Since the active power output status can intuitively reflect the health condition of the wind turbine (Gill et al., 2012), Pearson’s correlation principle (Yang et al., 2016) is applied to analyze the correlation of power outputs between two wind turbines and the correlation related to wind speed and power output time series for the same wind turbine to construct the wind turbine condition assessment index system.

Cross-correlation coefficient refers to quantitatively describing the correlation of the power output variation between two wind turbines, which can effectively reflect the health condition of wind turbine to some extent. The cross-correlation coefficient between wind turbine i to be evaluated and the adjacent wind turbine j can be described as r t P i , P j = ∑ s = 1 S P i , s − P i , a v P j , s − P j , a v ∑ s = 1 S P i , s − P i , a v 2 ∑ s = 1 S P j , s − P j , a v 2 (1)

Self-correlation coefficient refers to quantitatively describing the correlation between time series of the same variable. The difference between the self-correlation coefficients of power output and wind speed can reflect the operating conditions of wind turbines. As shown in formula (2). ζ r t , r w = r t P t 1 , P t 2 − r w V t 1 , V t 2 (2) Where r t P t 1 , P t 2 = ∑ s = 1 S P t 1 , s − P t 1 , a v P t 2 , s − P t 2 , a v ∑ s = 1 S P t 1 , s − P t 1 , a v 2 ∑ s = 1 S P t 2 , s − P t 2 , a v 2 (3) r w V t 1 , V t 2 = ∑ s = 1 S V t 1 , s − V t 1 , a v V t 2 , s − V t 2 , a v ∑ s = 1 S V t 1 , s − V t 1 , a v 2 ∑ s = 1 S V t 2 , s − V t 2 , a v 2 (4)

In accordance with the principles of index independence, applicability and appropriateness, indices of leading wind turbine operation status are screened based on the historical sample data of typical wind turbine condition and monitoring projects. As shown in Figure 1, the evaluation index system consists of two project layers: component performance and power output status. The performance of important components of the wind turbine is reflected by the selected index layer of the status of the generator, gearbox, nacelle and pitch control system, and is applied to mapped the overall state of the wind turbine from the intrinsic component characteristics. The power output status indices are applied to reflect the overall state from the external overall characteristics. The constructed evaluation index system is shown in Figure 1, in which indices R ₁₁₁-R ₁₄₃, wind speed and unit output power are obtained by the wind farm SCADA system, and indices R ₂₁₁-R ₂₂₂ is obtained by analyzing wind speed and unit output power based on Pearson correlation principle.

Since the units and magnitudes of indices are different. In order to effectively analyze the mapping relationship between indices and the overall state of wind turbine, the data of indices are pre-processed by Max-Min normalization (Nan et al., 2021), and all the indices are discrete distributed into the interval [0,1]. The closer the normalized data is to 1, the better the reflected state is.

There is no basis for the classification of wind turbine condition state in the existing wind turbine state evaluation models. Therefore, referring to Zhou et al. (2017), this paper divides the condition of wind turbines into four status levels, i.e., Z = [ z ₁, z ₂, z ₃, z ₄]. Where z ₁ indicates “normal state”, z ₂ indicates “attention state”, z ₃ indicates “abnormal state”, and z ₄ indicates “fault state”. The state descriptions and corresponding index thresholds are shown in Table 1.

In this paper, IAHP (Ge et al., 2019) is applied to subjective weighting for index layer as follows. Firstly, the indices of R _x,y,1,R _x,y,2, … ,R _x,y,n at R _x,y layer are ranked in descending order of importance. Then the relative importance of R _x,y,i and R _x,y,i+1 is compared to determine the scale value g _i (Zhao et al., 2019). and so on to obtain the scale values g ₁, g ₂, .., g _n-1 between all neighboring indices. Finally, the judgment matrix X as shown in (5) is obtained according to the transferability of the importance. Since the judgment matrix constructed by the scale values satisfies the consistency check, the subjective weights of the indices are calculated by (6). X = 1 g 1 g 1 g 2 ⋯ ∏ i = 1 n − 1 g i 1 g 1 1 g 2 ⋯ ∏ i = 2 n − 1 g i 1 g 1 g 2 1 g 2 1 ⋯ ∏ i = 3 n − 1 g i ⋮ ⋮ ⋮ ⋱ ⋮ 1 ∏ i = 1 n − 1 g i 1 ∏ i = 2 n − 1 g i 1 ∏ i = 3 n − 1 g i ⋯ 1 (5) w i s u b = ∏ j = 1 n x i j 1 n / ∑ i = 1 n ∏ j = 1 n x i j 1 n (6)

