Research on Fault Early Warning of Wind Turbine Based on IPSO-DBN

Abstract

Aiming at the problem of wind turbine generator fault early warning, a wind turbine fault early warning method based on nonlinear decreasing inertia weight and exponential change learning factor particle swarm optimization is proposed to optimize the deep belief network (DBN). With the data of wind farm supervisory control and data acquisition (SCADA) as input, the weights and biases of the network are pre-trained layer by layer. Then the BP neural network is used to fine-tune the parameters of the whole network. The improved particle swarm optimization algorithm (IPSO) is used to determine the number of neurons in the hidden layer of the model, pre-training learning rate, reverse fine-tuning learning rate, pre-training times and reverse fine-tuning training times and other parameters, and the DBN predictive regression model is established. The experimental results show that the proposed model has better performance in accuracy, training time and nonlinear fitting ability than the DBN model and PSO-DBN model.

1. Introduction

In recent years, the wind power industry has developed rapidly, and the installed scale of wind power continues to expand [1,2,3]. According to the statistics of the global wind energy council (GWEC), the total installed capacity of global wind power in 2020 is 743 GW, among which China ranks first in the world [4]. There are also great challenges behind the rapid development of the wind power industry. With the increase of the running time of wind turbines and the long-term working in the natural environment of changeable forces, difficult conditions and complex working conditions, the failure rate of main components such as generator, gearbox, main bearing, yaw system and so on increased significantly [5]. Generator failure is one of the main causes of wind turbine outage [6]. The use of accurate detection technology for early fault early warning of generators can effectively reduce the failure rate of wind turbines and increase the benefits of wind farms.

Wind turbine is a system with strong internal correlation, the components influence each other, and the fault types are varied [7,8]. At present, the fault early warning methods of wind turbine mainly focus on the parameters such as temperature signal, acoustic emission signal, vibration signal, electrical signal and so on [9]. In reference [10], the generator temperature is modified by linear regression technology, and the generator condition monitoring based on temperature signal is realized. In reference [11], the spatial neighborhood coefficient of data-driven threshold is used to avoid misdiagnosis caused by strong noise, and on this basis, an empirical wavelet transform generator bearing fault diagnosis method based on measured vibration signal is proposed. In reference [12], the minimum entropy deconvolution method and envelope analysis method are combined to realize the analysis and diagnosis of electric corrosion of generator bearings by using vibration signals.

At present, with the great advantage of deep mining data abstract features and inherent rules, the deep learning algorithm has made remarkable achievements in the fields of speech recognition [13], image classification [14] and target detection [15]. Because it can solve the problem of insufficient feature extraction ability of traditional diagnosis methods, deep learning algorithm has been applied to the field of fault diagnosis [16]. In reference [17], an improved deep learning model which combines SAE and depth neural network is proposed to realize the on-line condition monitoring of generator. In reference [18], the early fault early warning of wind turbine gearbox is realized by using depth variational self-coding network.

Wang and Liu [19] proposed a data-driven wind turbine condition monitoring method based on a new multivariable state estimation technology (Multivariate State Estimation Technique, MSET), which realizes the fault early warning of wavelet transform components. Su et al. [20] proposed a wind turbine state modeling and fault identification method based on a combined model on the basis of BP neural network and nonlinear state estimation method. Sun et al. [21] established a hidden Markov state monitoring model by using the characteristic variables of the supercapacitor of the pitch control system.

To summarize, the current mainstream fault early warning methods usually have some defects, such as low sensitivity and accuracy, small predictable time range, poor real-time performance and so on. When selecting state variables, most machine learning methods rely too much on expert experience and are highly subjective. Usually, the parameters are independent of each other by default, but in practice, the parameters of the unit are often related to each other, which leads to the introduction of some redundant or useless quantities with the prediction object when determining the input parameters, which affects the results.

In view of this, aiming at the problem of wind turbine fault early warning, an IPSO -DBN wind turbine fault early warning method is proposed in this paper. Firstly, multiple restricted Boltzmann machines (RBM) and one output layer are connected to form a depth confidence network. The unsupervised greedy layer-by-layer algorithm is used to pre-train the weights and biases of the network to generate better network parameters, and then the BP back propagation algorithm is used to fine-tune the whole network. For the problems that it is difficult to determine the parameters such as the number of neurons in the hidden layer of the DBN network, the pre-training learning rate, the reverse fine-tuning learning rate, the pre-training times and the reverse fine-tuning training times, the IPSO algorithm is used to optimize it intelligently. When the generator deviates from the normal workspace, the reconstruction error sequence changes obviously and deviates seriously from the original dynamic stable state, based on which the early fault detection of the generator is realized.

