Wind turbine fault detection based on expanded linguistic terms and rules using non-singleton fuzzy logic

Applied Energy 262 (2020) 114469

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Wind turbine fault detection based on expanded linguistic terms and rules using non-singleton fuzzy logic

T

⁎

Fuming Qub, Jinhai Liua,b, , Hongfei Zhub, Bowen Zhoub a b

State Key Laboratory of Synthetical Automaton for Process Industries, Northeastern University, Shenyang 110819, China Collage of Information Science and Engineering, Northeastern University, Shenyang 110819, China

H I GH L IG H T S

FIS fault detection method is proposed to detect early wind turbine faults. • AA non-singleton fuzzy input generation method is proposed. • A non-singleton mechanism of expanding linguistic terms and rules in FIS is put forward. • Based on the defuzzified result, fault factor is designed to measure fault severities. • Real wind turbine SCADA data are used in the experiments of this paper. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Fault detection Wind turbine SCADA data Non-singleton fuzzy inference system Expanded linguistic terms and rules

Wind power generation efficiency has been negatively affected by wind turbine (WT) faults, which makes fault detection a very important task in WT maintenance. In fault detection studies, fuzzy inference is a commonlyused method. However, it can hardly detect early faults or measure fault severities due to the singleton input and the limited linguistic terms and rules. To solve this problem, this paper proposes a WT fault detection method based on expanded linguistic terms and rules using non-singleton fuzzy logic. Firstly, a generation method of non-singleton fuzzy input is proposed. Using the generated fuzzy inputs, non-singleton fuzzy inference system (FIS) can be applied in WT fault detection. Secondly, a mechanism of expanding linguistic terms and rules is presented, so that the expanded terms and rules can provide more fault information and help to detect early faults. Thirdly, the consequent of FIS is designed by the expanded consequent terms. The defuzzified result, which is defined as the fault factor, can measure fault severities. Finally, four groups of experiments were conducted using the real WT data collected from a wind farm in northern China. Experiment results show that the proposed method is effective in detecting WT faults.

1. Introduction The rapid development of wind energy has boosted the installations of wind turbines (WTs) [1]. Meanwhile, an increasing demand for higher power generation efficiency has put more pressure on the operation and maintenance (O&M) of WTs [2]. One of the essential tasks of O&M is to deal with WT faults, which have negatively affected power generation efficiency and caused a heavy economic loss [3]. If WT faults are detected in time, it would greatly reduce O&M costs [4]. Therefore, due to its significant role in the O&M of WTs, there have been increasing studies on WT fault detection, such as the detection methods based on signal processing [5], image processing [6], machine learning [7], deep learning [8], etc.

⁎

Fault detection based on condition monitoring (CM) is one of the most commonly-used methods. The main principle of the method is to examine whether the collected on-line data are within the normal range. If the data are out of the normal range, there might be an anomaly or a fault. Furthermore, WT faults can be detected and diagnosed according to different anomaly data. Fault detection based on CM is effective and easy to operate. In [9], an unsupervised anomaly detection approach for WT condition monitoring was proposed. In [10], a temperature-based real-time aging monitoring method was presented for power converter modules. In [11,12], CM-based fault detection methods were put forward to detect the WT faults in gearbox and generator respectively. In fault detection methods based on CM, many types of data can be

Corresponding author at: State Key Laboratory of Synthetical Automaton for Process Industries, Northeastern University, Shenyang 110819, China. E-mail address: [email protected] (J. Liu).

https://doi.org/10.1016/j.apenergy.2019.114469 Received 20 June 2019; Received in revised form 28 November 2019; Accepted 25 December 2019 0306-2619/ © 2020 Elsevier Ltd. All rights reserved.

Applied Energy 262 (2020) 114469

F. Qu, et al.

and help to detect early faults. Moreover, the defuzzified fault factor can tell fault severities.

used, including Supervisory Control and Data Acquisition (SCADA) data [13], vibration data [14], strain data [15], acoustic data [16], and lubrication oil data [17]. However, the acquisition of the vibration data and other types of data requires additional sensors, which increases the maintenance cost [18]. Fortunately, modern wind farms (WFs) usually install SCADA system, which collect hundreds types of on-line WT data at a certain interval. SCADA data are cost effective, as no additional sensors are needed [19]. A lot of research based on SCADA data has been put forward to realize the fault diagnosis and fault prognosis. In [20], machine learning models based on domain knowledge were proposed to realize fault detection. In [21], deep neural network (DNN)-based framework was put forward to detect WT gearbox faults. In [22], many data-mining approaches for wind power prediction were evaluated, which can be used for fault detection. In [23], a fault detection method based on multiclass support vector machine algorithms was proposed. Meantime, fault prognosis has gained a rapid development in recent years [24]. Based on SCADA data, an on-line fault prognosis method [25] and a prior knowledge-based prognosis method [26] of WT pitch faults were proposed. Among the CM and fault detection approaches, one of the commonly-used method is the fuzzy inference system (FIS). FIS evaluates inputs with “if-then” rules based on fuzzy logic. There are two parts in the rule: “if” part gives the evaluation of the input and “then” part returns a fuzzy output according to the rule [27]. Based on FIS, many fault detection methods have been proposed. In [28], FIS was established with rare association rule to predict the spatiotemporal distribution of energy security weaknesses in transmission networks. In [29], an adaptive neuro-fuzzy inference system and hybrid models were developed. In [30], a system for WT condition monitoring using adaptive neuro-fuzzy interference systems was proposed, and it has achieved good experiment results. In [31], an effective generalized model for WT anomaly identification method based on fuzzy synthetic evaluation was put forward. In [32], a development of a fault diagnosis scheme based on identified fuzzy models was presented. In [33], a monitoring strategy of short-circuit fault between turns of the stator windings and open stator phases by fuzzy logic technique was proposed. However, several problems remain in the WT fault detection based on FIS: (1) Early faults cannot be detected using conventional FIS methods due to the averaged singleton input. The widely-applied methods usually use daily averaged data as the input to reduce false alarms of WTs. However, the details of the data are omitted. (2) Fault severities cannot be measured by conventional FIS methods due to the limited number of FIS consequent terms (for example, only “normal” and “fault”). In order to tackle the above problems, this paper proposes a WT fault detection method with SCADA data based on expanded linguistic terms and rules using non-singleton fuzzy logic. First, a method of generating non-singleton input is proposed. The non-singleton inputs can be obtained by transforming probability density functions (PDFs) of the grouped prediction errors, which enables the application of nonsingle FIS in WT faut detection. Second, more antecedent and consequent terms are expanded by the proposed method. The rules of fault detection are also expanded accordingly. Consequently, the fuzzy system can detect the fault at an early stage and provide more information about fault severities. Third, the FIS consequent is designed by the expanded consequent terms, and the defuzzified output is defined as the fault factor, which can tell the severity of the fault. The contributions of this paper include:

