Hybrid Self Adaptive Learning Scheme for Simple and Multiple Drift-like Fault Diagnosis in Wind Turbine Pitch Sensors Houari Toubakh and Moamar Sayed-Mouchaweh IMT Lille Douai, Univ. Lille, Unite de Recherche Informatique Automatique, F-59000 Lille, France e-mail: houari.toubakh@imt-lille-douai.fr Abstract task because of (i) the occurrence of pitch system faults in power optimization zone in which the fault consequences This paper presents a hybrid dynamic data-driven are hidden and (ii) the actions of the control feedback which approach to achieve simple and multiple drift like compensate the fault effects. The role of the pitch system fault detection of pitch system sensors. This is to adjust the pitch of a blade by rotating it depending on approach considers the system evolving in non- the pitch angle position reference provided by the controller. stationary environments and switching between The latter decides the pitch angle position reference accord- several control modes. This switching is entailed ing to the wind speed in order to allow an optimum energy by changes in the system environments. In each production. control mode, the system has a different dynam- ical behavior. The latter is described in a feature In the literature, there are several methods [6],[9],[11],[12],[1],[4],[15] that are used to achieve space sensitive to normal operating conditions in the corresponding control mode. These operating fault diagnosis in WTs. They achieve the fault diagnosis conditions are represented by restricted zones in by reasoning over differences between desired or expected the feature space called classes. The latter are behavior, defined by a model, and observed behavior characterized by a set of parameters represent- provided by sensors. They can be classified into two main ing their statistical properties, e.g. gravity center categories of methods: internal and external methods. and variance-covariance matrix. The occurrence The internal methods [17],[18],[20] use a mathematical of an incipient fault entails a drift in the system or structural model to represent the relationships between operating conditions until the failure takes over measurable variables by exploiting the physical knowledge completely. This drift manifests as a progressive or/and experimental data about the system dynamics. These change in the classes parameters in each control variables represent the internal parts of the wind turbine. mode over time. The proposed approach moni- The response of the mathematical model is compared to the tors normal classes parameters in order to detect observed values of variables in order to generate indicators a drift in their characteristics. This drift detection used as a basis for the fault diagnosis. Generally, the model allows achieving the fault in its early stages. It is used to estimate the system state, its output or its param- uses two drift indicators. The first indicator de- eters. The difference between the system and the model tects the drift and the second indicator confirms responses is monitored. Then, the trend analysis of this it. Both indicators are based on the observation of difference can be used to detect changing characteristics of changes in the normal operating conditions char- the system resulting from a fault occurrence. The internal acteristics over time. A wind turbine simulator is methods used to achieve the fault diagnosis of wind turbines used to validate the performance of the proposed are divided into three main categories: parameter estimation [8],[19], observer and state estimation based [3],[23] and approach. signal analysis or feature based [7],[21] approaches. These methods were applied successfully to achieve the diagnosis 1 INTRODUCTION of faults impacting the pitch system [19],[3],[16], the The search for alternative clean energy is undoubtedly be- generator [16],[14], the converter [25],[14], and the gearbox coming more and more important in modern societies. The [26],[16]. growing interest in wind energy production has led to the The major advantages of these methods are their ability design of sophisticated wind turbines (WTs). Like every to detect both the abrupt and progressive failures via trend other complex and heterogeneous system, WTs are faced to analysis, and they give a precise decision or isolation of a the occurrence of faults that can impact their performance failure. However, they suffer from the necessity to depth in- as well as their security. Therefore, it is crucial to design formation about system behavior and failures which is hard a reliable automated diagnostic system in order to achieve to obtain for complex and strong non-stationary systems as fault detection and isolation in early stage. wind turbines. Fault diagnosis of WTs is a challenging task because of An alternative to overcome this problem is the external the high variability of the wind speed and the confusion be- methods [17],[22],[9]. The external methods consider the tween faults and noises as well as outliers. However, the system as a black box, in other words, they do not need fault diagnosis of pitch system is particularly a challenging any mathematical model to describe the system dynami- cal behaviours. They use exclusively a set of measure- ments or/and heuristic knowledge about system dynamics to build a mapping from the measurement space into a decision space. They include expert systems and machine learning and data mining techniques. These methods are suitable for systems that are difficult to model, they are simple to imple- ment and require short processing time. However, since the obtained models are not transparent, the obtained results are hard to be interpreted and demonstrated. There are several machine learning and data mining methods used to achieve the fault diagnosis of wind turbines. Such methods are de- scribed and successfully applied in [24],[2]. Few approaches have been proposed to achieve early fault Figure 1: Wind turbine components. diagnosis of WTs, in particular pitch sensors. This is due to the fact that modeling component degradation in strong non-linear and complex non-stationary environments is very hard task. Examples of these methods, we can cite genetic algorithm [10], neural network, the boosting tree algorithm, and support vector machine [9]. These methods do not in- tegrate a mechanism to detect a drift by analyzing the char- acteristics of incoming data and to update the model param- eters and structure in response