2. Particle Swarm Optimization Algorithm

2.1. Basic Particle Swarm Optimization Algorithm

Particle swarm optimization (PSO) is an intelligent population optimization method to find the global optimal solution [22]. At present, it has been widely used in intelligent control [23], path planning [24], neural network training [25], image processing [26], feature selection [27] and other fields [28]. PSO randomly generates a batch of particles in the search space, which have no volume and mass, only position and speed, and update their positions according to their own memory and the information of other particles in the group. Through the competition and cooperation between particles, we continue to move closer to the historical optimal position of individuals and populations, so as to achieve the purpose of finding the optimal solution in the complex solution space. The velocity and position update formula of the particle is shown as follows [19].

(1)$\{\begin{array}{l}{v}_{id}^{k+1}=\omega v_{id}^k+c_1{r}_1(p_{id}-x_{id}^k)+c_2{r}_2(p_{gd}-x_{id}^k)\\ x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}\end{array}$

where $v_{id}^k$ is the optimal solutions of the d-dimensional speed of the i particle in the k-th iteration. $x_{id}^k$ is the optimal solutions of the d-dimensional position of the i particle in the k-th iteration. p_id is the optimal solutions of the d-dimensional individual of the i particle in the k-th iteration. p_gd is the optimal solutions of the d-dimensional population history of the i particle in the k-th iteration. $v_{id}^{k+1}$ and $x_{id}^{k+1}$ are the speed and position of the d-dimensional of the i-particle in the k + 1 iteration, respectively. ω is the inertia weight. c₁ and c₂ are the individual learning factor and population learning factor, respectively. r₁ and r₂ are a random number in the interval [0, 1].

2.2. Improved Particle Swarm Optimization Algorithm

When finding the global optimal solution of general problems, the basic PSO algorithm has a good performance, but for complex high-dimensional optimal problems, it is easy to fall into local convergence, premature convergence or even non-convergence [29,30,31]. In order to solve these problems, an improved particle swarm optimization algorithm with nonlinear decreasing inertia weight and exponential learning factor is proposed in this paper.

Inertia weight ω is a very important parameter in PSO, which controls the local and global optimization ability of PSO, and determines the optimization effect of the algorithm to a great extent. When ω is large, the global optimization ability is strong, the local optimization ability is weak, and the convergence speed is fast; when ω is small, it is just the opposite. Therefore, in order to ensure the global optimization of the population with larger inertia weights in the early stage of the iteration, the refined optimization is realized with smaller inertia weights at the end of the iteration, and the nonlinear inertia weight strategy and control factors are introduced, and the inertia weights are shown in Equation (2).

(2)$\omega (t)=\frac{{\omega }_{max}-{\omega }_{min}}{\sqrt{1+\left(\frac{Kt}{T}\right)}}+{\omega }_{min}$

where ω(t) is the inertia weight of the t iteration. ω_max and ω_min are the maximum and minimum inertia weights, respectively. T is the maximum number of iterations. K is the weight control factor.

Learning factor is also an important parameter in PSO. The larger the individual learning factor, the stronger the global search ability; the smaller the individual learning factor, the stronger the local search ability; and the population learning factor has the opposite attribute. At the beginning of the iteration, the individual learning factor should be larger and the population learning factor should be smaller; with the continuous increase of the number of iterations, the individual learning factor of particles gradually decreases and the group learning factor increases gradually. The use of exponential learning factors can well meet this requirement, and the updated formula is shown in Equation (3).

(3)$\{\begin{array}{l}{c}_1=c_{1min}+(c_{1max}-c_{1min})\cdot e^{-20{\left(\frac{t}{T}\right)}^6}\\ c_2=c_{2max}-(c_{2max}-c_{2min})\cdot e^{-20{\left(\frac{t}{T}\right)}^6}\end{array}$

where c_1min and c_2min are the minimum of individual learning factor and population learning factor, respectively. c_1max and c_2max are the maximum of individual learning factor and population learning factor, respectively.