The rest of this paper is organized as follows. Section 2 introduces the related work and the problem description. Section 3 describes the proposed method in detail. Experiments and comparisons are listed in Section 4. Section 5 is the conclusion of the present work. 2. Related work and problem description 2.1. Review of the FIS method in WT fault detection FIS method of WT fault detection based on SCADA data generally consists of the following three steps [30,31]. Step 1: Data prediction. First, the original normal SCADA data Dorg (x ) (consisting of n variables) are collected, as shown in Eq. (1). 1 2 n Dorg (x ) = [Dorg (x ), Dorg (x ), …, Dorg (x )]

(1)

i Dorg (x )

is the ith variable in Dorg (x ) . The SCADA data usually where, consist of various variables [34,35], including wind speed (m/s), active power (kw), generator temperature (°C), and bearing temperature (°C), etc. Then, fault-related variables of SCADA data are chosen. These variables are predicted by their relevant data (including current data, historical data and current data of other WTs [31]), as indicated in Eq. (2). k d (1) d (2) d (m) Dprd = fpredict [Dorg , Dorg , …, Dorg ]

(2)

d (j ) k where, Dprd is the fault-related variable and Dorg is the jth relevant data k . fpredict is the prediction method, which mainly includes time of Dprd series method [36], neural network method [37], etc. Step 2: Anomaly detection by the prediction error. With the colk k (x ) and its predicted data Dprd (x ) , the prediction error lected data Dorg k D (x ) can be calculated by Eq. (3). k k D k (x ) = Dorg (x ) − Dprd (x )

(3)

Then, probability distribution function (PDF) of the prediction errors can be obtained. Also, the upper bound Bup and the lower bound B dn of the PDF are calculated as follows: (1) A confidence interval τ is set, and (2) the value of the left endpoint of the confidence interval is defined as the lower bound and that of the right endpoint as the upper bound. For example, if τ is set as 99%, the value corresponding to 0.5% in the PDF is the lower bound and the value corresponding to 99.5% in the PDF is the upper bound. Therefore, if the collected on-line prediction error dr is greater than Bup , it is marked as “high”, whereas if dr is less than B dn , it is marked as “low” (in some researches, more bounds are introduced, such as “very high” and “very low” [30]). Step 3: Fault detection based on FIS. In order to detect a certain fault, prior knowledge is extracted as rules to detect WT faults [38]. According to certain combinations of data anomalies, WT faults can be diagnosed. Fig. 1 shows an example of the WT fault detection with the conventional FIS method. Two variables of WT SCADA data (Data 1 and Data 2) are collected and predicted. Then, PDFs of the two prediction errors are calculated and the lower bounds and the upper bounds are obtained. At a certain moment, Data 1 is marked as “high” and Data 2 is marked as “low” (as illustrated by red points in Fig. 1). Then, it is determined as Fault X according to Rule 001. 2.2. Problem description

(1) A generation method of non-singleton fuzzy input is proposed, and non-singleton FIS is applied to detecting WT faults. To the authors’ knowledge, it is the first time that non-singleton FIS has been applied to detecting WT faults. (2) A method of expanding linguistic terms and rules in FIS is proposed. The expanded terms and rules can provide more fault information,

There are several problems that prevent the conventional FIS method from detecting the early fault. The first problem is the limitation of singleton input in FIS. In order to reduce false alarms, daily averaged data, rather than the 10-min data, are often used by FIS methods, which would result in the lack of data details. Fig. 2 shows an 2

Applied Energy 262 (2020) 114469

F. Qu, et al.

Fig. 1. Schematic of the conventional FIS method of WT fault detection.

Phase 2: Non-singleton input transformation. Different from the conventional FIS method, the proposed method introduces non-singleton FIS input in WT fault detection. The prediction errors are divided into groups. The PDF of each group is calculated. Then each PDF is transformed to a non-singleton input. With the non-singleton input, non-singleton FIS can be applied in WT fault detection. Details are discussed in Section 3.2. Phase 3: Linguistic terms and rules acquisition. Similar to the conventional FIS method [41], linguistic terms and rules are extracted from prior knowledge and experts’ experience. First, rules for detecting WT faults, such as “IF A is High AND B is Low THEN Fault 01 (Fault)”, are acquired. Second, linguistic variables and terms are extracted from the rules, such as “A” is extracted as a linguistic variable, whereas “High”, “Normal”, “Low” are extracted as the linguistic terms of “A”. Consequently, the original membership functions (MFs) can be calculated by fuzzy statistics method [42]. There are many types of MFs, such as Gaussian MF [43] and interval type-2 MF [44]. In this paper, the triangular/trapezoid MFs are adopted. These MFs can be easily obtained by data-driven method, and many similar methods [30,31] have achieved good results using this type of MFs in detecting WT faults. Phase 4: Linguistic terms and rules expansion. Linguistic terms of antecedent are expanded, with the aim of enabling the FIS to detect early faults and measuring fault severities. Then according to different combinations of expanded antecedent terms, consequent terms at different fault levels are generated. Accordingly, the expanded rules are also obtained. Details are described in Section 3.3. Phase 5: Fuzzy inference. In this phase, fuzzy inference engine [45] is applied to processing fuzzy input sets into fuzzy output sets. First, firing levels are calculated by the non-singleton fuzzy inputs and antecedent MFs. Then, output sets are obtained by the calculation of

example. In this case, the gearbox oil temperature is monitored at an interval of 10 min. The blue dot region is a time window T, in which the data points are averaged as one value. It can be found that although the averaged value in T is lower than the upper bound, many data points in T are higher than the upper bound. Such case can be regarded as a potential anomaly, which cannot be detected by the conventional singleton-based FIS. The second problem is the limited number of linguistic terms of a fault. Linguistic terms in WT fault detection are extracted from the prior knowledge and experts’ experience. The number of linguistic terms is small due to the limited prior knowledge and experts’ experience. In practice, the consequent of rules usually include only two terms of “Normal” and “Fault”. Consequently, it prevents FIS from detecting early faults and telling fault severities. 3. The proposed method 3.1. Architecture of the proposed method The architecture of the proposed method is designed based on the process of conventional FIS, as shown in Fig. 3. There are six phases in this architecture (The red dotted parts are the originalities of the proposed method). Phase 1: Data prediction. As discussed in [30], according to the commonly-used FIS methods, the original data are collected and predicted. In this study, the current data and the historical data are selected to predict the target data. Many approaches can be used to predict data [39,40]. In this paper, the widely-applied neural network (NN) method is used to realize the prediction. The prediction error can be obtained by Eqs. (1)–(3).

