is robust robust against model model uncertainties which may arise arise due to nonlinearity nonlinearity ofaffecting the system. system. Moreover, the is to the are the power production in the method wind energy The effectiveness of which the monitoring scheme Moreover, the proposed proposed method is able ablesystem. to discriminate discriminate the faults faults which are affecting affecting the power production in the wind energy system. The effectiveness of the monitoring scheme is demonstrated thewind data energy collected from The different 2MW wind turbines. The superior power productionusing in the system. effectiveness of the monitoring scheme is the collected from different 2MW turbines. The superior performance of theusing proposed method is further compared the wind classical data-driven is demonstrated demonstrated using the data data collected from differentwith 2MW wind turbines. The methods superior performance of and the results are proposed discussed.method performance of the the proposed method is is further further compared compared with with the the classical classical data-driven data-driven methods methods and and the the results results are are discussed. discussed. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Wind energy conversion systems, Fault detection, Data-driven, Multimode Keywords: Wind Wind energy energy conversion conversion systems, systems, Fault Fault detection, detection, Data-driven, Data-driven, Multimode Multimode approaches Keywords: approaches approaches 1. INTRODUCTION historical data to develop monitoring scheme Ding (2014); 1. INTRODUCTION INTRODUCTION historical data 1. Haghani (2014). historical data to to develop develop monitoring monitoring scheme scheme Ding Ding (2014); (2014); Haghani (2014). With the fast growing capacity of the wind power instal- Haghani (2014). With the the fast growingoncapacity capacity ofoperation the wind wind and power instal- Artificial intelligence (AI), principal component analysis lations, thefast demands its secure availabilWith growing of the power instalArtificial intelligence (AI), component (PCA), fischer discriminant analysis (FDA) and analysis support intelligence (AI), principal principal component analysis lations, the demands on its its secure secure operation and availability havethe gained increasingly attention. Theand wind energy Artificial lations, demands on operation availabil(PCA), fischer discriminant analysis (FDA) and support vector machine (SVM) have been adapted to the monitor(PCA), fischer discriminant analysis (FDA) and support ity have gained increasingly attention. The wind energy conversion system (WECS) consists of The several interconity have gained increasingly attention. wind energy vector machine (SVM) have been adapted to the monitoring of WECS, their applications with the real plant data vector machine (SVM) have been adapted to the monitorconversion system (WECS) consists of several interconnected electrical and(WECS) mechanical components. A fault in a ing of WECS, their applications with the real plant data conversion system consists of several interconhave been reported in Kusiak and Verma (2012); Krueger ing of WECS, their applications with the real plant data nected electrical electrical and mechanical mechanical components. A fault in aa component can strongly affect thecomponents. production A rate as well nected and fault in have been reported in Kusiak and Verma (2012); Krueger et al. (2013a,b); Laouti et al. (2011); Zeng et al. (2013); have been reported in Kusiak and Verma (2012); Krueger component can strongly strongly affect the To production ratefinancial as well well as the availability of theaffect system. reduce the component can the production rate as et al. Laouti et Zeng al. Laouti et al. (2015). identification al. (2013a,b); (2013a,b); LaoutiSubspace et al. al. (2011); (2011); Zeng et et techniques al. (2013); (2013); as the the availability availability of faults the system. system. To reduce reduce the financial consequences of theof and guarantee thethe security of et as the To financial Laouti et al. (2015). Subspace identification techniques have been also adopted for identification of wind turbine, Laouti et al. (2015). Subspace identification techniques consequences of the faults and guarantee the security of the process, condition monitoring systemsthe aresecurity employed consequences of the faults and guarantee of have been also for wind turbine, van Veen etadopted al. (2013), well as sensorof haveder been also adopted forasidentification identification offault winddetection turbine, theWECS. process, condition monitoring systems are employed employed in State of the monitoring art techniques, methodologies and van der Veen et al. (2013), as well as sensor fault detection the process, condition systems are Wei et al. (2010). Luo et al. (2013) extended the datavan der Veen et al. (2013), as well as sensor fault detection in WECS. WECS. State State of the thefor artWEC techniques, methodologies and algorithms developed monitoring have been and dis- Wei et al. (2010). Luo et al. (2013) extended the datain of art techniques, methodologies driven scheme for fault-tolerant controlextended of WECS. Wei et al. (2010). Luo et al. (2013) the algorithms developed for WEC monitoring have been discussed in many reviewfor papers et al.have (2007, 2009); algorithms developed WECAmirat monitoring been dis- driven scheme for fault-tolerant control of WECS. datadriven scheme for fault-tolerant control of WECS. cussed in many review papers Amirat et al. (2007, 2009); Hameedinetmany al. (2009); et al.Amirat (2009).etHowever of However, on the one hand, the faulty data are not always cussed review Lu papers al. (2007,most 2009); Hameed et al. al.methods (2009); are Lu et et al. (2009). (2009). However mostand of However, on the one the are not always the available based on the limit sensing recorded in system, that data makes Hameed et (2009); Lu al. However most of However, onthe the SCADA one hand, hand, the faulty faulty data arethe nottraining always the available available methods are based based on the themodel-based limit sensing sensingfault and recorded in the makes training frequency domain analysis. Recently, for special classes system, become that difficult. other the methods are on limit and recorded in fault the SCADA SCADA system, that makesOnthe thethe training frequency techniques, domain analysis. analysis. Recently, model-based fault fault classes become difficult. On diagnosis Ding (2008), havemodel-based been appliedfault for for hand, in Krueger al. (2013b) it has been pointed outother that frequency domain Recently, for special special fault et classes become difficult. On the the other diagnosis techniques, Ding (2008), have been applied for hand, in et it been out that WECS monitoring. AsDing examples, Liuhave et al.been (2008); Wei and the uni-model method has a poor diagnosis techniques, (2008), applied for hand, in Krueger Krueger et al. al. (2013b) (2013b) it has hasperformance been pointed pointedon outWEC that WECS monitoring. As examples, Liu et al. (2008); Wei and the uni-model method has a poor performance on WEC Verhaegen (2008) have proposed Liu mixed H∞ /H− observer monitoring compare with multimode methods, since WECS monitoring. As examples, et al. (2008); Wei and the uni-model method hasthe a poor performance on WEC Verhaegen (2008) have have proposed mixedand H∞ /H compare with the methods, − observer for fault detection in proposed wind turbines Odgaard and monitoring the WECs are naturally and have severalsince difVerhaegen (2008) mixed H monitoring compare with nonlinear the multimode multimode methods, since ∞ /H − observer ∞ − for fault detection in wind turbines and Odgaard and are nonlinear have several Jakob Stoustrup (2009); Chenturbines et al. (2011) have utilized ferent operating modes. Due to this and inherent the WECs WECs are naturally naturally nonlinear and have nonlinearity several difdiffor fault detection in wind and Odgaard and the Jakob Stoustrup (2009); Chen et (2011) operating modes. Due to the unknown input observer concept sensorhave and utilized process ferent the extracted linear model datainherent is modenonlinearity dependent Jakob Stoustrup (2009); Chen et al. al.for (2011) have utilized ferent operating modes. Duefrom to this this inherent nonlinearity the input observer concept model is dependent faultunknown detection in wind WECS. and extracted may not linear be valid in from other data operating modes. This the unknown input observer concept for for sensor sensor and and process process the the extracted linear model from data is mode mode dependent fault and not be in operating modes. problem addressed in some recent publications, fault detection detection in in wind wind WECS. WECS. and may mayhas notbeen be valid valid in other other operating modes. This This Modern wind turbines are highly instrumented and are problem has been addressed in some recent publications, for instance see Ge and Song (2010); Yu and Qin (2008) problem has been addressed in some recent publications, Modern are highly and equipped with turbines Supervisory and Data Acquisition Modern wind wind turbines are Control highly instrumented instrumented and are are for instance see and Song Yu and Qin fault detection (2014) of instance see Ge Ge and and Haghani Song (2010); (2010); Yu for anddetection Qin (2008) (2008) equipped Supervisory Control and Data (SCADA) systems, which measure all kinds of for equipped with with Supervisory Controland andrecord Data Acquisition Acquisition for fault detection and Haghani (2014) for detection of product degradation. for fault detection and Haghani (2014) for detection of (SCADA) systems, which measure and record all kinds of WECS operating The rich historical data, (SCADA) systems,data. which measure and record allstored kinds in of product degradation. product degradation. WECS operating data. The rich historical data, stored in the SCADA systems, used to develop monitoring WECS operating data.can Theberich historical data, stored in In this paper, a finite mixture of regression models has the systems, can paper, aa finite mixture regression models systems. Data-driven areto suitable monitoring alternative In been adapted modeling of theof the SCADA SCADA systems, techniques can be be used used toa develop develop monitoring In this this paper,for finite mixture ofnonlinear regressioncharacteristic models has has systems. Data-driven techniques a alternative to model-based techniques whichare make use of the process been systems. Data-driven techniques are a suitable suitable alternative been adapted adapted for for modeling modeling of of the the nonlinear nonlinear characteristic characteristic to to model-based model-based techniques techniques which which make make use use of of the the process process Copyright © 2015, 2015 IFAC 633 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2015 IFAC 633 Peer review© of International Federation of Automatic Copyright ©under 2015 responsibility IFAC 633Control. 10.1016/j.ifacol.2015.09.597