Four performance test functions such as Rastrigin, Griewank, Acklet and Rosenbrock are used to analyze and verify the performance of IPSO, and compared with the basic PSO. The maximum number of iterations T is set to 300, and other parameters are shown in Table 1.

The optimal convergence ability of PSO and IPSO in the four performance test functions is shown in Figure 1. The value of x-coordinate is the number of iterations, and the value of y-coordinate is the fitness value (the average of 20 calculations).

As can be seen from Figure 1, compared with PSO, IPSO has faster convergence speed, higher accuracy and better stability.

3. Deep Belief Network

The deep belief network proposed by Geoffrey Hinton et al. [32] overcomes the problems of traditional neural network, such as low training efficiency, lack of small sample processing ability, easy to fall into local optimal solution and so on. The structure of the DBN network is shown in Figure 2. DBN is a deep Bayesian probability generation model composed of the input layer, multiple RBM and output layer [33]. The training process of the DBN model includes two parts: pre-training and parameter tuning [34]. First of all, the RBM is pre-trained layer by layer by unsupervised greed to generate better initial network parameters. Then the BP neural network is used to reverse fine-tune the network parameters to make the model optimal.

3.1. Pre-Training of the DBN Model

The pre-training of the DBN model uses the CD-k algorithm to train the weights and biases of each RBM in the network layer by layer unsupervised [35]. RBM basic structure is shown in Figure 3. RBM consists of a visible layer and a hidden layer. There is no connection within the layer, and no full connection between layers [36].

RBM is an energy-based model. When the energy is minimum and the network reaches the best state, the construction of the network is actually the process of minimizing the energy function [37]. The definition of RBM energy function is shown in Equation (4).

(4)$E_{\theta }(v,h)=-{\displaystyle \sum _{i=1}^n{b}_i{v}_i-}{\displaystyle \sum _{j=1}^m{c}_j{h}_j}-{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m{v}_i{w}_{ij}{h}_j}}$

where θ = {w_ij, b_i, c_j}. v_i is the i neuron state of the visible layer. h_j is the j neuron state of the hidden layer. w_ij is the connection weight between the i neuron of the visible layer and the j neuron of the hidden layer. b_i is the offset of the i neuron of the visible layer. c_j is the bias of the j neuron of the hidden layer.

The state of neurons in the RBM network can be described by statistical probability. According to Equation (4), the joint probability distribution of state (v,h) can be obtained, as shown in Equation (5).

(5)$P_{\theta }(v,h)=\frac{1}{Z_{\theta }}{e}^{-E_{\theta }(v,h)}$

where Z_θ is the distribution function, as shown in Equation (6).

(6)$Z_{\theta }={\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}$

Visible layer element distribution P_θ(v) is the key to solve practical engineering problems, which corresponds to the edge distribution of P_θ(v,h). The specific definition is shown in Equation (7).

(7)$P_{\theta }(v)=\frac{{\displaystyle \sum _h{e}^{-E_{\theta }(v,h)}}}{{\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}}$

Similar probability distributions with hidden layers:

(8)$P_{\theta }(h)=\frac{{\displaystyle \sum _v{e}^{-E_{\theta }(v,h)}}}{{\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}}$

In order to make the distribution under the RBM representation fit the original sample distribution as much as possible, the K-L distance in the information theory is introduced. The smaller the K-L distance, the better the fitting effect, so the real edge distribution can be transformed into the maximum likelihood estimation of some approximate distribution.

In the RBM model, the likelihood function can be expressed as:

(9)$\ln L(\theta )=\ln \prod _v{P}_{\theta }(v)={\displaystyle \sum _v\ln P_{\theta }(v)}$

To require maximum likelihood, we need to derive the likelihood function.