Fig. 2. An example of the anomaly which cannot be detected by the conventional FIS method. 3

Applied Energy 262 (2020) 114469

F. Qu, et al.

Fig. 3. Architecture of the proposed method.

consequent MFs and firing levels. Phase 6: Fault factor. Normally, the conventional FIS method only uses the output of the rule as the final result of the fault detection. In this paper, benefited from the expanded linguistic terms and rules, the fault detection can go a step further. The fuzzy output sets are defuzzified to a crisp output (fault factor), which is designed to measure fault severities. Details are described in Section 3.4.

The designed process is shown in Fig. 4. First, each obtained prediction error D k is regarded as a linguistic variable. Then, D k is divided into groups by Eq. (4).

Dtk = [D k (t ∗ P + 1), D k (t ∗ P + 2), …, D k (t ∗ P + P )]

(4)

where, t is the group number and P is the number of data points in each group (in this paper, P is set as 144). Next, each Dtk is converted to a fuzzy number. Different from singleton FIS, which uses a single value as the input, non-singleton FIS uses fuzzy number as the basic input unit. To qualify as a fuzzy number, a fuzzy set A must possess the following properties [41]: (1) A must be a normal fuzzy set; (2) Aα must be a closed interval for every α ∈ (0, 1] and (3) the support of A must be bounded. Normally, the distribution of Dtk is considered as a normal distribution in this method. Thus, ftk (PDF of Dtk ) can be estimated. It can be found that: (1) ftk is normal; (2) According to PDF properties, (ftk )α is

3.2. Non-singleton input transformation Compared with singleton FIS, fuzzy logic based on non-singleton input proved to be a more effective method in theory [45]. However, in practice, it has not been applied in the fault detection field. In this paper, the fuzzy number of non-singleton input is correlated to the PDF of prediction errors, which realizes the application of non-singleton FIS in WT fault detection.

Fig. 4. The process of non-singleton FIS on WT fault detection. 4

Applied Energy 262 (2020) 114469

F. Qu, et al.

a closed interval for every α ∈ (0, 1]; (3) By setting an appropriate confidence interval, the support of ftk is bounded. This means ftk completely meets the requirements of a fuzzy number. Thus, it can be used in non-singleton FIS. Therefore, the non-singleton input transformation can be implemented. First, the mean μtk and the standard deviation σtk of each Dtk are calculated by Eq. (5) and Eq. (6) respectively.

μtk = average(Dtk ) σtk =

1 p

(5)

p

∑i =1 (x − μtk )2

(6)

Then, the fuzzy number of non-singleton input can be obtained by transforming each ftk , as shown in Eq. (7).

Fnk (t , x , P ) = ftk (x ) =

(x − μtk )2 1 exp[− ], k 2π σt 2(σtk )2

x ∈ [t ∗ P + 1, t ∗ P + P ]

(7)

Fig. 6. Illustration of antecedent linguistic terms expansion. (a) Terms and their MFs before the expansion. (b) Terms and their MFs after the expansion.

Dk

and P is the number of data points in where, t is the group number of each group. The fuzzy number of non-singleton input is briefly marked as μϑk (x ) in Eq. (8).

μϑk (x ) = Fnk (t , x , P )

distribution of the input data set. The non-singleton input makes the calculated membership degree more accurately reflect the actual WT condition, which could help to detect early faults that are undetected by conventional FIS methods.

(8)

Therefore, the input data set μϑ (x1, x2…x q) of the linguistic terms) can be calculated by Eq. (9).

μϑ (x1, x2…x q) = μϑ1 (x1) ★ μϑ2 (x2) ★ … ★ μϑq (x q)

lth

Rule

Rl

(with q

3.3. Expanding linguistic terms and rules

(9)

In this section, a method of expanding linguistic terms and rules is proposed. The limited linguistic terms is a problem in FIS. In order to solve this problem, Jerry M. Mendel firstly proposed a basic theory on linguistic terms expansion [47]. The main idea is to extract new linguistic terms from the original ones according to their features. Inspired by this theory, a mechanism of expanding linguistic terms and rules for WT fault detection is designed in this paper. Part 1: The expansion of antecedent linguistic terms. Theoretically, the expanded terms should be generated from the existing ones. Therefore, in this paper, every two existing adjacent terms are used to generate a new term. Fig. 6 shows an example. First, the critical points (PL, PNL, PNH and PH in Fig. 6(a)) of the original MFs in antecedent are calculated by the statistical method. Then, the crossing points of MFs and their x-values are marked (PSL and PSH in Fig. 6(b)). The crossing point is the fuzziest point (take PSL for example, it is neither “Low” nor “Normal”). Thus, its membership degree in the new term is defined as 1. Finally, the vertical

where, ★ is the minimum t-norm operator [46]. Also, the antecedent set μ F l (x1, x2…x q) of Rl can be calculated by Eq. (10).

μ F l (x1, x2…x q) = μ F1l × F2l …× Fql (x1, x2…x q) = μ F1l (x1) ★ μ F2l (x2) ★ … ★ μ Fql (x q) (10) where, μ F l is the antecedent MF. Then, firing levels Fll are calculated with μϑ (x1, x2…x q) and μ F l (x1, x2…x q) by Eq. (11).

Fll =

max(X1)

Sup

x 1= min(X1)

{μϑ(1) (x1) ★μ F(1) (x1)} ★ l

max(Xq)

★

Sup x q = min(Xq)

max(X2)

Sup

x2 = min(X2)

{μϑ(q) (x q) ★μ F(lq) (x q)}

{μϑ(2) (x2) ★μ F(2) (x2)} ★ ⋯ l

(11)

where, X is the domain of the input sets. Fig. 5 shows an illustration of the computing process of non-singleton membership degrees. It can be found that the membership degree is no longer determined by a single input value, but by the

Fig. 5. Illustration of the computing process of non-singleton membership degrees. (a): The non-singleton fuzzy input and MFs of the antecedent. (b) and (c): The calculated membership degree (the red dot) of the antecedent terms. (d) Calculation results. 5

Applied Energy 262 (2020) 114469

F. Qu, et al.

line through the crossing points is made and the original critical points are connected. The obtained triangles (pink dotted lines in Fig. 6(b)) are the MFs of the expanded terms. Operator ⊙ is defined as the above generation process. Thus, a new linguistic term can be obtained by Eq. (12).