to this drift. Therefore, they do not achieve a reliable early diagnosis. Consequently, the diagnosis performance (diagnosis delay) is decreased sig- nificantly for faults occurring in WT critical subsystems as pitch systems ones. This paper presents a new data-driven based approach in order to achieve a reliable drift monitoring and diagnosis of Figure 2: Reference power curve for the WT depending on simple and multiple drift-like faults that can affect wind tur- the wind speed. bine pitch sensors. This approach takes into account the dif- ferent dynamical behaviors of WTs according to the wind 2 Pitch system within wind turbines speed. The goal is to detect a drift from normal operating conditions using only the recent and useful data. Initial off- The wind turbine model under study is composed of five line modeling allows constructing initial classes based on principal parts: the blades, the drive train, the generator with the historical data set. These classes characterize the op- the converter, and the controller (see Figure 1). It can be erating conditions of the pitch system (normal/faulty) and seen that the blades are fixed to the main axis, which in turn are represented by restricted zones in the feature space. The is connected to the generator through the drive train. The latter is formed by sensitive features to pitch sensor oper- generator is electrically connected to the converter, which ating conditions in order to distinguish any drift from nor- in turn is connected to a transformer. The blades are pitched mal to fault operating conditions. The modeling tool is an by the pitch actuators. algorithm called AuDyC (Auto-Adaptive Dynamical Clus- tering) used to initialize the classes that will be dynamically updated. In this work, two-dimensional feature space is con- structed, for the sensor faults. The faulty classes, represent- ing the failure operating conditions of pitch sensor, are con- sidered to be a priori unknown. There is one known class in advance.The class represents the pitch sensor normal oper- ating conditions. It considers gradual degradations in pitch sensor operating condition as a drift in the characteristics of normal class over time. Detecting and following this drift can help to predict the occurrence of pitch sensor failure. The drift-like fault is monitored using two drift indica- tors: one to detect a drift and the second one to confirm it. When the drift is detected by the first indicator, a warning is Figure 3: Controller operating zones modeled by a finite emitted to human operators. Then, the second drift indicator state automaton. confirms this drift in order to inform human operators of the necessity to react by taking the adequate correction actions. The controller operates in four zones (see Figure 2). Zone The proposed data-driven approach is composed of five 1 is the start-up of the turbines, zone 2 is power optimiza- main steps: processing and data analysis, clustering and tion, zone 3 is constant power production and zone 4 is no classification, drift monitoring, updating and interpretation power production due to a too high wind speed. steps. In order to handle transitions between the control modes, the controller checks the operating zone in which the WT When e(t) = ωr (t) − ωnom . In this case the converter ref- is by observing the wind speed. The transitions between erence is used to suppress fast disturbances: the control modes change the dynamics of the pitch system. Each control mode is active in one zone thus it is modeled Pr (t) τg,r (t) = (4) by a finite state automaton. Each zone is represented by a ωt (t) state in which a specific control mode or strategy is defined. The control mode should switch from mode 1 to mode 2 if According to the wind speed, the control mode changes the following condition is satisfied: by switching from one mode or state to another mode or state. This switching between control modes is achieved E23 : ωg (t) ≥ ωnom (5) by discrete events. As an example, if the WT was initially The satisfaction of this condition generates a discrete in control mode related to the zone 1, as long as the wind event, E23 , allowing the switching from control mode 1 to speed is less than a predefined threshold (5 m/s in Figure 2) control mode 2. The goal to obtain Pg equal to Pr . This E11 will be generated. E11 keeps the WT in control mode condition is satisfied when the wind speed is greater than 1. If the wind speed is greater than the predefined threshold predefined threshold for zone 2 (12.5 m/s in Figure 2). Like- for zone 1 (5 m/s in Figure 2), The event E12 is generated wise, the control mode should switch from control mode 2 leading to switch the WT from the control mode related to to control mode 1 if the following condition is satisfied: zone 1 to the control mode related to zone 2 (see Figure 3). Same reasoning can be applied for the other events. E32 : ωg (t) < ωnom − ω∆ (6) Where ωnom is the nominal generator speed and ω∆ is a The focus of this benchmark model is on the operation of small offset subtracted from the nominal generator speed to WT in zones 2 and 3. Two control strategies are applied to introduce some hysteresis in the switching scheme, thereby optimize the energy production and keep it constant at its avoiding that the control modes are switching all the time optimal value: the converter torque control in zone 2 and [15]. The satisfaction of this condition generates a discrete the blades angle control in zone 3 (see Figure 4). In zone event, E32 , allowing the switching from control mode 2 to 2, the WT is controlled so that it produces as much energy control mode 1. This condition is satisfied when the wind as possible. To do so, the blades angle is maintained equal speed is less than the wind speed threshold defined for zone to 0◦ and the tip speed ratio is kept constant at its optimal 3 (12.5 m/s in Figure 2). value. The latter is regulated by the rotating speed control by tuning the converter torque. Once the optimal power pro- duction is achieved, the blades angle control maintains the converter torque constant and adjusts the rotating speed by controlling the blades angle. The latter modifies the trans- fer of the aerodynamic power of the wind on the blades. In this work, the controller modes are modeled by a finite state automaton containing two states (see Figure 4). In the fol- lowing, zones 2 and 3, respectively, correspond to control modes 1 and 2: Figure 4: Controller modes modeled by a finite state