# A Novel Capsule Network Based on Wide Convolution and Multi-Scale Convolution for Fault Diagnosis
## 1 Introduction  
The large-scale rise of the industrial Internet has brought global industry into a new era of technological innovation and change. Industrial machinery systems are developing toward complexity, precision, and integration [1]. At the same time, the operation safety of equipment is facing greater challenges. As the core component of rotating machinery, the normal operation of rolling bearings is critical. Once a bearing fails, it will not only cause performance degradation and productivity reduction [2] but also lead to safety accidents in serious cases, resulting in huge property losses and serious casualties. Therefore, research on intelligent fault diagnosis algorithms for bearings is very important [3; 4; 5]. In recent years, as the most mainstream algorithms of artificial intelligence, deep learning algorithms have achieved excellent results in intelligent applications such as target recognition, speech recognition, and machine translation, etc. [6; 7; 8]. At the same time, deep learning has also received more and more attention in the field of fault identification. On the one hand, fault features do notneed to be designed manually but are automatically and efficiently extracted through neural networks, which reduces dependence on expert experience. On the other hand, the deep network structure can establish complex non-linear mapping relationships between monitoring signals and faults, which is critical to improve the diagnosis accuracy of complex mechanical equipment. Therefore, deep learning algorithms have gradually replaced traditional fault diagnosis algorithms and become mainstream algorithms for fault diagnosis. In the current research, deep belief network (DBN) and its variants are widely used in fault diagnosis. DBN consists of multiple stacked restricted Boltzmann machines (RBMs) [9], which can be used for both supervised and unsupervised learning. Unsupervised layer-by-layer greedy pre-training is the first step in DBN training. Next, the parameters of the neural network are fine-tuned using the back-propagation (BP) algorithm based on class labels. Compared with the traditional neural network only relying on the BP algorithm for model training, DBN's training method can achieve a higher performance in pattern recognition [10]. [PERSON] et al. [11] combined two layers of DBN to form a new hierarchical diagnosis network (HDN) which identified the types of faults and the degree of faults hierarchically. [PERSON] et al. [12] proposed an improved hierarchical adaptive DBN. The input of the network is frequency domain information and it is optimized using Nesterov momentum. This method achieved a high performance in the diagnosis of bearing fault types and damage levels. The training process of stacked autoencoder (SAE) is similar to DBN, except that the basic module of SAE is autoencoder (AE). [PERSON] et al. [13] used stacked denoising autoencoder (SDA) for fault diagnosis and pointed out that the algorithm is robust to noise pollution and changing working conditions. Based on the data collected by multiple accelerometers, [PERSON] et al. [14] combined SAE and DBN to diagnose bearing faults. Specifically, this method first extracts time-domain and frequency-domain features based on multiple sensor data. On this basis, SAE is used for feature fusion and DBN is trained to identify bearing faults. [PERSON] et al. [15] proposed an unsupervised diagnosis model that uses normalized frequency-domain signal as an input and integrates sparse autoencoder, DBN, and binary processor. The above SAE and DBN methods have achieved good fault diagnosis results to a certain extent, but on the network structure, they adopt a fully connected mode between different layers. The above method performs poorly when the feature has translation or scaling [16]. The convolutional neural network (CNN) is the first image processing method proposed by [PERSON] [17], and has opened a new era of computer vision [18].