# Rolling Bearing Fault Diagnosis Based on Wavelet Packet Transform and Convolutional Neural Network
## 1 Introduction  
Bearings are the core component of rotating machinery such as wind turbines, aircraft and automobiles. Bearing failures may cause great economical loss and pose threats to operator security. Thus, the effective fault diagnosis of bearings is an important measure to maintain proper operation and reduce downtime of rotating machinery [1; 2; 3; 4; 5]. Up to now, the development of efficient bearing fault diagnosis methods has attracted many investigations [6; 7]. Fault diagnosis methods mainly include two types, namely, model-based methods and data-driven methods [8; 9; 10]. The model-based methods generally relied on an accurate failure mechanism model, in which the mathematical methods were applied to demonstrate the failure and phenomenon of the monitored components. The type of methods is appropriate for fault diagnosis when the mechanism model can be constructed for these monitored components. In fact, it is difficult to construct an accurate failure mechanism model to cater for the changes of operation environments and the physical structure of the machine. In contrast, a data-driven method, needs not to consider the failure mechanism, and the fault diagnosis can be achieved just based on the condition signals without any failure mechanism knowledge. A data-driven method generally includes two main phases: feature extraction and model selection and construction [11; 12]. For the feature extraction, it has been proved that the useful feature extraction could improve the performance of fault diagnosis. As common feature extraction methods, time domain,frequency domain, and time-frequency domain analysis methods have been widely used to obtain the features from signals. Time domain analysis method extracts features such as kurtosis and skewness as the condition features of bearings. Frequency domain analysis methods are applied to unveil features such as the hidden frequency information from time series signals. Popular time-frequency domain analysis methods like the short-time Fourier transform and Hilbert-Huang transform are able to extract the frequency component and retain the time domain information, which also build a relationship between time domain and frequency domain. However, there are some limitations in those mentioned methods, such as fault features and noise interference being still difficult to separate effectively. For the model selection and construction, machine learning models, such as hidden Markov models [13], Bayesian networks [14], neural networks, and support vector machines [15], are commonly employed as the classification tool in the filed of fault diagnosis. Those methods often need to consider the tradeoff between fault diagnosis training cost, training efficiency, and applicability performance. In the past, development of fault diagnosis, deep learning methods have emerged as an effective tool to achieve feature extraction and fault recognition due to their easy trainability and accurate classification performance. Generally, in a deep learning-based method, the features are extracted by multiple stacked layers, and then, output probabilities are calculated based on the last high-level abstraction data through the non-linear fitting operation of classification layer. Popular deep learning methods, such as deep neural networks (DNNs) [16] and auto-encoder [17], have been investigated, and they have shown their promising capability to capture representative features from input data by the linear and non-linear fitting operations. [PERSON] et al. [18] developed an end-to-end fault diagnosis method based on sparse auto-encoder and DNN to address the fault identification problem, in which the representative features were extracted automatically from condition signals by the auto-encoder. However, when more layers are added to the deep learning model, the network parameters explode, which might lead to overfitting.