au- tomaton Control Mode 1 In this control mode, the power opti- mum value is achieved by setting the pitch reference to zero As we said before, the benchmark model allows simulat- β[t] = 0 and the reference torque to the converter τg,r as ing the WT behavior in two power zones: 1) zone 2 (power follows: optimization) where τg is controlled and βr is equal to zero  2 and; 2) zone 3 (optimal energy production) where τg is kept ωg [t] βr constant and is controlled. In this paper, we focus on τg,r = Kopt × (1) Ng pitch sensor faults as it is discussed in subsection 2. Ng is the gear ratio and n is the sampling time. Where 3 Pitch system description 1 CP The considered WT is horizontal-axis based with three Kopt = ρAR3 3max (2) blades. Each blade is equipped with an actuator. The role 2 λopt of the pitch actuator is to adjust the pitch of a blade by ro- with ρ the air density, A the area swept by the turbine tating it; Each actuator is provided by the same pitch angle blades, CPmax the maximum value of power coefficient, and reference βr . The pitch angle of a blade is measured on λopt the optimal value of λ is found as the optimum point the cylinder of the pitch actuator, each pitch position (an- in the power coefficient CP mapping of the WT. The power gle) βmi where i ∈ {1, 2, 3} is measured with two sensors coefficient mapping characterizes the efficiency of energy where index mi represents the ith sensor of the correspond- and it depend on λ and β. ing variable (see Figure 5). The pitch system feedback βf is an internal variable used to model the pitch position error Control Mode 2 In this mode, the major control actions caused by sensor faults: are handled by the pitch system using a Proportional Integral 1 (PI) controller trying to keep ωg [t] at ωg . βf = βr − (βk,m1 + βk,m2 ) (7) 2 The controller is fed by the mean value of the readings of the βr (t) = βr (t − 1) + kp .e (t) + (ki .Ts .kp ) .e (t − 1) (3) two sensors. Hence, this sensor fault is modeled as a change in the pitch references, meaning that a sensor fault resulting speeds in pitch sensor βm1 and pitch sensor βm2 , and in in changed mean value should also change the pitch refer- both pitch sensors βm1 and βm2 . ence accordingly [15]. 5.1 Sensor drift-like fault Each blade is equipped with an actuator. Each actuator is provided by the same pitch angle reference βr . In addi- tion, each pitch position, (angle) βmi is measured with two sensors where index i represents the ith sensor of the cor- responding variable. The fault scenarios related to simple drift-like fault in pitch sensor n◦ 1 and sensor n◦ 2 and mul- tiple drift-like fault in both pitch position sensor n◦ 1 and sensor n◦ 2 in blade n◦ 3 are summarized respectively in Ta- ble 1, Table 2 and Table 3. The state representation of the pitch system after the integration of a fault in sensor βmi , i ∈ {1, 2} is defined as follow: Figure 5: Block diagram of pitch system for the blade k, (k = 1, 2, 3) . xp = Axp + Bu yp = Cxp + f (t) (9) f (t) = λi . (tb − te ) 4 Pitch system modeling Therefore the parameter λi , i ∈ {1, 2} is used in the sim- The hydraulic pitch system is modeled in the benchmark as ulation to generate a fault in sensor βmi during the time pe- a closed loop of dynamic system. The state representation riod (tb − te ) where tb is the start time and te is the end time of the nominal pitch system dynamics is defined as follows of sensor drift-like fault. [15]: Simple drift-like fault in sensor βm1 · In this paper the simple drift-like fault scenarios in pitch x = Ap xp + Bp (βr + βf ) p sensor 1 (βm1 ) scenarios are modeled as a gradual change yp = Cp xp in the coefficient λ1 of pitch sensor n◦ 1 in blade n◦ 3 where   tb is the beginning of the drift and te is the end of the drift. 0 1 Nine scenarios for simple sensor drift-like fault are gener- Ap = −ωn2 −2ζωn (8) ated in order to simulate slow, moderate and high degra-   dation speeds represented by slow, moderate and high drift 0 speeds (see Figure 6). Each drift speed scenario is gener- Bp = ωn2 ated at three different time instances. Thus, parameter λ1 is changed linearly from λ1N to λ1F in a period of 30s, 60s Cp = [ 0 1 ] and 90s, corresponding respectively to high, moderate and slow drift speeds. Then, the fault remains active for 200s. iT Finally the parameter λ1 decreases again to return to its ini- h . The state vector xp = βk βk is composed of pitch tial value λ1N (see Figure 6 for the case of high drift speed . in sensor 1 (βm1 )). angular speed βk , and position βi for each blade k : (k = 1, 2, 3). yp is the measured pitch position, βr is the pitch angle position reference provided by the controller, and βr is the feedback pitch system (see Figure 5). ωn , ζ are the pa- rameters of the pitch system where ωn represent the natural frequencies and ζ is the damping ratio. The pitch system represent a hybrid dynamic system and especially it belongs to the class of Discretely Controlled Jumping Systems (DCJS), In these systems, the continuous state variables change discontinuously under the influence of an external action (e.g., a command) as the case for elec- tromagnetic systems with pulse inputs [?]. The pitch system h . iT state variable xp = βk βk changes discontinuously under the influence of an external action defined by Equa- tion 5 and 6. Figure 6: Simple drift-like fault scenarios in pitch sensor 1 (βm1 ), corresponding to high drift speed in 3 different time instances tb is the beginning time of the drift and te is the 5 Pitch system drift-like fault scenarios end of the drift. generation In this paper the types of fault which are considered in this work are simple and multiple drift-like fault in pitch sensors. Simple drift-like fault in sensor βm2 The following subsections detail the generation of several The simple drift-like fault scenarios in pitch sensor 2 (βm2 ) scenarios representing drift-like faults with three different scenarios are modeled as a gradual change in the coefficient Fault N ◦ Drift speed Simple drift-like fault Period in pitch sensor βm1 F4h 30s λ1N → λ1F 2500s (High) -2730s F4m 60s λ1N → λ1F 2500s (Medium) -2760s F4s 90s λ1N → λ1F 2500s (Slow) -2790s F5h 30s λ1N → λ1F 2600s -2830s F5m 60s λ1N → λ1F 2600s -2830s F5s 90s λ1N → λ1F 2600s -2890s Figure 7: Simple drift-like fault scenarios in pitch sensor 2 F6h 30s λ1N → λ1F 2700s (βm2 ), corresponding to high drift speed in 3 different time -2930s instances. F6m 60s λ1N → λ1F 2700s -2960s F6s 90s λ1N → λ1F 2700s Multiple sensor