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of wind turbine. It estimates the relation between the process measurements with the quality variable in the production system (in this case the generated power) and is further used for detection of those faults in the system which affect the quality. The main assumption is that the nonlinear model can be approximated with a piecewise linear model where each sub-model is valid in a specific region close to an operating point. Moreover, it has been assume that the data in each mode follows Gaussian distribution and therefore their relation to the quality variable can be specified with a Gaussian regression model. The rest of this paper is organized as follows. Section 2 describes some preliminaries in data-driven quality monitoring and the standard approaches are briefly discussed. In Section 3, the mixture of regression model is derived and its application to multimode quality monitoring is shown. Section 4 demonstrates the application on an industrial wind turbine installation and the results are compared and discussed. Conclusions based on results of this study constitute Section 5. 2. PRELIMINARIES Partial least squares (PLS) is one of the basic data-driven method which has been widely used for detection of quality related faults Helland (1988); H¨ oskuldsson (1988); Ding (2014). Its applications such as KPI based process monitoring, fault detection and diagnosis, have been reported in different industrial fields, Haghani et al. (2014). In standard PLS approach the offline measurements are first normalized and are arranged in an input data set X ∈ RN ×n , which contains N samples of n-dimensional process input variables, and output data set Y ∈ RN ×m which contains N samples of m-dimensional quality variable. By projecting X ∈ RN ×n and Y ∈ RN ×m onto the latent variables T ∈ RN ×γ the underling correlation structure of the measurements can be obtained as: ˜ =X ˆ +X ˜ X = TPT + X Y = T QT + Ey = XM + Ey (1) where γ is the number of latent variables which is normally determined by using cross-validation test Wold (1978). P ∈ Rn×γ and Q ∈ Rm×γ are loading matrices of X and Y . The matrix M ∈ Rn×m is known as regression coefficient. The input data matrix X has been decomposed ˆ = T P T which is highly correlated into two subspaces X ˜ which contains the subspace which is not with Y and X correlated to the Y . Ey is the residual term in Y and is assumed to be uncorrelated with X. Usually the so called T 2 and SP E test statistics are used for monitoring of these two subspaces in on-line step. The standard PLS approach for modeling the industrial process is described in Helland (1988) and H¨ oskuldsson (1988). In order to improve the standard PLS algorithm, a new modified approach has been proposed in Yin et al. (2011), which avoids drawbacks of the standard algorithm. These drawbacks are studied in Zhou et al. (2010). Moreover the modified approach is computationally much more simple and is briefly described in the sequel. When the available samples of the measurements N  max(n, m), (1) can be written as follows 634