After the normalization of index data pretreatment, this paper uses the inverse entropy weighting method to calculate the objective weights of the indices. The basic steps are as follows.

1) Calculating inverse entropy.

For the evaluation index matrix R = [ r ij * ] m × n including n data for each index 1, 2, …, m. The inverse entropy of index i is named as h _i in (7). h i = − ∑ j = 1 n v i j ⁡ ln 1 − v i j v i j = r i j * / ∑ j = 1 n r i j * (7)

2) Determine objective weight w i obj

Based on the subjective weight w i sub and objective weight w i obj obtained above, the comprehensive weight W i * could be obtained by solving the model as follows. min ⁡ J W i * = ∑ i = 1 n W i * ⁡ ln W i * w i s u b + W i * ⁡ ln W i * w i o b j ∑ i = 1 n W i * = 1 , W i * ≥ 0 (9)

The comprehensive weight value is equal to the optimal solution of (9) as follows. W i * = w i s u b w i o b j / ∑ i = 1 n w i s u b w i o b j (10)

Set pair analysis is a method for quantitative analysis of uncertainty. The basic idea is to study the certainty and uncertainty of two objects from three aspects of identity, difference and contrary to describe the relationship between the two objects (Zhang et al., 2019).

For the set pairs H= (B ₁, B ₂) composed of two sets B ₁ and B ₂, the correlation degree of B ₁ and B ₂ can be expressed as (11). μ H = a + b i + c j (11)

In order to meet the multiple correlation requirements in some cases, coefficient b is expanded to obtain D-element correlation degree as (12). μ H = a + ∑ t = 1 D − 2 b t i t + c j s . t .   a + ∑ t = 1 D − 2 b t + c = 1 (12)

In this paper, the set pair analysis is used to quantify the degree to which each index belongs to the state level, and then the weighted average operator is used to push forward the degree to which the whole wind turbine belongs to the state level, i.e., the degree of membership of the target layer. Suppose a certain subproject layer set is R _x,y = {r _x,y,1, r _x,y,2,..., r _x,y,n }, and the status level set Z = {z ₁, z ₂, z ₃, z ₄}. If a set pair H = {R _x,y , Z}is composed of the set R _x,y and set Z, then the 4-element correlation degree μ _x,y,l between the lth index in R _x,y and Z can be expressed as (13). μ x , y , l = a x , y , l + b x , y , l , 1 i 1 + b x , y , l , 2 i 2 + c x , y , l j (13)

If the relationship between the status level and the threshold value of the index interval is shown in Table 2. The correlation degree between the normalized values of r _x,y,l and the 4-level status, i.e., the membership degree between the index layer and the status levels, can be determined based on the fuzzy attribute rule as (14). μ x , y , l = 1 + 0 i 1 + 0 i 2 + 0 j , r x , y , l < s 1 s 1 + s 2 − 2 r x , y , l s 2 − s 1 + 2 r x , y , l − 2 s 1 s 2 − s 1 i 1 + 0 i 2 + 0 j , s 1 ≤ r x , y , l ≤ s 1 + s 2 2 0 + s 2 + s 3 − 2 r x , y , l s 3 − s 1 i 1 + 2 r x , y , l − s 1 − s 2 s 3 − s 1 i 2 + 0 j , s 1 + s 2 2 < r x , y , l ≤ s 2 + s 3 2 0 + 0 i 1 + 0 i 2 + 1 j , r x , y , l ≥ s 3 (14)