drift-like fault -2990s In this chapter the generated scenarios of the multiple drift- like fault in pitch sensor 1 (βm1 ) and sensor 2 (βm2 ) are Table 1: Simple drift-like fault scenarios in pitch sensor 1 modeled as a gradual change at the same time in the drift (βm1 ). coefficient (λ1 and λ2 ) of both pitch sensors n◦ 1 and pitch sensors n◦ 2 in blade n◦ 3. As for the case of simple drift- λ2 of pitch sensor n◦ 2 in blade n◦ 3 where tb is the begin- like fault in pitch sensor scenarios, nine scenarios for multi- ning of the drift and te is the end of the drift. As for the ple sensor drift-like fault are generated in order to simulate case of simple drift-like fault in pitch sensor βm1 scenarios, slow, moderate and high degradation speeds representing by nine scenarios for simple sensor drift-like fault are gener- slow, moderate and high drift speeds (see Table 3). Each ated in order to simulate slow, moderate and high degra- drift speed scenario is generated at three different time in- dation speeds represented by slow, moderate and high drift stances. Thus, parameters λ1 and λ2 are changed linearly speeds (see Figure 7). Each drift speed scenario is gener- from λ1N and λ2N to λ1F and λ2F in a period of 30s, 60s ated at three different time instances. Thus, parameter λ2 is and 90s, corresponding respectively to high, moderate and changed linearly from λ2N to λ2F in a period of 30s, 60s slow drift speeds. Then, the fault remains active for 200s. and 90s, corresponding respectively to high, moderate and Finally the parameter decreases again to return to their ini- slow drift speeds. Then, the fault remains active for 200s. tial values (see Figure 8 for the case of high drift (degrada- Finally the parameter λ2 decreases again to return to its ini- tion) speed in both sensor 1 (βm1 ) and sensor 2 (βm2 )). tial value λ2N (see Figure 7 for the case of high drift speed in sensor 2, (βm2 )). Fault N ◦ Drift speed Simple drift-like fault Period in pitch sensor βm2 F7h 30s λ2N → λ2F 2800s (High) -3030s F7m 60s λ2N → λ2F 2800s (Medium) 3060s F7s 90s λ2N → λ2F 2800s- (Slow) -3090s F8h 30s λ2N → λ2F 2900s -3130s F8m 60s λ2N → λ2F 2900s -3130s F8s 90s λ2N → λ2F 2900s -3190s F9h 30s λ2N → λ2F 3000s 30s -3230s F9m 60s λ2N → λ2F 3000s -3260s F9s 90s λ2N → λ2F 3000s -3290s Figure 8: Multiple sensor drift-like fault scenarios in sen- sors (βm1 ) and (βm2 ) corresponding to high drift speed in 3 Table 2: Simple drift-like fault scenarios in pitch sensor 2 different time instances. (βm2 ). Fault N ◦ Drift speed Multiple drift-like fault in Period in pitch sensors βm2 and βm2 F10h 30s (High) λ1 N → λ1F and λ2N → λ2F 3100s- 3330s F10m 60s (Medium) λ1 N → λ1F and λ2N → λ2F 3100s- 3360s F10s 90s (Slow) λ1 N → λ1F and λ2N → λ2F 3100s- 3390s F11h 30s λ1N → λ1F and λ2N → λ2F 3200s- 3430s F11m 60s λ1N → λ1F and λ2N → λ2F 3200s- 3460s F11s 90s λ1N → λ1F and λ2N → λ2F 3200s- 3490s F12h 30s λ1N → λ1F and λ2N → λ2F 3300s- 3530s F12m 60s λ1N → λ1F and λ2N → λ2F 3300s- 3560s F12s 90s λ1N → λ1F and λ2N → λ2F 3300s- 3590s Table 3: Multiple drift-like fault scenarios in pitch sensors (βm1 ) and (βm2 ). 6 Proposed approach of the desired value of the pitch angle βr and the feedback In this section, hybrid dynamic data-driven approach is de- pitch system βf (see Figure 5). The residual is computed veloped in order to achieve condition monitoring and drift within a time window which is tuned to be several times the like fault detection of pitch sensor. It performs predictive actuator time response. diagnosis by detecting a drift of the system operating condi- The evolution of these residuals with respect to each of tions from normal to faulty modes. The proposed approach the two sensors is considered as meaningful features. In- is based on 5 steps developed in the following subsections deed, the residual ∆βs1 respectively ∆βs2 , is equal to zero (see Figure 9). when the corresponding sensor βm1 respectively βm2 , is in normal operating conditions. When, the sensor βm1 respec- 6.1 Processing and data analysis tively βm2 , is in faulty operating conditions, the residual This step aims at finding the features that are sensitive to the ∆βs1 , ∆βs2 will be different of zero because this sensor system operating conditions in order to construct the feature will not measure the new value of command (βr + βf ) (see space. A feature space representing the operating conditions Figure 5). Indeed, the command (βr + βf ) will change in of each assembly of WT is defined, this feature space will be order to compensate the difference between the two sensors responsible of the detection and isolation of faults impacting due to the fault of sensor βm1 respectively βm2 . this components. The research of sensitive features is based 6.2 Classifier learning and updating on the signals provided by the pitch sensors as well as the prior knowledge about the system dynamics. These features The clustering looks to determine the number of classes con- are chosen in order to maximize the discrimination between tained in the learning set and to initialize their parameters. operating conditions in the feature space. In this paper, two- The classification aims at designing a classifier able to as- dimension feature space is constructed for the sensor fault. sign a new pattern to one of the learnt classes in the feature The goal of the feature space use, at the level of component, space. A new pattern characterizes the actual operating con- is to facilitate the drift-like fault isolation and to enhance the ditions (normal or faulty in response to the occurrence of a diagnosis robustness. certain fault) of the system. Examples of these approaches The position of the pitch actuators is measured by two re- are present in [5] as well as in the references of this paper. dundant sensors for each of the three pitch positions βk,mi , Auto-adaptive Dynamical Clustering Algorithm (Au- k = 1, 2, 3, i = 1, 2, with the same reference angle βr pro- DyC) [13] is selected in this work in order to achieve both vided to each of them. In order to enhance the robustness clustering and classification. AuDyC computes the param- against noise, the measurements are filtered by a first order eters of initial classes based on the statistical properties of filter using time constant τ = 0.06. data which are the mean and the variance-covariance matrix. For the drift like fault detection and isolation of the sen- These classes characterize the normal operating conditions sor faults, we propose to