# Anomaly Detection of Wind Turbines Based on Deep Small-World Neural Network
## 1 Introduction
Deep belief network (DBN) [14], denoise auto-encoder (DAE) [15], and stacked auto-encoder (SAE) [16] are the most representative unsupervised deep learning networks. In the field of fault diagnosis, auto-encoder is the most widely used. The process of the auto-encoder is to first explore the fusion rules of hidden features from the unlabeled input data by encoding, and then interpret the hidden features through decoding to give a more prominent output than the original data. [PERSON] [17] used a DBN to diagnose the fault of the planetary gearbox in wind turbines and proposed an improved Logistic-sigmoid unit and pulse characteristic method to solve the problem that DBN is prone to gradient disappearance in the back propagation. [PERSON] and [PERSON] built a deep-stacked auto-encoder network based on a multilayer back propagation (BP) neural network [18]. First, the SAE network neurons are trained layer by layer through unsupervised greedy learning by using the bearing data collected from the SCADA system. Then the trained weights are used as the initial weights of the deep BP neural network, and the labeled data, in a supervised manner, to continue training the network. In addition, [PERSON] proposed a deep auto-encoder network based on multiple RBMs to implement early abnormality detection and fault detection of wind turbine components [19]. However, deep learning networks with different structures are not born equal, one kind of network for specific tasks may be superior to others. For example, a convolution neural network is suitable for image recognition, while the recurrent neural network is adept in speech analyzing. Hence the structures of the neural networks will be improved with the changing application field. At present, the improved methods for neural networks mainly include deepening network level, dropout and drop-connect, batch normalization, and so on. Among them, increasing the connection edges between non-adjacent hidden layers (add-edge) is the current research focus of neural networks to alleviate gradient disappearance. From the view of network structure, the add-edge improvement makes the traditional neural network become a small-world neural network, which is a middle topology between regularity and disorder. The authors of this paper have improved a BP neural network into a small-world one and then used it to predict the wind power [20]. On this basis, a selective ensemble strategy combining multiple small-world neural networks has been proposed to diagnose and detect the WT pitch failures [21]. Combined with the characteristics of wind turbines' SCADA data, this paper proposed a deep small-world neural network (DSWNN) for anomaly detection of wind turbines. First, a DSWNN prototype using multiple restricted Boltzmann machines (RBM) was constructed based on the classical deep auto-encoder network. Previously unlabeled SCADA data from wind turbines were used to pre-train this DSWNN prototype to extract implied features. Then, the regular neural network was transformed into a small-world one though a randomly add-edge method, and the labeled data were used to train the reconstructed DSWNN model within the supervised case to fine-tune the global parameters of the network. Due to the acute changes and disturbances of wind speed in actual operation, the fixed thresholds for judging failures are always unreasonable and can cause false alarms. Therefore, an adaptive threshold determined by extreme value theory was presented as the criterion of anomaly judgment. Finally, the effectiveness of the proposed method was verified by two failure cases of wind turbine pitch systems. The remainder of this paper is organized as follows. Section 2 describes the proposed DSWNN model and its training method; Section 3 gives the estimating method of the adaptive threshold; Section 4 presents and discusses two failure cases of wind turbine pitch system. Finally, Section 5 lists the conclusion of the study. All abbreviations and symbols used in this paper are shown in Tables 1 and 2 of the Appendix A.