1 1 1 Y TX = M T XT X + ET X N −1 N −1 N −1 y XT X . (2) ≈ MT N −1 This is due to the fact that cov(ey , x) = 0. Thus, the regression coefficient can be calculated using least squares approach as (3) M = (X T X)† X T Y. By projecting the input data matrix X to the subspaces ˆ spanned by M and its orthogonal complement M ⊥ , X ˜ can be obtained, respectively. X ˆ is fully correlated and X ˜ is orthogonal to X ˆ and has no contribution to Y and X in predicting Y . To detect the faults which may affect the product quality Y , an index is proposed based on ˆ subspace monitoring the X P T X T XPM −1 T ) PM x (4) Txˆ2 = xT PM ( M N −1 where PM ∈ Rn×m is obtained by performing SVD on MMT  T    ΛM 0 PM  (5) M M T = PM P˜M T 0 0 P˜M and the threshold for fault detection follows m(N 2 − 1) Jth,Txˆ2 = Fα (m, N − m) (6) N (N − m) where Fα (m, N − m) is F -distribution with parameters m and N − m and α is the confidence level. If the number of training samples is large enough then (7) Jth,Txˆ2 = χ2α,m where χ2α,m is χ2 distribution with m degrees of freedom and confidence level α. 3. MIXTURE OF REGRESSION MODELS FOR MULTIMODE PROCESS MONITORING In order to use the modified PLS method describe in Section 2 for multimode process monitoring, a mixture of multiple regression models is used to describe the process behavior. In the sequel, the model structure for mixture of regression models is defined, its identification is elaborated and its application in fault detection is explained. 3.1 Model definition Consider the PLS regression model in (1) and assume that the process to be monitored is working in K different operating modes M1 , M2 , · · · , MK , in which, each mode is characterized by (1) with different model parameters Mk : Y k = X k Mk + Ey,k X k ∼ N (µx,k , Σxx,k )