explore the physical redundancy in of pitch sensors. AuDyC was chosen because it is unsu- order to generate residuals as follows: pervised classification method and is able to model streams of patterns since it always reflects the final distribution of ∆βs1 = |βr + βf − βm1 | (10) patterns in the features space. It uses a technique that is in- spired from the Gaussian mixture model [13]. Let E d be a ∆βs2 = |βr + βf − βm2 | (11) d-dimensional feature space. Each feature vector x ∈ E d To do so, the residual ∆βsn , n = 1, 2, is generated by the is called a pattern. The patterns are used to model Gaus- comparison between the pitch angle measurement βmi , i = sian prototypes P j characterized by a center µP j ∈ Rd×1 and a covariance matrix P j ∈ Rd×d . Each Gaussian pro- P 1, 2, m = 1, 2, 3 and the command computed by the sum Figure 9: Proposed on-line adaptive scheme steps. totype characterizes a class. A minimum number of Nwin Equation 10 and 11. In zone 2, the effects of this fault are patterns are necessary to define one prototype, where Nwin hidden because the actuators are not operated. Moreover, it is a user-defined threshold. A class models operating condi- is strongly difficult to distinguish the fault occurrence to the tions and gathers patterns that are similar one to each other. noise in the case of small angles. Therefore an overlapping The similarity criterion that is used is the Gaussian member- region is created between the normal and failure classes (see ship degree. Faults will affect directly this distribution and Figure 10 and Figure 15). this will be seen through the continuously updated parame- In order to answer the challenges inherent to the system ters. More details about AuDyC related to merging classes, operation, the normal and failure classes are split into five splitting classes, rules of recursive adaptation, similarity cri- classes and the pitch actuator dynamics are represented by teria, etc., can be found in [13]. two different control modes. The first one corresponds to In the sensor feature space, four classes are considered: the case of zone 2 low wind speed; while the second control the fault of sensor 1, βm1 , the fault of sensor 2, βm2 , the mode represents the case of zone 3 high wind speed (see fault of both sensor 1,βm1 and sensor 2 βm2 , and the nor- Figure 16). Class 1 is the ambiguity class. It gathers the mal functioning. Figure 10 shows the classes representing patterns representing pitch sensor normal or faulty operat- normal and failure operating conditions of pitch sensor in ing conditions. This class represents the control mode 1. the feature space constituted by the two residuals defined by Class 2 represents the normal operating conditions class in Figure 10: Large view of overlapping region for the pitch sensor normal and failure operating conditions in case of Figure 13: Feature space of the pitch sensor normal and fail- simple fault in pitch sensor 1, (βm1 ). ure operating conditions in case of simple fault in pitch sen- sor 2, (βm2 ). Figure 11: Feature space of the pitch sensor normal and fail- Figure 14: Large view of overlapping region for the pitch ure operating conditions in case of simple fault in pitch sen- sensor normal and failure operating conditions in case of sor 1, (βm1 ). multiple fault in pitch sensor 1, (βm1 ) and pitch sensor 2, βm2 . Figure 12: Large view of overlapping region for the pitch sensor normal and failure operating conditions in case of simple fault in pitch sensor 2, (βm2 ). Figure 15: Feature space of the pitch sensor normal and fail- ure operating conditions in case of multiple fault in sensor βm1 and βm2 . control mode 2. Class 3 represents failure class caused by simple drift-like fault in pitch sensor 1, βm1 in control mode 2, class 4 represents failure class caused by simple drift-like performance over time is preserved. fault in pitch sensor 2, βm2 in control mode 2 and class 5 represents failure class caused by multiple drift-like fault in pitch sensor 1, βm1 and sensor 2, βm2 in control mode 2. µe (t) = µe (t − 1) + f (µe (t − 1), xnew , xold , Nwin ) (12) The updating step aims at reacting to the changes in X X X classes characteristics in the feature space. AuDyC continu- (t) = (t−1)+g( (t−1), µe (t−1), xnew , xold , Nwin ) ously updates the classes parameters by using the recursive e e e adaptation Rules 12 and 13. In such a way, its validity and (13) operating conditions is a risky decision since normal and failure classes are overlapped in this region of the feature space. In order to reduce this risk, the decision about the status (normal or faulty) of any pattern classified in this re- gion is delayed by assigning the label (A) (ambiguity deci- sion). Then, this ambiguity can be removed by analyzing the past and future decisions of this pattern. The analysis of the pattern decision sequence is achieved by using a set of decision rules allowing assigning to ambiguity patterns label (N) or label (F) (normal or faulty) as follows. Let us suppose that XA = {xt , xt+1 , . . . , xt+n } is a set of patterns associated with decision (A). Let xt−1 be the previous pat- tern arrived just before xt . Let D (xt−1 ) ∈ {A, N, Fi } be the decision of this pattern. Let xt+n+1 the pattern arrived just after xt+n . Let D (xt+n+1 ) ∈ {A, N, Fi } be the deci- sion for this pattern. Then, the decision can be updated as follows: D (xt−1 ) = N ∧D (xt+n+1 ) = N ⇒ D (x) = N, ∀x ∈ XA (14) Figure 16: (a) Sensor decision space. (b) Control modes 1 D (xt−1 ) = F ∧D (xt+n+1 ) = F ⇒ D (x) = F, ∀x ∈ XA and 2 modeled by a finite state automaton. (15) D (xt−1 ) = N ∧D (xt+n+1 ) = F ⇒ D (x) = A, ∀x ∈ XA (16) where xnew and xold are respectively, the newest and the D (xt−1 ) = F ∧D (xt+n+1 ) = N ⇒ D (x) = A, ∀x ∈ XA oldest arrived pattern in the time window Nwin . (17) Initial off-line modeling allows the construction of ini- Where ∧ refers to And logical operation. tial classes that characterize knowledge from historical data. The historical data are usually sensor data that are saved. Rule 16 signifies that the fault has occurred somewhere AuDyC is used to initialize the parameters of classes that in control mode 1 where its consequences on the pitch sys- will be dynamically updated. Knowledge of failure modes tem dynamical behavior can be observed. Rule 17 indicates given from (labeled) historical data can help building a clas- that the failure has disappeared in the control mode 1 either sification scheme for fault diagnosis. However, in