Tmnew = Tmleft ⊙ Tmright

(12)

where, Tmnew is the expanded new term. Tmleft and Tmright are its two adjacent terms. Part 2: Expanding rules and consequent linguistic terms. With the expansion of antecedent linguistic terms, rules are accordingly expanded. Supposing that the original rule R of a fault has N antecedents, each term in the antecedent is expanded to more new terms according to the expansion method described in Part 1. Thus, each antecedent in R has two types of terms, the original term Tmorg and the expanded term Tmexp . Through different combinations of Tmorg and Tmexp , new rules are generated. If the new rule has m original terms (accordingly, there will be N − m expanded terms), the consequent of the rule is defined as Error Level m. Consequently, there is only one error result before the expansion, whereas N + 1 Error Levels after the expansion, with the most serious fault Error Level N and the least serious fault Error Level 0. Next, consequent linguistic terms are expanded. Each Error Level is defined as a new consequent linguistic term. Thus, there would be N + 1 consequent linguistic terms of the fault. The linguistic terms and rules expansion algorithm is summarized in Algorithm (1).

Fig. 7. The designed consequent and the process of calculating the fault factor. (a) The designed consequent and the calculated firing levels. (b) The gravity center of the intercepted consequent.

Then, the triangular MF, which has been effectively used in consequent definition, is applied in all consequent terms, as shown in Fig. 7(a). To get the output data set of the lth rule, the lth consequent is calculated by the lth firing level obtained by Eq. (11), as shown in Eq. (14).

Algorithm 1. Linguistic Terms and Rules Expansion

Input: R - original rule, Tmtant - antecedent term of R (t is the ranking of Tmtant in its linguistic variable), N - the number of antecedent terms of R, Tmcsq - consequent term of R. Output: Rexp - expanded rules, Tmexp − ant - expanded antecedent terms, Tmexp − csq expanded consequent terms. 1: R = {Tmant (1), Tmant (2)…Tmant (N ) → Tmcsq}

μ Bl (δ ) = μϑ ∘ Rl (δ ) = μGl (δ ) ☆ Fll

where, l is the index of rules, μ Bl (δ ) is the output data set of the lth rule, ϑ is the input data set, Rl is the lth rule, ∘ is the operator of max-min relation composition [46] and μGl (δ ) is the consequent of the lth rule. Next, the output data set μ (lvl ) (in the same linguistic variable lv but B different rules) are intergraded by Eq. (15), as shown in Fig. 7(b).

2: for each Tmtant in R do 3:

ant find the adjacent terms of Tmtant (in its linguistic variable): Tmtant − 1 and Tmt + 1 (if exist)

4:

ant Tm ant ⊙ Tmtant −1 dn ← Tmt

5:

ant Tm ant ⊙ Tmtant up ← Tmt +1

6: 7:

save expanded terms of antecedent: ant Tmexp − ant ← [Tm ant dn , Tm up ]

μB(lv) (δ ) = μ B(lv1 ) (δ )⊕ μ B(lv2 ) (δ )⊕⋯⊕ μ B(lvn ) (δ )

t

t

t

t

define ith new term of the consequent: Tmexp − csq (i) replace any i terms of Tmant with any i terms of Tmexp − ant

12:

Rexp (new )

13: 14: 15:

← R {[(Tmant ) N − i , (Tmexp − ant )i ] → Tmcsq (i) } save expanded terms of consequent and rules: Tmexp − csq ← Tmexp − csq (i)

B

(lv ) (lv ) δ ̂ represents fault severities. The range of δ ̂ is between 0 and 100. (lv ) ̂ The greater the δ , the more serious the fault is. (lv ) δ̂ =

16: Rexp ← Rexp (new ) 17: end for

M

∑i = 1 δi μB(lv) (δi ) M

∑i = 1 μB(lv) (δi )

,

δi ∈ [0, 100] (16)

In summary, the technologies of the proposed method are described as follows: NN-based data predictions and non-singleton transformation (Section 3.2) are used to obtain non-singleton inputs. Expanded linguistic terms and rules are obtained by prior knowledge and the expanding method (3.3). Then, the non-singleton FIS is applied in fault detection. The defuzzified fault factor (3.4) can tell the severity of the fault. Moreover, multiple types of faults can be detected by one FIS of the proposed method with sufficient rules.

3.4. Design of the consequent and fault factor In the conventional FIS method, the process of WT fault detection ends once the fuzzy consequent (for example, “fault” or “normal”) is obtained. However, this result could neither help to find early faults nor tell fault severities due to its limited consequent terms. In this section, defuzzification is applied and the fault factor (used to measure fault severities) is designed. Fig. 7 is an illustration of the designed consequent and the process of calculating the fault factor. First, original consequent terms Tmcsq and the expanded consequent terms Tmexp − csq are combined, as shown in Eq. (13).

G = [Tmcsq , Tmexp − csq]

(15)

where, ⊕ denotes the operation of getting the maximum value and μB(lv) (δ ) is the output data set of the linguistic variable lv. Finally, the fault factor can be obtained by getting the gravity center (lv ) of μ (lv) (δ ) , as shown in Eq. (16). δ ̂ is the fault factor and the value of

8: end for 9: for each i in [1, N] do 10: 11:

(14)

4. Experiments and discussion 4.1. Experiment settings In order to verify the effectiveness of the proposed method, four groups of experiments are conducted using real WT SCADA data collected in a wind farm (WF) in northern China. There are altogether 22 WTs in this WF. All the WTs are of the same type. The capacity of each

(13) 6

Applied Energy 262 (2020) 114469

F. Qu, et al.

⎧0 ⎪ 0.1698x + 1.0692 μnml (x ) = 1 ⎨− 0.1763x + 1.1467 ⎪ ⎩0

WT is 2 MW. The SCADA data collected in two years (with a time interval of 10 min) are used in the study. The commonly-used back propagation neural network (BPNN) method is adopted to make the prediction. Moreover, similar to the previous studies [30,31,33], the number of data points in each group is set as 144 in this paper, so that the daily condition of the WT can be properly monitored. (1) If the number of data points in a group is set too large, the condition would be monitored at a long time interval. (2) If the number is set too small, the statistical characteristics of the data would be weakened. Therefore, the number of data points in each group is set as 144 in this paper. In the following experiments, the faults used for evaluation are all real faults, and they undergo the development from early faults to serious faults. The earlier these faults are detected, the more conducive it is for WT maintenance. Experiments are designed as follows: the proposed non-singleton input is verified to detect the early anomaly in Section 4.2. The effectiveness of the proposed method for detecting early faults is tested in Section 4.3 (with multivariate input) and Section 4.4 (with one-variable input), respectively. Finally, the robustness of the method is verified in experiments in Section 4.5.