Y k ∼ N (µy,k , Σyy,k ) (8) for k = 1, . . . , K, and θk = {µx,k , Σxx,k , µy,k , Σyy,k , Mk } are the unknown parameters to be estimated from data and N (µ, Σ) is multivariate normal distribution with mean value µ and covariance matrix Σ. The data sets X k and Y k are the measurements collected in operating mode   k. xi In the presence of N samples of unsorted data di = yi

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for i = 1, . . . , N a random mechanism z is introduced to indicate the mode in which the process is working. It is assumed throughout the paper that zi s for i = 1, . . . , N are independent with unknown probability distribution. Therefore the conditional likelihood of data fixing the unknown parameters can be written as: p(di |Θ) = where:

K 

Pr(zi = k)g(di |θk ).

k=1

(9)

The M-step in EM algorithm is carried out by derivation of Q(Θ|Θold ) with according to the unknown parameters and setting it to zero. It has been shown by Haghani (2014) that the update of parameters in M-step are as shown in (16). N N   p(Mk |di )xi p(Mk |di )yi i=1 µx,k = i=1 = , µ y,k N N   p(Mk |di ) p(Mk |di ) i=1

T −1 1 1 e[− 2 (d−µk ) Σk (d−µk )] , g(d|θk ) = m/2 1/2 (2π) |Σk | and Θ = {θ1 , . . . , θk }.

Σxx,k =

Given N samples of offline data D = {d1 , . . . , dN }, its loglikelihood can be described as: N  p(di |Θ) log p(D|Θ) = log =

i=1

log

K 

k=1

Pr(zi = k)p(di |Θk ).

N 

i=1

i=1

p(Mk |di )(xi − µx,k )(xi − µx,k )T N 

p(Mk |di )

N 

p(Mk |di )

N 

p(Mk |di )

i=1

Σyy,k =

i=1

N 

635

N 

i=1

p(Mk |di )(yi − µy,k )(yi − µy,k )T i=1

N 

(10)

Σxy,k = i=1

3.2 Estimation of model parameters

p(Mk |di )(xi − µx,k )(yi − µy,k )T i=1

In order to construct the monitoring scheme, the following set of parameters should be estimated in advance (11) Θk = {wk , µx,k , µy,k , Σxx,k , Σxy,k , Σyy,k } for k = 1, 2, · · · , K. The maximum likelihood estimate can be achieved by maximizing the log-likelihood function in (10): ˆ M LE = arg max{log p(D|Θ)}, (12) Θ Θ

The solution of (12) can be obtained by means of the expectation-maximization (EM) algorithm. EM method is based on the assumption that D is an incomplete data set in which the missing part in finite mixture modeling can be interpreted as N tags, Z = {z1 , · · · , zN }. EM method is an iterative algorithm, which in expectation step (Estep) the conditional expectation of the log-likelihood for complete data C = {D, Z} is calculated as follows (13) Q(Θ|Θold ) = E{log p(D, Z|Θ)|D, Θold } and the estimation of parameters is updated in maximization step (M-step) using Θ = arg max Q(Θ|Θold ).