reality, because of maintenance actions or because the fault is inter- these data are hard to obtain. mittent. In this work, we suppose that only data corresponding to normal operating conditions (normal classes) are known in 6.4 Drift monitoring and interpretation advance. The training of the process by applying AuDyC The key problem of drift monitoring is to distinguish be- is made based on features that are extracted from historical tween variations due to stochastic perturbations and varia- sensor data once finished; the class corresponding to normal tions caused by unexpected changes in a system’s state. If operating conditions is retained. We denote this class by the sequence of observations is noisy, it may contain some CN = (µN , ΣN ). inconsistent observations or measurements errors (outliers) In on-line functioning, the parameters of CN are dynam- that are random and may never appear again. Therefore, it ically updated by AuDyC for each new pattern arrived in is reasonable to monitor a system and to process observa- control mode 2. This yields changes in the class parameters tions within time windows in order to average and reduce which continuously reflect the distribution of the newest ar- the noise influence. Moreover, the information about pos- riving patterns. We denote by Ce = (µe , Σe ) the evolving sible structural changes within time windows can be inter- classes in feature space. We have Ce (t = 0) = (µe , Σe ) = preted and processed more easily. As a result, a more reli- CN . able classifier update can be achieved by monitoring within In control mode 1 of pitch system, pitch sensor nor- time windows. The latter must include enough of patterns mal and faulty behaviors cannot be distinguished. Thus, in representing the drift. the proposed approach, the decisions about the status (nor- To distinguish the useful patterns, the pitch sensor dy- mal/faulty) of patterns located in this region are delayed. namics are represented by two different control modes. In Therefore in this case, the classifier will not be updated in the control mode 2, the degradation consequences of pitch order to avoid integrating in the drift time window useless sensor can be observed. Therefore, all patterns in this mode patterns. In order to detect the drift as soon as possible, Au- are useful to be analyzed and to be included in the drift DyC updates the classes parameters by using a window that time window. In the control mode 1, the degradation conse- contains only the patterns belonging to control mode 2. Au- quences are masked. Patterns representing normal operating DyC is dynamic by nature in the sense that it continuously conditions cannot be distinguished from patterns represent- updates the parameters of the classes as new patterns arrive. ing pitch sensor degradations. Therefore in this case, no decision (normal/drift) will be taken in order to avoid inte- 6.3 Pattern decision analysis grating in the drift time window useless patterns. When a new pattern is classified in the ambiguity class (A), The proposed scheme makes use of classes parameters in sensor feature space, assigning it to normal or failure (Mean, Variance-covariance matrix) which are dynamically updated at each time but only with the patterns belonging to control mode 2. Drift indicators are defined based on these − →(x) · − parameters and the detection of faults inception will be µe µ→ e2 (x) = kµe (x)k · kµe2 (x)k · cos θ2 (25) made based on their values. We define two drift indicators If the drift is detected and confirmed by the two drift in- Ih1 (x) , Ih2 (x) as follows: dicators Ih1 (x) and Ih2 (x), then the drift isolation (to de- termine if sensor 1 or sensor 2 or both is the source of this drift) is achieved as follows: Ih1 (x) = dM ah (CN , µe ) (18) Ih2 (x) = dE (µN , µe ) (19) Where dM ah and dE are, respectively, the Mahalanobis and If Dr = θ1 − θ2 > tha and θ1 > θ2 ⇒ DI = 1 : Euclidean metrics. fault in sensor 1 (βm1 )(26) Euclidean metric computes the distance between the cen- ter µn of the normal class CN and the center µe of evolving class Ce ; on the other side Mahalanobis metric computes If Dr = θ1 − θ2 > tha and θ2 < θ1 ⇒ DI = 2 : the distance between the normal class CN and the evolving class center µe . Therefore, these two distances are calcu- fault in sensor 2 (βm2 ) (27) lated as follows: q If Dr = θ1 − θ2 < tha ⇒ DI = 3 : dM ah (CN , µe ) = (µN − µe ) Σ−1 N (µN − µe )T fault in both sensors (βm1 andβm2 ) (28) (20) where tha is the angle threshold. tha is defined accord- q ing to the variation of patterns within the normal class CN . dE (µN , µe ) = (µN − µe ) × (µN − µe )T (21) Therefore, tha is determined experimentally using the pat- terns belonging to CN . The drift is detected when the Mahalanobis indicator The interpretation step aims at interpreting the detected Ih1 (x), defined by Equation 18, exceeds a certain thresh- changes within the classifier parameters and structure. This old thd : interpretation is then used as a prediction about the tendency of the future development of the WT current situation. This Ih1 (x) > thd ⇒ drift is detected (22) prediction is useful to formulate a control or maintenance After the drift detection, the drift is confirmed when Eu- action. clidean indicator Ih2 (x) defined by Equation 19, exceeds thd as follows: 7 Experimentation and obtained results Ih2 (x) > thd ⇒ drift is confirmed (23) The failures of pitch sensors are caused by a continuous degradation of its performance over time. This degradation The selection of thd is motivated statically by taking three can be seen as a continuous drift of the normal operating σ (standard deviations) of the data in the normal operating conditions characteristics (normal class) of the pitch sensor. conditions. Detecting and following this drift can help to predict the oc- In the case of pitch sensor faults, three scenarios may ap- currence of the pitch sensor failures. The two monitoring pear in the sensor feature space: fault impacting sensor 1 indicators defined by Equation 18 and Equation 19 are used (βm1 ), fault impacting sensor 2 (βm2 ) or fault impacting to detect and to confirm this drift for the twenty-seven sce- both sensors (βm1 and βm2 ) at the same time. The direction narios of simple and multiple drift-like fault in pitch sensors of the evolving class in the sensor feature space depends on are defined in section 2. which of these scenarios happened. Therefore, for sensor fault isolation, we use a drift direction