x < 0.8325 ⎧0 μhigh (x ) = 0.1763x − 0.1468 0.8325 ⩽ x < 6.5056 ⎨1 x ⩾ 6.5056 ⎩

(18)

(19)

where, μlow (x ), μnml (x ) and μhigh (x ) are the MFs of “low”, “normal” and “high”, respectively. In this experiment, the conventional FIS method, such as the method in [33], is selected to make comparison with the proposed method. In order to make a better comparison, the setting of the proposed method in this experiment is the same as that of the conventional FIS method except for the fuzzy input part. The conventional FIS method uses singleton input, while the proposed method uses the nonsingleton input. Fig. 9 shows the experiment results. Fig. 9(a) and (c) show the averaged prediction errors in one day (APE-D) and in every 10 min (APE-M) respectively. (1) Using the conventional FIS method, APE-D exceeds the upper bound on 2015-06-24, triggering an alert, as shown in Fig. 9(b). However, from 2015-06-19 to 2015-06-23, although APE-D does not exceed the upper bound due to the high data variance, many APE-M exceed the upper bound, which could be considered as a potential anomaly. As can be seen, the conventional FIS method cannot capture these early anomalies. (2) Using the proposed non-singleton FIS method, the anomaly detection is improved, as shown in 9(d). It can be noted that the anomaly is detected on 2015-06-19, five days earlier than the conventional FIS method. Some details of the anomaly detections are shown in Fig. 10. On 2015-06-15, both the data calculated by the conventional FIS method (DTM) (the blue point in Fig. 10), and the data calculated by the proposed method (DPM) (the red point in Fig. 10) are below the upper bound, which indicates that the WT is in normal condition. On 201506-19, DTM is below the upper bound while DPM is above the upper bound. It can be found that due to the large data variance, DPM increases. As a result, the anomaly can be detected in advance by the proposed method. It is not until 2015-06-24 that DTM exceeds the upper bound, which is five days later. From this experiment, it can be concluded that the proposed non-singleton FIS method can effectively detect early WT anomalies.

4.2. Experiment 1: effectiveness of the non-singleton FIS This experiment is conducted to verify the effectiveness of the proposed non-singleton input in WT fault detection. In June 2015, the gearbox oil temperature of WT 12 started increasing due to the aging of the oil. The high temperature of gearbox oil is a sign of a potential fault. In order to detect this anomaly, the data of gearbox oil temperature is used in this experiment. First, BPNN method is used to predict data and prediction errors are obtained. Fig. 8(a) shows the prediction errors of the historical data and Fig. 8(b) shows the PDF of the prediction errors. Then, the upper bound (3.71 °C) and the lower bound (−3.28 °C) are calculated. Then, the corresponding MFs are obtained by the fuzzy statistics method [42]. The mathematical description of the MFs are listed as follows:

x < − 6.2966 ⎧1 μlow (x ) = − 0.1698x − 0.0694 − 6.2966 ⩽ x < − 0.4088 ⎨0 x ⩾ −0.4088 ⎩

x < − 6.2966 − 6.2966 ⩽ x < − 0.4088 − 0.4088 ⩽ x < 0.8325 0.8325 ⩽ x < 6.5056 x ⩾ 6.5056

(17)

4.3. Experiment 2: comparative experiment with multivariate input In this section, two groups of experiments are carried out to verify the effectiveness of the proposed method in WT fault detection with multivariate FIS input. Similar to Experiment 1, the conventional FIS method, such as the method in [33], is selected to make comparison with the proposed method. 4.3.1. Experiment 2.1: detecting cooling system fault In early 2015, the cooling systems of WTs were improved to enhance their heat dissipation capability. However, several WTs were poorly updated. The converter fan was improperly installed, leading to an increase of converter temperature. As there are no sensors that can directly measure the converter temperature,the converter choke coil temperature (CCCT) and converter controller top temperature (CTT) are monitored instead. The rule of the fault from the prior knowledge is summarised as: IF (CCCT is high) AND (CTT is high) THEN (the converter temperature is high and there are faults in WT’s cooling system), which is listed as the first rule in Table 1. First, the prediction errors and their PDFs of CCCT and CTT are calculated. Also, the corresponding MFs are obtained by the fuzzy statistics method. Second, the original MFs and rules are expanded. (1) As has been described in Section 3, the antecedent terms are expanded

Fig. 8. The prediction errors and their PDF of gearbox oil temperature (WT 12). (a) Prediction errors of the historical data. (b) PDF of the prediction errors. 7

Applied Energy 262 (2020) 114469

F. Qu, et al.

Fig. 9. The anomaly of gearbox oil temperature (WT 12) and the detection results. (a) Averaged prediction errors in one day. (b) Anomaly detection result using the conventional FIS method. (c) Averaged prediction errors in every 10 min. (d) Anomaly detection result using the improved non-singleton input.

Fig. 10. The fault detection based on non-singleton fuzzy input. (a), (b), (c) and (d) are four cases in the fault detection. (a): 2015-06-15. (b): 2015-06-19. (c): 2015-06-24. (d): 2015-06-30. The blue point indicates the data calculated by the conventional FIS method and the red point indicates the data calculated by the proposed non-singleton FIS method.

8

Applied Energy 262 (2020) 114469

F. Qu, et al.

Table 1 The Expanded Rules in Experiment 2. No.

Rules

1 2 3 4

If If If If

(CCCT (CCCT (CCCT (CCCT

Type is is is is

high) and (CTT is high) then Converter Temp. high (major fault) sub-high) and (CTT is high) then Converter Temp. high (minor fault) high) and (CTT is sub-high) then Converter Temp. high (minor fault) sub-high) and (CTT is sub-high) then Converter Temp. high (warning)

Original Expanded Expanded Expanded

CCCT is the converter choke coil temperature and CTT is the converter controller top temperature.

errors of CCCT and CTT. The conventional FIS method fails to detect such early faults. Different from the conventional FIS method, the proposed method uses non-singleton input, expanded terms and rules in WT fault detection. Moreover, the conventional FIS method depends on upper and lower bounds, while the proposed method uses fuzzy areas to determine membership degrees. From the experiment results, it can be found that: (1) The fault is detected 5 days earlier by the proposed method. (2) On 2015-04-28, the fault factor rises above zero and a warning is triggered. From 2015-04-28 to 2015-05-10, the fault factor keeps increasing, indicating that the fault is getting worse. From the results of the experiment, it can be concluded that compared with the conventional FIS method: (1) the proposed method can detect faults at an early stage, and (2) it can tell the severity of the fault.