After obtaining the comprehensive weights and the membership of the indices, the membership of the subproject layer can be calculated by using the weighted average operator as (15). The schematic diagram of the membership degree of the indices is shown in Figure 2. Similarly, the membership degree of subproject layer and target layer in Figure 1 can be calculated. μ x , y = ∑ i = 1 n W x , y , l * a x , y , l + ∑ i = 1 n W x , y , l * b x , y , l , 1 i 1 + ∑ i = 1 n W x , y , l * b x , y , l , 2 i 2 + ∑ i = 1 n W x , y , l * c x , y , l j (15)

Different from the maximum membership principle that only the maximum membership component is used to evaluate the wind turbine status, the asymmetric proximity method takes all membership components into consideration to evaluate wind turbines comprehensively. In addition, the asymmetric proximity method can avoid the setting of the reliability value which may lead to failure in wind turbine evaluation based on reliability criterion. Therefore, this paper applies he method of asymmetric proximity to calculate the closeness of status level and membership, and the wind turbine condition is determined according to the proximity principle.

Define the fuzzy sets K ^p (∀p = 1,2,3,4) representing status levels of wind turbine as K ¹= (1, 0, 0, 0), K ²= (0, 1, 0, 0), K ³= (0, 0, 1, 0), K ⁴= (0, 0, 0, 1), respectively. Then the membership degree μ = {μ ₁, μ ₂, μ ₃, μ ₄} of the target layer and the fuzzy set K ^p corresponding to the status level should be standardized. The standardization process of μ is shown in Figure 3, and the following steps to evaluate wind turbine condition based on asymmetric proximity are as follows.

1) Given Q = {q ₁,q ₂, q ₃,q ₄} = {1,2,3,4} and initialize p = 1.

Similarly, K ^p is standardized to obtain K ^p' . K p ′ = k 1 p ′ , k 2 p ′ , k 3 p ′ , k 4 p ′ (17)

Based on the standardized result above, the asymmetric proximity between the membership degree of the target layer and the status level z _p can be expressed as (18). N μ p , K p ′ = 1 − 1 D ∑ r = 1 D μ r p v − k r p ′ v r (18)

After obtaining the asymmetric proximity degree between the membership degree of the target layer and all status levels through (18), the status level z _p corresponding to max N (μ ^p , K ^p’ ) is the status level evaluation result of the overall wind turbine (Li et al., 2008). If the evaluated wind turbine status level is abnormal or fault, the component of wind turbine to be maintenance could be found by the fuzzy fault Petri net model (Huang et al., 2022) according to the condition monitoring information of pitch system, generator and gearbox, et al.

The state evaluation process of the whole wind turbine is shown in Figure 4.

Figure 5 shows the output cross-correlation coefficients of the four adjacent wind turbines in normal or attentional state for 7 days from 1 October2021 to 7 October2021. It can be found that the cross-correlation coefficient of adjacent wind turbine power outputs in normal or attentional condition are above 0.85, and the output power correlation is very strong.

Figure 6 shows the statistical data of the difference between the self-correlation coefficients of the output and wind speed with the corresponding self-correlation delay of 1min and 5min. The statistical data is derived from the SCADA data which dates from 1 October2021 to 7 October2021. The values corresponding to 1min and 5min delay are below 0.035 and 0.04 respectively, and it can be concluded that there is a strong correlation between wind turbine power output and wind speed in normal or attentional state.

The output state of wind turbine can reflect the operating state of the whole machine to a certain extent. The mapping relationship between the output characteristics of wind turbine and the operating state of wind turbine is defined based on the statistical samples from August 2019 to October 2021, as shown in Table 3 and Table 4.

The following section combines the condition monitoring information of each subsystem and sets up different cases to accurately evaluate the wind turbine monitoring data.

In order to verify the feasibility and advantages of the proposed wind turbine evaluation method in this paper, three groups of historical SCADA data set of a 1.5 MW double-fed induction generator in the farm (as shown in Table 5) are selected as the test data sets. From the operation and maintenance log, the actual condition of the wind turbine corresponding to data1, data2, and data3 is “attention state”, “attention state” and “fault state” respectively in which the gearbox inlet oil temperature R ₁₃₁ in data one deviate slightly from its benchmark, the generator rotor temperature R ₁₂₂ in data two is higher than that in normal state since the overload operation of the wind turbine which leads to a slightly tendency to deteriorate, and the screen inlet oil and inlet oil pressure of gearbox in data3 are too low, which lead to poor gearbox lubrication and serious gearbox gear wear. On the basis of comprehensive weighting, four cases are presented for detailed comparative analysis.