(10)$\begin{array}{l}\frac{\partial \ln P_{\theta }(v)}{\partial \theta }=\frac{\partial \ln {\displaystyle \sum _h{e}^{-E_{\theta }(v,h)}}}{\partial \theta }-\frac{\partial \ln {\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}}{\partial \theta }\\ \hspace{1em}\hspace{1em} =\frac{1}{{\displaystyle \sum _h{e}^{-E_{\theta }(v,h)}}}\frac{\partial {\displaystyle \sum _h{e}^{-E_{\theta }(v,h)}}}{\partial \theta }-\frac{1}{{\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}}\frac{\partial {\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}}{\partial \theta }\\ \hspace{1em}\hspace{1em} =\frac{{\displaystyle \sum _h{e}^{-E_{\theta }(v,h)}}(-\frac{\partial E_{\theta }(v,h)}{\partial \theta })}{{\displaystyle \sum _h{e}^{-E_{\theta }(v,h)}}}-\frac{{\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}(-\frac{\partial E_{\theta }(v,h)}{\partial \theta })}{{\displaystyle \sum _{v,h}{e}^{-E_{\theta }(v,h)}}}\end{array}$

Bringing in the expressions of P(v,h) and P(h|v), Equation (11) is obtained:

(11)$\begin{array}{l}\frac{\partial \ln P_{\theta }(v)}{\partial \theta }={\displaystyle \sum _h(P_{\theta }(h|v)(-\frac{\partial E_{\theta }(v,h)}{\partial \theta }}))-{\displaystyle \sum _{v,h}(P_{\theta }(v,h)(-\frac{\partial E_{\theta }(v,h)}{\partial \theta }))}\\ \hspace{1em}\hspace{1em} =E_{P_{\theta }(h|v)}(-\frac{\partial E_{\theta }(v,h)}{\partial \theta })-E_{P_{\theta }(v,h)}(-\frac{\partial E_{\theta }(v,h)}{\partial \theta })\end{array}$

Replacing θ with w, b, c to derive respectively, and bringing into the E(v,h) expression, we can obtain:

(12)$\frac{\partial \ln P_{\theta }(v)}{\partial w_{ij}}=P_{\theta }(h_i=1|v)v_j-{\displaystyle \sum _v{P}_{\theta }(v)P_{\theta }(h_j=1|v)v_j}$

(13)$\frac{\partial \ln P_{\theta }(v)}{\partial b_i}=v_i-{\displaystyle \sum _v{P}_{\theta }(v)v_i}$

(14)$\frac{\partial \ln P_{\theta }(v)}{\partial c_i}=P_{\theta }(h_i=1|v)-{\displaystyle \sum _v{P}_{\theta }(v)P_{\theta }(h_i=1|v)}$

Because there is no connection between RBM layers, the activation functions of RBM visible layer neurons and hidden layer neurons can be expressed as follows:

(15)$P_{\theta }(v_i=1|h)=f(b_i+{\displaystyle \sum _{i=1}^n{w}_{j,i}{v}_i})$

(16)$P_{\theta }(h_j=1|v)=f(c_j+{\displaystyle \sum _{j=1}^m{w}_{i,j}{h}_j})$

(17)$f(x)=\frac{1}{1+e^x}$

where f(x) is the activation function.

The RBM parameters are updated by the CD-k algorithm, and the update criterion of θ = {w_ij, b_i, c_j} can be obtained by combining the neuron activation functions of visible layer and hidden layer, as shown in Equation (18).

(18)$\{\begin{array}{l}{w}_{ij}^{k+1}=w_{ij}^k+\epsilon \left\{{⟨v_i{h}_j⟩}_{P_{\theta }(h|v)}-{⟨v_i{h}_j⟩}_{recon}\right\}\\ b_i^{k+1}=b_i^k+\epsilon \left\{{⟨v_i⟩}_{P_{\theta }(h|v)}-{⟨v_i⟩}_{recon}\right\}\\ c_j^{k+1}=c_j^k+\epsilon \left\{{⟨h_j⟩}_{P_{\theta }(h|v)}-{⟨h_j⟩}_{recon}\right\}\end{array}$

where ε is the learning rate. ⟨·⟩_Pθ(h|v) is the expectation of the partial derivative under the P_θ(h|v) distribution. ⟨·⟩recon is the expectation of the partial derivative under the reconstructed model distribution.

3.2. Fine Tuning of the DBN Model

After the unsupervised layer-by-layer training of the DBN network using the contrast divergence algorithm, a better initial weight and bias of the model are obtained. Because the RBM of each layer is trained separately, it can only ensure that the feature extraction of the RBM visible layer of each RBM output layer is optimal but cannot guarantee the optimal feature vector mapping of the whole DBN network. Therefore, it is necessary to use the BP back propagation algorithm to fine-tune the error between the output and input of the network from top to bottom to further optimize the weights and biases of the DBN network to optimize the parameters of the whole DBN.