(14)

Θ

The iteration is stopped when certain convergence criterion is satisfied, McLachlan and Krishnan (2008). In order to expand (13) and solve the optimization problem in (14), the dynamics of the process is neglected, i.e. following assumptions are made: • yi only depends on zi and not its past values • there is no serial correlation in measurements, i.e. yi is independent of its past values and only depends on current value of xi Therefore, (13) can be represented as Q =E{log p(Y|X , Z, Θ)p(X |Z, Θ)p(Z|Θ)|D, Θold } (15) 635

wk =

N 

i=1

p(Mk |di )

N where p(Mk |di ) is calculated in E-step as wk g(di |Θk ) p(Mk |di ) = K .  wk g(di |Θk )

(16)

(17)

k=1

After obtaining the unknown parameters the regression coefficients for each modes M1 , · · · , MK in PLS model (1) can be calculated as shown in (3) using Mk = Σ−1 xx,k Σxy,k

(18)

for k = 1, · · · , K. In the following section, the estimated parameters Mk , µx,k , µy,k , Σxx,k Σyy,k will be utilized for fault detection purpose in the multimode system. Since the focus is detection of quality related faults, the Txˆ2 index for each mode will be calculated and will be combined with the posterior probability of each mode to have a global indicator of faults. 3.3 Design of monitoring scheme For detection of the fault in online step, the probability that the given sample belongs to a fault, Pr(xi ∈ F ), is used as a fault indicator. Knowing the mixture model, the indicator can be obtained by marginalization as K  Pr(xi ∈ F |xi ∈ Mk )Pr(xi ∈ Mk ). Pr(xi ∈ F ) = k=1

(19)

where Pr(xi ∈ Mk ) represents the probability that a sample belongs to mixture component Mk and Pr(xi ∈ F |xi ∈ Mk ) represents that it is faulty under the assumption that it comes from Mk . Since (20) 0 ≤ Pr(xi ∈ F ) ≤ 1

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a confidence level (1 − α) can be determined for fault detection purpose with the following hypothesis:  Pr(xi ∈ F ) ≤ 1 − α fault free (21) Pr(xi ∈ F ) > 1 − α faulty

where α represents the false alarm rate. The procedure for design of the proposed monitoring scheme is summarized in Algorithm 1. Algorithm 1. Design of fault detection scheme

Step 1 Collect the normal operation data from different operating modes. Step 2 Apply the EM algorithm to estimate the parameters shown in (11) using (16) and (17). Step 3 Obtain Mk using (18) for k = 1, · · · K. Step 4 In on-line step when a new sample of measurements is available, for k = 1, · · · , K: 4.1 Compute Txˆ2 (xi , k) using (4) and the identified parameters of Mk . 4.2 Compute p(x(i) ∈ Mk ) using the multivariate Gaussian probability density function. 4.3 Compute p(x(i) ∈ f |x(i) ∈ Mk ). Step 5 Calculate the fault detection index in (19). Step 6 Use the fault detection hypothesis shown in (21) to detect fault and go to step 4.

Table 1. Selected Measurements ID

Measurement description

Component

Unit

1

Generator Bearing 1 Temperature

Generator

◦C

2

Generator Bearing 2 Temperature

Generator

◦C

3

Generator Stator Temperature

Generator

◦C

4

Gearbox Bearing 1 Temperature

Gearbox

◦C

5

Gearbox Bearing 2 Temperature

Gearbox

◦C

6

Gearbox Inlet Temperature

Gearbox

◦C

7

Gearbox Oil Sump Temperature

Gearbox

◦C

8

Gearbox Speed

Gearbox

rpm

9

Generator Speed

Generator

rpm

10

Rotor Speed

Rotor

rpm

4. APPLICATION ON WEC In order to demonstrate the effectiveness and performance of the algorithm introduced in Section 3, data collected from different wind turbines are tested with the multimode process monitoring method and the results are compared with the standard PLS method. Table 1 displays the process measurements that considered in this study. Three main components of a WECS are included in these measurements: Rotor, Gearbox and Generator. All the variables are sampled in 10 minutes intervals. In order to detect the faults which affect the reliability of the system, the gearbox temperature is chosen as the performance indicator (Y in (1)), since it indicate the lubrication and cooler effect of the gearbox. Two different fault scenarios are considered in this study: a fault in gearbox cooling system and sensor fault in bearing temperature. The WEC systems are well known for their large operating range. As shown in Figure 1, the blue circles with N 1 and N 2 denote two different operating ranges. The red circles denoted by F 1 and F 2 are the same kind of fault that occurred in different operating ranges. The black dashed line represents the validity range of the normal operating data based on the standard multivariate analysis (e.g PCA and PLS). It is obvious that if the system is treated as a multimode system, it would be quite easy to separate the normal and faulty cases. However, as shown with the black circle, if the WEC is taken as uni-model, then it might cause difficulties to detect the fault, especially when the fault is around the operating range N 2, e.g. Fault F 2.