Case 1

wind turbine condition evaluation method based on the maximum membership principle (Li et al., 2013).

Case 2

wind turbine condition evaluation method based on reliability criterion, in which the reliability value is set to be 0.6 (Liao et al., 2010).

Case 3

wind turbine condition evaluation method based on reliability criterion, in which the reliability value is set to be 0.7.

Case 4

the proposed method in this paper.

The comparison of wind turbine condition evaluation results in four cases are listed in Table 6.

Case 1 has a good performance when evaluating the status of wind turbine based on data one and data 3. However, the evaluated status of wind turbine corresponding to data two is “abnormal” deviating from the actual status “attention”. The reason that case 1 fails to evaluate the wind turbine status corresponding to data two accurately is that the maximum membership component of data2 is 0.3336 and the sub-maximum membership component is 0.3333. The maximum and sub-maximum membership components are too close to comprehensively assess the status of wind turbines relying solely on the maximum membership component especially when the health condition of wind turbine is of being in transition.

Case 2and Case 3 both apply the reliability criterion to determine the status of the wind turbine, but the reliability value settings are different. By comparing the results of case 2 with case 3, the evaluated result of case 3 on data 2 is abnormal which deviates from the actual attention state due to the improper setting of the reliability value.

The evaluation results of case 4 corresponding to data 1, data 2, and data three are all consistent with the actual status of the wind turbine. Case 4 not only makes full use of the information of each component to avoid the limitations of the maximum membership principle that fail to evaluate status of wind turbine during state transition period, but also avoids the issue of the improper setting of the reliability value which may lead to the failure of the state assessment of wind turbine.

We verify the effectiveness of the method proposed in this paper further by using 100 data sets similar to Table 5 from the wind farm. The data sets were collected from 32 wind turbine SCADA data in the wind farm from August 2019 to October 2021 consisting of 25 SCADA data sets for each state (normal, attention, abnormal and fault state) recorded in the operation and maintenance log. The overall state of the wind turbine is evaluated by case 1, case 2 and case 4 respectively. The comparison results of the positive judgment rates of different cases are shown in Table 7.

As can be seen from Table 7, the average positive judgment rate of the case4 is 97%, which is 6% and 8% higher than case 1 and case 2, respectively. In the state of transition process, case 1 fails in some samples due to the maximum membership component approximately equaling to the second maximum component. The accurate of case 2 depends on the setting of reliability value. That is why the reliability criterion method encounters failure in assess some samples of wind turbine status. Case 4 can overcome the limitations of the subjective selection of reliability value and the maximum membership principle. Although the method proposed in this paper is relatively complex, it has a higher positive judgment rate and is more suitable for evaluating wind turbines of being in transition state. It should be pointed out that the proposed method will still face the limitations of failing to evaluate the wind turbines accurately when the maximum proximities of the evaluated sample data to different states are approximately equal.

In order to illustrate the effectiveness of the weighting method used in this paper, we using the data sets in Table 5 to present a detailed analysis and comparison of the following two weighting methods to evaluate the status of wind turbine base on asymmetric proximity.

Case 1Subjective weighting based on AHP method (Liu et al., 2022).

Case 2Comprehensive weighting based on IAHP- inverse entropy method.

Table 8 shows the results of the wind turbine condition assessment in two cases. Case 1 only uses AHP to calculate index weights subjectively ignoring weighting from an objective perspective. As a result, the evaluation result of data2 in case 1 deviates from its actual state. However, the evaluation results of data1∼data three in case2 are the same to the actual state. As can be seen from the comparison, the comprehensive weighting method that takes subjective and objective weights into consideration is more reasonable and effective in the weighting process of wind turbine state assessment.