4. Fault Early Warning Method of Wind Turbine Generator Based on IPSO-DBN

The fault early warning process of wind turbine generator based on IPSO-DBN is shown in Figure 4. As can be seen from Figure 4, it is mainly divided into: data input processing module, IPSO training module and IPSO-DBN fault early warning module.

4.1. Selection and Preprocessing of State Parameters

In order to establish the wind turbine generator fault early warning model, it is necessary to reasonably select the SCADA variable as the input of the model. The generator state parameters selected in this paper are shown in Table 2.

During the model training, the SCADA data parameters in Table 2 generated by the wind turbine generator in a certain time range are used as training samples to train the DBN network. The input vector x can be expressed as:

(19)$x=[v_o,P,\Omega ,T_t,T_{ai},T_{ba},T_{bb},T_{u1},T_{v1},T_{w1},T_{ssi}]$

Data pre-processing is a very important step in the process of fault early warning modeling, which mainly includes two parts: elimination of outliers and data normalization. In order to eliminate the influence of attributes and dimensions between different parameters of SCADA data, the data are normalized by Formula (20).

(20)$x_i^{*}=\frac{x_i-x_{min}}{x_{max}-x_{min}}$

where x_i and $x_i^{*}$ are the data before and after normalization. x_max and x_min are the maximum and minimum value of the original data, respectively.

4.2. Fitness Function

When using the IPSO algorithm to optimize the DBN parameters globally, the Equation (21) is taken as the fitness function.

(21)$f_{fitness}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m({\widehat{x}}_{ij}-x_{ij}}}{)}^2$

where n is the number of data samples. m is the dimension of each piece of data. x_ij and $\widehat{x}$_ij are the j-dimensional data of the i original sample and the j-dimensional data of the i reconstructed sample, respectively.

4.3. Reconstruction Error

In the normal working state, the SCADA data of the wind turbine maintain relatively stable internal characteristic rules, and the reconstruction error R_e is relatively stable; when the generator deviates from the normal workspace, the internal characteristic rules of SCADA data change, the DBN model constructed by the normal state data does not match with the current state, and the Re trend changes obviously. Therefore, Re can be selected as the generator condition detection index. The Re calculation method is shown in Equation (22).

(22)$R_e={\Vert \widehat{x}-x\Vert }^2$

where $\widehat{x}$ and x are the reconstructed data vector and the original data vector respectively.

4.4. Reconstruction Error Threshold

• Fixed threshold

The fault of the wind turbine generator is judged by the reconstruction error threshold. The 3σ principle is introduced to set the threshold and calculate the mean value and root mean square error of R_e.

(23)$\{\begin{array}{l}\mu =\frac{1}{N}{\displaystyle \sum _{i=1}^N{R}_e(i)}\\ \sigma =\sqrt{\frac{1}{N-1}{\displaystyle \sum _{i=1}^N{\left(R_e(i)-\mu \right)}^2}}\end{array}$

where R_e(i) is the i reconstruction error. μ and σ are the mean and root mean square errors of R_e, respectively. N is the length of R_e, that is, the number of reconstruction errors.

According to the 3σ principle, the reconstruction error threshold U_th is set to:

(24)$U_{\mathrm{th}}=\mu +3\sigma$

If the reconstruction error does not exceed the threshold, the running state of the generator is normal. If the reconstruction error exceeds the threshold, the running state of the generator is abnormal, and the fault early warning information is issued at the same time.

• Adaptive threshold based on sliding window

In addition to the operation status of wind turbines, wind speed is also an important reason that affects the variation of SCADA parameters. Sometimes, even if the operation status of wind turbines is kept within the normal workspace, the trend of reconfiguration error will have a great sudden change due to the change of wind speed. At this time, if a constant threshold is set, some poles may exceed the threshold, thus misjudging the status of the unit. Therefore, in order to prevent the disadvantages caused by the fixed threshold, on the basis of the fixed threshold, the adaptive threshold based on sliding window is introduced as the condition to judge the occurrence of wind turbine failure.

Suppose that within a certain period of time, the reconstruction error order of some part of the unit is {R_e(0), R_e(1), ···, R_e(N), ···,}. For this sequence, take a sliding window with N width, as shown in Figure 5. First, the mean and standard deviation of continuous N reconstruction error sequences in the window are calculated by using the Formula (23), and then the first fixed threshold is calculated according to the Formula (24), which is used as the threshold of the initial reconstruction error. Starting from the position of the first sliding window, the thresholds of subsequent reconstruction errors are obtained according to the same method, and these thresholds are concatenated to form an adaptive threshold based on sliding window.