indicator in order to 7.1 Simple drift-like fault in sensor βm1 monitor the direction of the evolving class. This will allow Figure 18 and Figure 19 represent, respectively, first and to determine which of these three scenarios happened and second residuals used in the pitch sensor feature space in hence to isolate the abnormal drift source. When drift oc- presence of an abnormal drift in pitch sensor 1, βm1 . We curs, the evolving class will migrate from normal operating can see in the case of an abnormal drift in pitch sensor 1, condition to failure. The direction indicator Dr and direc- βm1 , that only residual ∆βs1 is impacted, while residual tion isolation DI are used to isolate the sensor which caused ∆βs2 has similar behavior as the one without abnormal drift the drift-like fault. The idea is to consider the angle θ1 re- in βm1 . spectively θ2 , between the vector µe relating the center of Table 4 show the values of the drift indicators Ih1 (x) and the evolving class and the origin of the feature space, and Ih2 (x) for the nine defined drift-like fault scenarios. These the vector µe1 respectively µe2 relating the origin with the values represent the required time (starting from the drift projection of the center of the evolving class according to beginning) to detect and confirm the drift occurrence. Thus, feature 1 respectively feature 2, of the feature space. These they can be used as an evaluation criterion to measure the angles define the movement direction of the evolving class. time delay to detect a drift before its end. In order to calculate θ1 and θ2 , the scalar products be- Figures 20 and 21 show the obtained results using the tween − µ→ − → −→ − → e1 and µe and between µe2 and µe are calculated as two drift detection indicators Ih1 (x) and Ih2 (x), for sim- follows: ple drift-like fault in pitch sensor βm1 . The degradation is observed when the pitch actuator operate in control mode 2, − →(x) · − µ µ→ (x) = kµe (x)k · kµe1 (x)k · cos θ1 (24) the drift like fault in pitch sensor is successfully detected by e e1 Figure 17: Drift direction angles in the pitch sensor feature space in the case of (a) simple drift-like fault in pitch sensor 1 (βm1 ), (b) simple drift-like fault in pitch sensor 2 (βm2 ), (c) multiple drift-like fault in both pitch sensors (βm1 ) and (βm2 ). Fault N Drift speed Ih1 Ih2 Period F4h 30s(High) 5.25s 11.00s 2500s (High) -2730s F4m 60s(Medium) 8.60s 18.70s -2760s (Medium) -2760s F4s 90s 14s 26.30s 2500s (Slow) -2790s F5h 30s 6.90s 13.30s 2600s -2830s F5m 60s 11.50s 20.20s 2600s -2860s F5s 90s 14.25s 27.10s 2600s -2890s F6h 30s 6.05s 11.90s 2700s -2930s Figure 19: Second residual used in the pitch sensor feature F6m 60s 12.60s 23.50s 2700s space in the case of the simple drift-like fault in pitch sensor -2960s 1 (βm1 ). F6s 90s 15.10s 29.40s 2700s -2990s Table 4: Results of simple drift-like fault detection and con- firmation in pitch sensor 1 (βm1 ), for the nine drift scenar- ios. Figure 20: Drift indicator Ih1 (x) based on Mahalanobis dis- tance of the simple drift-like fault in pitch sensor 1 (βm1 ). both indicator Ih1 (x) and Ih2 (x), for all drift speeds (see Figure 18: First residual used in the pitch sensor feature Figure 20 and Figure 21). space in the case of the simple drift-like fault in pitch sensor The drift-like fault in pitch sensor 1 (βm1 ), is detected in 1 (βm1 ). early stage before the end of this drift (arriving to the fail- ure mode due to drift fault in pitch sensor). As an example, in the case of a drift of slow speed (F6s) (see Table 4), the Figure 21: Drift indicator Ih2 (x) based on Euclidean dis- Figure 23: Direction isolation DI of the simple drift-like tance of the simple drift-like fault in pitch sensor 1 (βm1 ). fault in pitch sensor 1 (βm1 ). pitch sensor reaches the failure mode resulting from a drift- Table 5 show the values of the drift indicators Ih1 (x) and like fault in λ1 (degradation in λ1 ) after 90 seconds of the Ih2 (x) for the nine defined drift-like fault scenarios. These beginning of the drift. In the proposed approach, this drift is values represent the required time (starting from the drift detected 15.10 seconds and confirmed 29.40 seconds after beginning) to detect and confirm the drift occurrence. Thus, its beginning. Therefore, the drift like fault in pitch sen- they can be used as an evaluation criterion to measure the sor is confirmed 60 seconds before its end. This enables time delay to detect a drift before its end. to achieve an early fault diagnosis and therefore helps the human operators of supervision to take efficiently the right Fault N Drift speed Ih1 Ih2 Period actions. F7h 30s 6.07s 12.15s 2800s Figure 22 and Figure 23 represent, respectively, evolving (High) -3030s class angle and the direction indicator of the pitch sensor F7m 60s 8.90s 19.05s 2800s fault. These figures show the obtained results in presence of (Medium) -3060s simple drift-like fault in pitch sensor 1, based on Figure 22 F7s 90s 14.20s 27s 2800s and Figure 23 the sensor 1 (βm1 ), fault is successfully iso- (Slow) -3090s lated by the direction indicator. Indeed, the direction angle F8h 30s 5.70s 11.80s 2900s shows that the evolving class exceeds the angle threshold -3130s (see Figure 17.a). Based on Equation 26, the drift-like fault F8m 60s 8.25s 18.40s 2900s in sensor 1 (βm1 ), is isolated (see Figure 29). -3160s F8s 90s 13.70s 26.18s 2900s -3190s F9h 30s 6.90s 12.70s 3000s -3230s F9m 60s 9s 20.30s 3000s 3260s F9s 90s 14.90s 28.10s 3000s 3290s Table 5: Results of simple drift-like fault detection and con- firmation in pitch sensor 2(βm2 ), for the nine drift scenarios. Figures 26 and 27 show the obtained results using the two drift detection indicators Ih1 (x) and Ih2 (x), for simple Figure 22: Direction indicator Dr of the evolving class an- drift-like fault in pitch sensor 2 (βm2 ). The degradation is gle of the simple drift-like fault in pitch sensor 1 (βm1 ). observed when the pitch actuator operate in control mode 2, the drift-like fault in pitch sensor 2 is successfully detected by both indicators Ih1 (x) and Ih2 (x) for all drift speeds (see Figure 26 and Figure 27). 