Fig. 1. Scatter plot of gearbox speed vs. gearbox temperature based on standard PLS method is performed with two test statistics: T 2 , SPE. In Figure 2 the fault detection results from PLS and GMM methods are illustrated, where the fault began at sample 1618. For the sake of clarity, the TP2 LS and SP EP LS test statistics are represented in logarithmic scale. It can be seen that the abnormality could be detected by both monitoring methods. In Table 2, detection rates of different test statistics are listed, where GMM fault indicator provides a better fault detection result with a much lower false detection rate, compared with the standard PLS method. By comparing the fault detection results of GMM with the standard limit sensing method, which is implemented in the SCADA system, the multi-mode algorithm would trigger an alarm about 12 hours before the SCADA system did, according to maintenance report. It could be noticed that an incipient fault may not go across the limit set for the entire system operating range, however, it could be detected by the multi-mode method where for each operating mode, a separate monitoring model is considered. 4.2 Sensor fault detection

4.1 Process fault detection A gearbox air cooler fault has been investigated in this subsection. For the implementation of GMM based fault detection, several training tests have been carried out in order to achieve the best model. WEC monitoring 636

In this subsection, the aforementioned methods have been tested on a sensor fault. According to the maintenance report, gearbox bearing 1 temperature sensor has been suffered from a malfunction in this episode. Figure 3 demonstrates the fault detection results from PLS and

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Table 3. Sensor fault detection rates and false alarm rates

Table 2. Gearbox air cooler fault detection rates and false alarm rates Monitoring method

Detection rate

test statistic

False alarm rate

Monitoring method PLS

T2

Detection rate

98.8%

8%

63.3%

2.7%

88.6%

5.75%

PLS SPE test statistic

50.2%

4.6%

GMM fault indicator

100%

1.2%

GMM T 2 test statistic

95.1%

2%

1

0.8

0.8

Pr(x∈F)

1

0.6 0.4

0.6 0.4 0.2

0.2

0

0 0

500

1000

1500

0

2000

600

700

800

500

600

700

800

400 500 Samples

600

700

800

(a)

(a)

PLS

T2

0

T2 PLS

T

2 PLS

400

500

5

−5

0

10

T2

PLS

Threshold

0

−5

10

500

1000

1500

2000

0

Threshold 100

200

300

400

5

5

10

10

SPE

SPE

PLS

PLS

PLS

Threshold

0

SPE

PLS

300

10

10

10

0

Threshold

0

10

−5

10

−5

10

200

Samples

5

10

100

Samples

10

SPE

test statistic

False alarm rate

PLS SPE test statistic

Pr(x∈F)

PLS

T2

637

500

1000 Samples

1500

2000

0

100

200

300

(b)

(b)

Fig. 2. Process fault detection results: (a) with GMM (b) with PLS GMM methods, where the fault begins at sample 433. Table 3 gives the detection rate and false alarm rate of different test statistics. It is obvious that the GMM method provides better detection results than standard PLS method, because of its multimode property.

Fig. 3. Sensor fault detection results: (a) with GMM (b) with PLS timode GMM method delivers a promising fault detection result with lower false alarm rate.

5. CONCLUSION In this paper, the data-driven multimode process monitoring method has been applied for the fault detection of WEC systems. A typical wind turbine works in wide range of operating points. Due to the inherent nonlinearity of the system, the linearized models of the plant in each operating points are different. For such nonlinear systems, the standard multivariate statistical monitoring techniques provide poor fault detection performance, since they are based on the linearity assumption. To avoid this problem, the multimode technique has been used which considers the process as a piecewise linear system. The performance of this technique has been addressed with application examples based on real WEC data. Test results for both sensor and process faults have been compared with the well-known standard PLS method, where the mul637

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