4.5. Evaluation Index

The root mean square error (RMSE), the mean absolute error (MAE) and the mean absolute percent error (MAPE) of the reconstruction error are calculated respectively to quantitatively analyze the model, and the performance of different models is compared. The calculation method is as follows:

(25)$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m({\widehat{x}}_{ij}-x_{ij}}}{)}^2}$

(26)$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m|{\widehat{x}}_{ij}-x_{ij}|}}$

(27)$MAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m\left|\frac{{\widehat{x}}_{ij}-x_{ij}}{{\widehat{x}}_{ij}}\right|}}$

where n and m are the number and dimension of data samples respectively. x_ij is the j-th dimensional data of the i original sample. $\widehat{x}$_ij is the j-th dimensional data of the i reconstructed sample.

The smaller the value of the above three quantitative evaluation indicators, the higher the accuracy of the model reconstruction of the original data, and the better the network performance.

5. Example Analysis

5.1. Modeling Data Statement

This paper takes the E15 wind turbine generator in a wind farm as the research object and uses the SCADA data from 00:00 on 23 December 2018 to 23:50 on 23 April 2019, as the data source to carry on the wind turbine fault early warning analysis. The data source contains 69 kinds and 17,567 pieces of information-rich 10-min sampling frequency data.

5.2. Model Parameter Setting

The IPSO-DBN model consists of four hidden layers, the optimization interval of the number of neurons in the hidden layer is [1, 100]. The optimization interval of learning rate is [0, 0.1], and the optimization interval of training times is [1, 500], pre-training 100 data per batch and reverse fine-tuning 4 data per batch. The initial parameters of IPSO are as follows: the population size is 20, ω_min = 0.45, ω_max = 0.95, c_min = 0.45, c_max = 0.95. The maximum number of iterations is 40, and the weight control factor is 8. The optimization results are shown in Table 3.

5.3. Early Warning Analysis of Generator Fault

5.3.1. Comparison of Learning Effects of Different Models

The comparison results of evaluation indicators of different models are shown in Table 4.

It can be seen from Table 4 that the IPSO-DBN wind turbine fault early warning model proposed in this paper has the best performance in RMSE, MAE and MAPE, compared with the DBN and PSO-DBN models.

The learning effect of the three models is shown in Figure 6.

From Figure 6, the reconstruction error sequence of the IPSO-DBN model is the smallest, followed by the PSO-DBN model, and the reconstruction error of the DBN model is the largest. To sum up, the IPSO-DBN model proposed in this paper has stronger nonlinear fitting ability, stronger robustness and higher accuracy, and is more suitable for early fault early warning of wind turbines.

5.3.2. Early Warning Model Testing under Normal Condition

The first 9100 groups of data of the data sample are selected as the training set. Under the normal operation state of the wind turbine, the reconstruction error sequence of the generator operation data is shown in Figure 7, and the red line in the figure is the early warning threshold. Figure 7a is a fixed threshold, and Figure 7b is an adaptive threshold based on the principle of sliding window. In this paper, the length of sliding window is set to 300.

As can be seen from Figure 7b, under normal operating conditions, because the wind speed is always fluctuating, there are fluctuations and a few extreme points in the generator reconstruction error, but it is always within the threshold range. Based on the sliding window method, the threshold changes with the change of reconstruction error, and the threshold accuracy and effectiveness are higher.

5.3.3. Early Warning Model Testing in Fault State

The fault samples of the generator in the data source are input into the trained IPSO-DBN fault early warning model, the reconstruction value is the output and the reconstruction error is calculated, and the trend change diagram of the reconstruction error sequence is obtained. Then the above fixed threshold and adaptive threshold based on sliding window are used to verify and analyze the fault early warning function of the model. Finally, the trend of residual sequence of generator related variables is analyzed to judge the possible fault types of generator.

The following 3908 data samples of the training data set are inputted into the IPSO-DBN model, and the calculated reconstruction error sequence is shown in Figure 8. Figure 8a adopts a fixed early warning threshold and Figure 8b adopts an adaptive threshold based on sliding window. In the state of generator failure, the fixed threshold is set to 0.223, and the sliding window length of the adaptive threshold is set to 300.