7.2 Simple drift-like fault in sensor βm2 The drift-like fault in pitch sensor 2 (βm2 ), is detected in Figure 24 and Figure 25 represent, respectively, first and early stage before the end of this drift (arriving to the fail- second residuals used in the pitch sensor feature space in ure mode due to drift fault in pitch sensor). As an example, presence of an abnormal drift in pitch sensor sensor 2, βm2 . in the case of a drift of slow speed (F9s) (see Table 5), the We can see in the case of an abnormal drift in pitch sensor pitch sensor reaches the failure mode resulting from a drift- 2, βm2 , that only residual ∆βs2 is impacted, while residual like fault in λ2 (degradation in λ2 ) after 90 seconds of the ∆βs1 has similar behavior as the one without abnormal drift beginning of the drift. In the proposed approach, this drift is in βm2 . detected 14.90 seconds and confirmed 28.10 seconds after Figure 24: First residual used in the pitch sensor feature Figure 27: Drift indicator Ih2 (x) based on Euclidean dis- space in the case of the simple drift-like fault in pitch sensor tance of the simple drift-like fault in pitch sensor 2 (βm2 ). 2 (βm2 ). show the obtained results in presence of simple drift-like fault in pitch sensor 2, based on Figure 28 and Figure 29 the sensor 2 (βm2 ), fault is successfully isolated by the di- rection indicator. Indeed, the direction angle shows that the evolving class exceeds the angle threshold (see Figure 17.b). Based on Equation 27, the drift-like fault in sensor 2 (βm2 ), is isolated (see Figure 29). Figure 25: Second residual used in the pitch sensor feature space in the case of the simple drift-like fault in pitch sensor 2 (βm2 ). Figure 28: Direction indicator Dr of the evolving class an- gle of the simple drift-like fault in pitch sensor 2 (βm2 ). Figure 26: Drift indicator Ih1 (x) based on Mahalanobis dis- tance of the simple drift-like fault in pitch sensor 2 (βm2 ). its beginning. Therefore, the drift like fault in pitch sen- sor is confirmed 60 seconds before its end. This enables to achieve an early fault diagnosis and therefore helps the human operators of supervision to take efficiently the right actions. Figure 29: Direction isolation DI of the simple drift-like For the drift isolation, Figure 28 and Figure 29 are used. fault in pitch sensor 2 (βm2 ). They represent, respectively, evolving class angle and the direction indicator of the pitch sensor fault. These figures 7.3 Multiple drift-like fault in sensors βm1 and βm2 Figure 30 and Figure 31 represent, respectively, first and second residuals used in the pitch sensor feature space in presence of an abnormal drift in both pitch sensor βm1 and βm2 at the same time. We can see that both residual ∆βs1 and ∆βs2 are impacted by the occurrence of the abnormal drift in βm1 and βm2 . Table 6 show the values of the drift indicators Ih1 (x) and Ih2 (x) for the nine defined drift-like fault scenarios. These values represent the required time (starting from the drift beginning) to detect and confirm the drift occurrence. Thus, they can be used as an evaluation criterion to measure the time delay to detect a drift before its end. Figure 31: Second residual used in the pitch sensor feature space in the case of the multiple drift-like fault in pitch sen- Fault N Drift speed Ih1 Ih2 Period sor 1 (βm1 ), and sensor 2 (βm2 ). F10h 30s 5.04s 10.9s 3100s (High) -3330s F10m 60s 9s 19.04s 3100s fault in pitch sensor is successfully detected by both indi- (Medium) -3360s cator Ih1 (x) and Ih2 (x) for all drift speeds in both sensors F10s 90s 13.68s 26.23s 3100s (see Figure 32 and Figure 33). (Slow) -3390s F11h 30s 6.55s 15.50s 3200s -3430s F11m 60s 10.05s 19.30s 3200s -3460s F11s 90s 13.80s 27.50s 3200s -3490s F12h 30s 7.10s 16.10s 3300s -3530s F12m 60s 9.55s 22.80s 3300s -3560s F12s 90s 14.70s 28.25s 3300s -3590s Table 6: Results of multiple drift-like fault detection and confirmation in pitch sensor 1 (βm1 ), and pitch sensor 2 Figure 32: Drift indicator Ih1 (x) based on Mahalanobis dis- (βm2 ), for the nine drift scenarios. tance of the multiple drift-like fault in both pitch sensor 1 (βm1 ), and sensor 2 (βm2 ). Figure 30: First residual used in the pitch sensor feature space in the case of the multiple drift-like fault in pitch sen- Figure 33: Drift indicator Ih2 (x) based on Euclidean dis- sor 1 (βm1 ), and sensor 2 (βm2 ). tance of the multiple drift-like fault in both pitch sensor 1 (βm1 ), and sensor 2 (βm2 ). Figures 32 and 33 show the obtained results using the two drift detection indicators Ih1 (x) and Ih2 (x), for mul- The multiple drift-like faults in pitch sensors are detected tiple pitch sensor fault. The degradation is observed when in early stage before the end of these drifts (arriving to the the pitch actuator operate in control mode 2. The drift like failure mode due to drift fault in both pitch sensors). As an example, in the case of a drift of slow speed (F12s) (see Ta- a classifier able to achieve a reliable drift monitoring and ble 6), the pitch sensors reache the failure mode resulting early diagnosis of simple and multiple pitch sensors faults. from a drift-like fault in λ1 and λ2 (degradation in λ1 and This approach considers the system switching between sev- λ2 ) after 90 seconds of the beginning of the drift. In the eral control modes. This approach based on the monitoring proposed approach, this drift is detected 14.70 seconds and of the drift of the characteristics of classes representing the confirmed 28.25 seconds after its beginning. Therefore, the normal operating conditions of pitch system in each con- multiple drift-like fault in pitch sensor is confirmed 60 sec- trol mode. These characteristics are described by the mean onds before its end. This enables to achieve an early fault and variance covariance matrix of these classes. They are diagnosis and therefore helps the human operators of super- monitored using two indicators in order to monitor and fol- vision to take efficiently the right actions. low the drift. Both are defined based on the computation For the drift isolation, Figure 34 and Figure 35 are used. of the distance between the class representing normal oper- They represent, respectively, evolving class angle and the ating conditions and the evolving class. The first indicator direction indicator of the pitch sensor fault. These figures is based on the Mahalanobis distance and is used to detect show the obtained results in presence of a multiple drift-like the drift; while the second indicator is based on Euclidean fault in both pitch sensors βm1 and βm2 , as we can see in distance and is used to confirm the drift. The drift indica- Figure 34 and Figure 35 the fault is successfully isolated by tors have detected successfully all drift scenarios of three the direction indicator. 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