Fig. 11. The consequent of converter high-temperature fault.

from three (low, normal and high) to five (low, sub-low, normal, subhigh and high). (2) Accordingly, the original rules are expanded from one to four, as shown in Table 1. As can be seen, the expanded MFs and rules enrich the outputs. Then, the FIS consequent is designed according to the descriptions in Section III, as shown in Fig. 11. The designed consequent has four terms: Normal, Warning (2 sub-highs), Minor error (1 sub-high and 1 high) and Major error (2 highs). It can be found that the original method has a consequent of two terms whereas the proposed method has four. Fig. 12 shows the monitored data during the fault and the detection results using the conventional FIS method and the proposed method. It can be found that during this period, both the prediction errors of CCCT and CTT increases. In the conventional FIS method, on 2015-05-01, CCCT exceeds its upper bound, but CTT remains normal. On 2015-05-03 CTT also exceeds its upper bound, triggering an alarm (as shown in Fig. 12(a), (b) and (c)). However, it can be found that from late April to early May, there are tendencies of increasing temperatures in both the prediction

4.3.2. Experiment 2.2: detecting blade angle sensor fault In August 2014, the output active power of WT 16 decreased. After a shutdown inspection, a fault of blade pitch angle sensor was found. The measured angle is inconsistent with the actual angle, leading to a misjudgment of the control system. Consequently, the output active power is lower than it should be. According to this fault type, a rule can be summarized: “IF (wind speed is normal) AND (output active power is low) AND (pitch angle is normal) THEN (possible fault: pitch angle sensor fault)”. Then, (1) the conventional method (such as the method in [33]) and (2) the proposed method are used to detect this fault. Similar to Experiment 2.1, first, the PDFs of the prediction errors of wind speed, output active power, and pitch angle are estimated. Then, the upper bounds and the lower bounds of these PDFs are obtained, and MFs are established by the fuzzy statistics method. The prediction errors of wind speed, active output power and pitch angle are shown in Fig. 13(a), Fig. 13(b), and Fig. 13(c) respectively. The experiment

Fig. 12. The monitored data and detection results of Experiment 2. (a) The averaged prediction errors of CCCT in one day. (b) The averaged prediction errors of CTT in one day. (c) Detection result of the conventional FIS method. (d) The averaged prediction errors of CCCT in every 10 min. (e) The averaged prediction errors of CTT in every 10 min. (f) Detection result of the proposed method. 9

Applied Energy 262 (2020) 114469

F. Qu, et al.

Fig. 13. The monitored data and detection results of Experiment 2.2. (a) Prediction errors of wind speed. (b) Prediction errors of active output power. (c) Prediction errors of pitch angle. (d) Detection result of the conventional FIS method. (e) Detection result of the proposed method.

a single prediction model or with multi-prediction models. The proposed method can detect the fault at an early stage. Therefore, it can be concluded that: (1) The proposed method can effectively detect the early fault. (2) Both the proposed non-singleton input and the proposed expansion of terms and rules are effective in WT fault detection.

results are shown in Fig. 13(d) and Fig. 13(e). It can be found that the proposed method detects the fault (on 201408-15) two days earlier than the conventional method (on 2014-08-17). From the experiment results, it can be concluded that the proposed method is effective in detecting WT faults with multivariate inputs.

4.5. Experiment 4: verification of the robustness of the proposed method

4.4. Experiment 3: comparative experiment with single-input

Robustness has always been an important factor for evaluating the methods in industrial applications [48,49]. In this section, experiments are conducted to verify the robustness of the proposed method. The experiment settings are the same as those in Experiment 3. The normal data of 300 days are added in the experiments. All the data of 300 days are used to test the false alarm rate of the proposed method. In order to further verify the robustness of the proposed method, noises are added to the experiment data. First, through the measurement, it can be found that the normal data themselves have a signal-to-noise ratio (SNR) of 40 dB. Then, different Gaussian white noises are added to the data to test the robustness of the method. As a result, the experiment data have the additional SNR from 45 dB to 25 dB. Fig. 15 shows some examples of the experiment data (has a SNR of 40 dB itself) and the data with the added noise. Table 3 shows the result of the experiments. It can be found that: (1) When the experiment data of 300 days (before adding noise) are used, there is no false alarm. Therefore, it can be concluded that the proposed method has a low false alarm rate in WT fault detection. (2) Moreover, the proposed method has no false alarm when the noise (no less than 35 dB) is added. The experiment result shows that the proposed method has certain anti-noise capability. (3) In reality, in most cases, the noise which affects the data is not as intense as that in the experiments. Thus, it can be concluded that the method could keep robust and maintain a low false alarm rate in practice. (4) The missing detection rate is zero in all the experiments. Therefore, it can be concluded that the proposed method is robust in detecting WT faults.

This experiment is designed to show the effectiveness of the proposed method in WT fault detection with one-variable FIS input. Similar to Experiment 1, the conventional FIS method, such as the method in [33], is selected to make comparison with the proposed method. In July, 2015, due to the aging of the generator front bearing of WT 06, its temperature rose rapidly within a few days. On July 20th, WT 06 had a sudden breakdown. In this experiment, the monitored generator front bearing temperature (GFBT) is used. The same as that in the above experiments, GFBT is predicted and the prediction errors are obtained. The upper bound and the lower bound of the predicted errors are 6.24 °C and −5.96 °C. The critical points of the antecedent MFs are −9.41 °C, −2.71 °C, 3.26 °C and 9.02 °C. As can be seen in Fig. 14(a) and (b), the prediction errors of GFBT increases rapidly from 2015-07-17 to 2015-07-19. The fault detection results of the conventional FIS method and the proposed method are shown in Fig. 14(c) and (d). It can be found that: (1) The conventional FIS method does not detect the fault until 2015-07-19, only one day before the breakdown. (2) Using the proposed method, the fault is detected on 2015-07-17, three days before the breakdown, giving more time for maintenances. (3) From 2015-07-17 to 2015-07-19, the fault factor is increasing, which indicates that the fault is getting worse. It can be concluded that: (1) the proposed method is effective in detecting early WT faults with one-variable input. (2) The proposed fault factor can also tell the severity of the fault. Furthermore, in order to make a good comparison of the proposed method with more different FIS methods. Another group of experiments is conducted. The experiment setting is the same as that in Experiment 3. The following methods are compared with the proposed method: (1) the FIS method with a single prediction model (such as the method in [30]), (2) the FIS method with multiple prediction models (such as the method in [31]), (3) the proposed method without non-singleton input, (4) the proposed method without rule expansion. Table 2 shows the experiment results. It can be found that conventional FIS methods cannot effectively detect early faults, either with