It can be seen from Figure 8 that the reconstruction error sequence dynamically changes within the early warning threshold for a period of time before the fault occurs (about 3000 points), which proves that the generator does not deviate from the normal workspace during this period of time. On the other hand, the reconstruction error exceeds the early warning threshold at the ① point of Figure 8a and the X point of Figure 8b (which corresponds to the data sample point 3129 in the state of generator failure), and the fault early warning is triggered.

Combined with the change of reconstruction error sequence of generator variables, the fault early warning of generator is realized by setting the strategy of fixed threshold and adaptive threshold in this paper. The sampling period of SCADA data used in this paper is too long to detect the slow change of generator-related variables, which leads to a sudden and dramatic reconstruction error exceeding the early warning threshold in Figure 8. This problem can be overcome by increasing the adoption period. For the SCADA system in wind turbine field, the data sampling period can usually reach seconds, when it can be observed that the reconstruction error rises slowly some time before the fault occurs, and then exceeds the set threshold before causing a serious fault to achieve the purpose of detecting the potential fault of the wind turbine.

5.3.4. Residual Analysis of Each Variable

According to the change of the trend of the reconstruction error sequence and the set early warning threshold, the fault can be predicted, so that the staff can check the hidden trouble in time and prevent the fault from getting worse. In order to determine the specific fault location as soon as possible and improve the maintenance efficiency, the residual trend chart can be used to analyze the SCADA parameters of each component of the wind turbine to realize the preliminary judgment of the fault type and fault location. The trend of wind speed residual series and active power residual series in the event of wind turbine generator failure is shown in Figure 9.

As can be seen from Figure 9, the wind speed and power residual series of wind turbines always fluctuate slightly around zero in the early stage, and only fluctuate in a slightly larger range in the later stage. On the whole, the fluctuation of their residuals is always within the normal range, and the larger changes in the later period must have been affected by other variables. Basically, it can be judged that the wind speed is always in a steady change for a period of time before and after the generator failure. Therefore, the generator failure caused by the natural environment can be ruled out. There is a fault caused by the generator itself or by long-term operation.

The temperature residual change trend of generator stator winding u1, v1, w1 and bearing temperature is shown in Figure 10.

It can be seen from Figure 10a that the trend of temperature residual of generator stator winding is not obviously abnormal, so the possibility of failure of generator coil winding can also be ruled out. From Figure 10b, it can be seen that the residual sequence of generator bearing temperature a (that is, generator front shaft) deviates obviously and changes sharply, which proves the previous conjecture from the positive side. This is due to the long sampling period and no slow temperature change process. Combined with the fault records of the SCADA system, the report shows that the generator has the front axle overheating. It is proved that the model proposed in this paper is effective for wind turbine fault early warning.

6. Conclusions

Aiming at the problem of wind turbine fault early warning, the deep confidence network is used to mine the characteristic information of SCADA data layer by layer under the normal operation state of the generator and intelligently learn the internal relationship among the parameters, and a multivariable DBN reconfiguration network model of wind turbine is proposed. For the problem that it is difficult to determine the parameters of the DBN network, the improved particle swarm optimization algorithm can better solve this problem. The fault early warning of generator can be realized through the reconstruction error of the IPSO-DBN model and the residual variation of each input variable. Compared with the DBN wind turbine fault model and the PSO-DBN wind turbine fault model, this model has better performance in accuracy, training time and nonlinear fitting ability, so it can better meet the needs of practical engineering.

Author Contributions

Conceptualization, Z.Z. and S.W.; methodology, Z.Z.; software, P.J.; validation, S.W. and P.J.; formal analysis, S.W.; investigation, H.Z.; resources, P.W.; data curation, Z.Z.; writing—original draft preparation, S.W.; writing—review and editing, Z.Z.; visualization, H.Z.; supervision, P.J.; project administration, P.W.; funding acquisition, P.W. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

Acronyms and abbreviations
DBN	deep belief network
IPSO	improved particle swarm optimization
PSO	particle swarm optimization
SCADA	supervisory control and data acquisition
Indices
i	index of particle
k	number of iteration
d	number of dimensional
Variables
bi	offset of the i neuron of the visible layer
v	particle speed
x	particle position
pid	optimal solutions of the d-dimensional individual of the i particle
pgd	optimal solutions of the d-dimensional population history of the i particle
ω	inertia weight
c 1	individual learning factor
c 2	population learning factor
c 1min	minimum of individual learning factor
c 2max	population learning factor
c 1min	minimum of individual learning factor
c 2max	population learning factor
cj	bias of the j neuron of the hidden layer
r 1	random number in the interval [0, 1]
r 2	random number in the interval [0, 1]
ωmax	maximum inertia weights
ωmin	minimum inertia weights flow of node
T	maximum number of iterations
K	weight control factor
Eθ	RBM energy
vi	i neuron state of visible layer
hj	j neuron state of the hidden layer
wij	connection weight between the i neuron of the visible layer and the j neuron of the hidden layer
Pθ	joint probability distribution function
Zθ	distribution function
L(θ)	likelihood function
f(x)	activation function
ε	learning rate
n	number of neurons
vo	wind speed
P	generator power
Ω	generator speed
Tt	generator torque
Tai	air cooling temperature of generator
Tba	temperature of generator front axle A
Tbb	temperature of generator front axle B
Tu 1	generator winding u1 temperature
Tv 1	generator winding v1 temperature
Tw 1	generator winding w1 temperature
Tssi	side temperature of spindle impeller
xi	data before normalization
x I	data after normalization
Xmax	maximum value of the original data
xmin	minimum value of the original data
ffitness	fitness function
n	number of data samples
m	dimension of data samples
xij	j-dimensional data of the i original sample
$\widehat{x}$ ij	j-dimensional data of the i reconstructed sample
Re	reconstruction error
$\widehat{x}$	reconstructed data vector
X	original data vector
μ	mean errors of Re
σ	root mean square errors of Re
N	length of Re
U th	reconstruction error threshold

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Figures and Tables

Figure 1. PSO and IPSO optimization results. (a) Fitness value under Rastrigin test function. (b) Fitness value under Griewank test function. (c) Fitness value under Acklet test function. (d) Fitness value under Rosenbrock test function.

Figure 2. DBN network structure.

Figure 3. RBM basic structure.

Figure 4. Forecasting results between before and after rough set correction.

Figure 5. Reconstruction error sliding window.

Figure 6. Reconstruction error results of different models.

Figure 7. Training set reconstruction error. (a) Fixed threshold. (b) Adaptive threshold based on sliding window.

Figure 8. Validation set reconstruction error. (a) Variation trend of residual wind speed. (b) Change trend of power residual.

Figure 9. Test set reconstruction error. (a) Fixed threshold. (b) Adaptive threshold based on sliding window.

Figure 10. Test set reconstruction error. (a) Variation trend of temperature residual of generator stator windings. (b) Variation trend of temperature residual of generator bearing.

Table 1

PSO and IPSO parameter setting.

Arithmetic	Population Size (N)	Dimension (D)	ω	c 1	c 2
PSO	100	30	0.8	2.0	2.0
IPSO	100	30	0.9~0.4	2.5~0.5	0.5~2.5

Table 2

Description of generator condition variables.

Variable Name	Numerical Value	Unit
Wind speed	vo	m/s
Generator power	P	kW
Generator speed	Ω	r/min
Generator torque	Tt	N·m
Air cooling temperature of generator	Tai	°C
Temperature of generator front axle A	Tba	°C
Temperature of generator front axle B	Tbb	°C
Generator winding u1 temperature	Tu 1	°C
Generator winding v1 temperature	Tv 1	°C
Generator winding w1 temperature	Tw 1	°C
Side temperature of spindle impeller	T ssi	°C

Table 3

IPSO optimization results.

Parameters	Numerical Value
The number of neurons in the first hidden layer	65
The number of neurons in the second hidden layer	68
The number of neurons in the third hidden layer	21
The number of neurons in the fourth hidden layer	98
Pre-training learning rate	0.0185
Reverse fine-tuning learning rate	0.0456
Number of pre-training	27
Number of reverse fine-tuning	431

Table 4

Hidden layer neuron selection results.

Model	RMSE	MAE	MAPE
DBN	0.1256	0.2638	8.0291
PSO-DBN	0.0807	0.1685	16.0129
IPSO-DBN	0.0623	0.1315	4.9700

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