4.6. Discussions Four groups of experiments have been conducted in this section, and the experiment results show that: (1) The real faults in experiments have been successfully detected at an early stage and their severities are told by the proposed method. (2) No false alarms occur using the normal data of 300 days. It can be concluded that the detection results 10

Applied Energy 262 (2020) 114469

F. Qu, et al.

Fig. 14. The monitored data and detection results of Experiment 3. (a) The averaged prediction errors of GFBT in one day. (b) The averaged prediction errors of GFBT in every 10 min. (c)–(f): Detection results. (c) The conventional FIS method. (d) The proposed method. (e) The proposed method without non-singleton input. (f) The proposed method without terms & rules expansion. Table 2 Experiment results of different types of FIS.

Table 3 The Results of the Robustness Experiments.

Method

Detection result

FIS with single prediction model [30] FIS with muti-prediction models [31] Proposed FIS without non-singleton Proposed FIS without expansion Proposed FIS with non-singleton and expansion

1 1 2 2 3

Type

day early day early days early days early days early

False alarm rate Missing detection rate

SNR (dB) 45

40

35

30

25

0% 0%

0% 0%

0% 0%

10% 0%

44% 0%

Fig. 15. The experiment data (has a SNR of 40 dB itself) and the noise-added data of generator phase 3 temperature (one of the data used for predicting GFBT). (a) 40 dB. (b) 35 dB. (c) 30 dB. (d) 25 dB. 11

Applied Energy 262 (2020) 114469

F. Qu, et al.

are correct and the proposed method can effectively detect early WT faults and provide more information on fault severities. Similar to other FIS methods, linguistic variables and terms are used in the proposed method. In fault detection, each linguistic term is involved in calculating the fuzzy output according to the rules, and the detection result is obtained by combining all the fuzzy outputs. The fuzzy process makes the fault detection more flexible. Moreover, the proposed method has the advantage of detecting multi-class faults. In the FIS of the proposed method, there could be many rules (for multi-class fault) in the rule base. Therefore, if more rules are added to the rule base, more fault types could be detected. In the experiments of the paper, four different types of WT faults are detected by only one FIS of the proposed method. In conventional methods, if the upper bound is adjusted as a very low value, or the lower bound is adjusted as a very high value, the early fault can also be detected. However, in such case, many “Normal” samples can be misjudged as “Abnormal”, which could result in higher false alarm rate. In comparison, using the proposed method, early faults can be effectively detected without adjusting the upper bound and the lower bound.

[6] Ruiz M, Mujica LE, Alférez S, Acho L, Tutivén C, Vidal Y, et al. Wind turbine fault detection and classification by means of image texture analysis. Mech Syst Signal Process 2018;107:149–67. [7] Moghaddass R, Sheng S. An anomaly detection framework for dynamic systems using a bayesian hierarchical framework. Appl Energy 2019;240:561–82. [8] Yu D, Chen Z, Xiahou K, Li M, Ji T, Wu Q. A radically data-driven method for fault detection and diagnosis in wind turbines. Int J Electr Power Energy Syst 2018;99:577–84. [9] Yang W, Liu C, Jiang D. An unsupervised spatiotemporal graphical modeling approach for wind turbine condition monitoring. Renew Energy 2018;127:230–41. [10] Wang Z, Tian B, Qiao W, Qu L. Real-time aging monitoring for igbt modules using case temperature. IEEE Trans Industr Electron 2016;63(2):1168–78. [11] Sheng S. Monitoring of wind turbine gearbox condition through oil and wear debris analysis: a full-scale testing perspective. Tribol Trans 2016;59(1):149–62. [12] Peng G, Infield D, Yang X. Wind turbine generator condition-monitoring using temperature trend analysis. IEEE Trans Sustain Energy 2011;3(1):124–33. [13] Castellani F, Astolfi D, Sdringola P, Proietti S, Terzi L. Analyzing wind turbine directional behavior: Scada data mining techniques for efficiency and power assessment. Appl Energy 2017;185:1076–86. [14] Teng W, Wang F, Zhang K, Liu Y, Ding X. Pitting fault detection of a wind turbine gearbox using empirical mode decomposition. Strojniški vestnik-J Mech Eng 2014;60(1):12–20. [15] Crabtree CJ, Zappalá D, Tavner PJ. Survey of commercially available condition monitoring systems for wind turbines, 2014. http://dro.dur.ac.uk/12497/. [16] Stamboliska Z, Rusiński E, Moczko P. Proactive condition monitoring of low-speed machines. Proactive condition monitoring of low-speed machines. Springer; 2015. p. 53–68. [17] Zhu J, Yoon JM, He D, Bechhoefer E. Online particle-contaminated lubrication oil condition monitoring and remaining useful life prediction for wind turbines. Wind Energy 2015;18(6):1131–49. [18] Salameh JP, Cauet S, Etien E, Sakout A, Rambault L. Gearbox condition monitoring in wind turbines: a review. Mech Syst Signal Process 2018;111:251–64. [19] Qiao W, Lu D. A survey on wind turbine condition monitoring and fault diagnosispart ii: signals and signal processing methods. IEEE Trans Industr Electron 2015;62(10):6546–57. [20] Hu R, Granderson J, Auslander D, Agogino A. Design of machine learning models with domain experts for automated sensor selection for energy fault detection. Appl Energy 2019;235:117–28. [21] Wang L, Zhang Z, Long H, Xu J, Liu R. Wind turbine gearbox failure identification with deep neural networks. IEEE Trans Industr Inf 2017;13(3):1360–8. [22] Schlechtingen M, Santos IF, Achiche S. Using data-mining approaches for wind turbine power curve monitoring: a comparative study. IEEE Trans Sustain Energy 2013;4(3). [23] Gangsar P, Tiwari R. Comparative investigation of vibration and current monitoring for prediction of mechanical and electrical faults in induction motor based on multiclass-support vector machine algorithms. Mech Syst Signal Process 2017;94:464–81. [24] de Azevedo HDM, Araújo AM, Bouchonneau N. A review of wind turbine bearing condition monitoring: state of the art and challenges. Renew Sustain Energy Rev 2016;56:368–79. [25] Chen B, Matthews PC, Tavner PJ. Automated on-line fault prognosis for wind turbine pitch systems using supervisory control and data acquisition. IET Renew Power Gener 2015;9(5):503–13. [26] Chen B, Matthews PC, Tavner PJ. Wind turbine pitch faults prognosis using a-priori knowledge-based anfis. Expert Syst Appl 2013;40(17):6863–76. [27] Jang JSR, Sun CT. Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice-Hall, Inc.; 1996. [28] Sun C, Wang X, Zheng Y. An ensemble system to predict the spatiotemporal distribution of energy security weaknesses in transmission networks. Appl Energy 2020;258. [29] Halabi LM, Mekhilef S, Hossain M. Performance evaluation of hybrid adaptive neuro-fuzzy inference system models for predicting monthly global solar radiation. Appl Energy 2018;213:247–61. [30] Schlechtingen M, Santos IF, Achiche S. Wind turbine condition monitoring based on scada data using normal behavior models. part 1: system description. Appl Soft Comput 2013;13(1):259–70. [31] Sun P, Li J, Wang C, Lei X. A generalized model for wind turbine anomaly identification based on scada data. Appl Energy 2016;168:550–67. [32] Simani S, Farsoni S, Castaldi P. Fault diagnosis of a wind turbine benchmark via identified fuzzy models. IEEE Trans Industr Electron 2015;62(6):3775–82. [33] Merabet H, Bahi T, Halem N. Condition monitoring and fault detection in wind turbine based on dfig by the fuzzy logic. Energy Procedia 2015;74:518–28. [34] Liu J, Qu F, Hong X, Zhang H. A small-sample wind turbine fault detection method with synthetic fault data using generative adversarial nets. IEEE Trans Ind Informat 2019;15(7). [35] Astolfi D, Castellani F, Garinei A, Terzi L. Data mining techniques for performance analysis of onshore wind farms. Appl Energy 2015;148:220–33. [36] Mills TC. Applied time series analysis. Academic Press; 2019. [37] Marugán AP, Márquez FPG, Perez JMP, Ruiz-Hernández D. A survey of artificial neural network in wind energy systems. Appl Energy 2018;228:1822–36. [38] Schlechtingen M, Santos IF. Wind turbine condition monitoring based on scada data using normal behavior models. part 2: application examples. Appl Soft Comput 2014;14:447–60. [39] Tan M, Zhang Z. Wind turbine modeling with data-driven methods and radially uniform designs. IEEE Trans Industr Inf 2016;12(3):1261–9. [40] Zhang J, Yan J, Infield D, Liu Y, Lien F-S. Short-term forecasting and uncertainty

5. Conclusion This paper presents a WT fault detection method based on expanded linguistic terms and rules using non-singleton FIS. Different from the conventional FIS methods, the proposed method is improved to detect early WT faults and to tell fault severities. There are two main contributions of this paper. First, this paper proposes an effective WT fault detection method based on FIS. For the first time, a fuzzy number transformation method is introduced to convert the PDFs of the prediction errors of the WT SCADA data into fuzzy numbers, so that the non-singleton FIS can be applied to detecting WT faults. Second, this paper presents a method of expanding linguistic terms and rules generated from the original ones. With the expansion, FIS could detect WT faults at an early stage and fault severities could be told with the defuzzified fault factor. Four groups of experiments are conducted, using the SCADA data collected in a real wind farm. The experiment results show that the proposed method can effectively detect early WT faults and provide more information on fault severities. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported by the National Natural Science Foundation of China (61973071, 61627809), and the Liaoning Natural Science Foundation of China (2019-KF-03-04). References [1] Leite GdNP, Araújo AM, Rosas PAC. Prognostic techniques applied to maintenance of wind turbines: a concise and specific review. Renew Sustain Energy Rev 2018;81:1917–25. [2] Artigao E, Martín-Martínez S, Honrubia-Escribano A, Gómez-Lázaro E. Wind turbine reliability: a comprehensive review towards effective condition monitoring development. Appl Energy 2018;228:1569–83. [3] Li Z, Outbib R, Giurgea S, Hissel D, Jemei S, Giraud A, et al. Online implementation of svm based fault diagnosis strategy for pemfc systems. Appl Energy 2016;164:284–93. [4] Helsen J, Devriendt C, Weijtjens W, Guillaume P. Condition monitoring by means of scada analysis. Proceedings of European Wind energy association international conference Paris. 2015. [5] Li J, Yang Q, Mu H, Le Blond S, He H. A new fault detection and fault location method for multi-terminal high voltage direct current of offshore wind farm. Appl Energy 2018;220:13–20.

12

Applied Energy 262 (2020) 114469

F. Qu, et al.

[41] [42] [43]

[44] [45]

application. IEEE Press; 1997. [46] Mendel JM. Uncertain rule-based fuzzy systems. Springer; 2017. [47] Mendel JM. Explaining the performance potential of rule-based fuzzy systems as a greater sculpting of the state space. IEEE Trans Fuzzy Syst PP 2017(99). 1-1. [48] Wang J, Cheng F, Qiao W, Qu L. Multiscale filtering reconstruction for wind turbine gearbox fault diagnosis under varying-speed and noisy conditions. IEEE Trans Industr Electron 2018;65(5):4268–78. [49] Xiao F, Shi Y, Ren W. Robustness analysis of asynchronous sampled-data multiagent networks with time-varying delays. IEEE Trans Autom Control 2018;63(7):2145–52.

analysis of wind turbine power based on long short-term memory network and gaussian mixture model. Appl Energy 2019;241:229–44. Klir GJ, Yuan B. Fuzzy sets and fuzzy logic: theory and applications. 1995. Wang Peizhuang. Fuzzy set theory and its applications. Shanghai Science and Technology Press; 1983. Pourabdollah A, John R, Garibaldi JM. A new dynamic approach for non-singleton fuzzification in noisy time-series prediction. 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE), IEEE. 2017. p. 1–6. Liu J, Wu C, Wang Z, Wu L. Reliable filter design for sensor networks using type-2 fuzzy framework. IEEE Trans Industr Inf 2017;13(4):1742–52. Mouzouris GC, Mendel JM. Nonsingleton fuzzy logic systems: theory and

13