# A Novel Capsule Network Based on Wide Convolution and Multi-Scale Convolution for Fault Diagnosis
## 1 Introduction
CNN is generally constructed by alternately stacking convolutional layers and pooling layers and finally adding a fully connected (FC) layer. CNN has the characteristics of local connection, weight sharing, and pooling mechanism. This makes CNN well able to cope with the features of translation and scaling. On the other hand, it reduces the network parameters to be trained and reduces the computational complexity. Based on the classic CNN network structure LeNet-5, [PERSON] et al. [19] proposed an innovative CNN algorithm for bearing fault diagnosis. The algorithm converts vibration signals into two-dimensional grayscale images by means of signal stacking. [PERSON] et al. [20] proposed a new diagnostic framework, namely the spatiotemporal convolutional neural network (ST-CNN) framework, which includes a spatiotemporal pattern network (STPN) for spatiotemporal feature learning and CNN for condition classification. In [21; 22; 23], the authors used 1D-CNN for fault diagnosis and used raw data as the input. Among them, [PERSON] et al. [22] first analyzed the characteristics of the vibration signal and proposed a deep CNN method with a wide convolution kernel for the first layer. The algorithm directly inputs the original one-dimensional vibration signal into the model and achieves good results in generalization. At the same time, they also show that in a low signal to noise ratio (SNR) environment, a wide first-layer convolution kernel can more effectively extract low-frequency features and prevent noise interference. Although CNN and its variants have achieved good results in identifying bearing faults, the existence of the pooling layer causes the valuable spatial information between the layers to be lost. The capsule network with dynamic routing mechanism proposed by [PERSON] et al. [24] perfectly solves this problem. In the capsule network, the capsule replaces some neurons and becomes the \"basic unit\" of the neural network. The low-layer capsule is transmitted to the high-layer capsule through dynamic routing. Unlike max-pooling, the dynamic routing mechanism enables transmission between layers without discarding information about the precise location of entities in the area. Recently, some researches have applied capsule networks to the field of fault diagnosis. [PERSON] et al. [25] first obtained the time-frequency diagram of the fault through a wavelet time-frequency analysis and then combined the capsule network with the Xception module for intelligent fault diagnosis. This algorithm has a better fault classification ability and high reliability through experimental verification. [PERSON] et al. [26] introduced the inception module and a regression branch for diagnosing fault damage based on the classic capsule network. In the data pre-processing phase, they converted the original vibration signal into time-frequency graphs by means of short-time Fourier transform. The algorithm was tested on different bearing datasets, and the experimental results verify the strong generalization of the algorithm. In general, the above-mentioned deep learning algorithms have been widely used in bearing fault diagnosis and have achieved a high recognition accuracy in specific tasks. However, these algorithms have some shortcomings that need further improvement. First of all, most algorithms require the preprocessing of the original signal. Taking the DBN and SAE algorithms as examples, the input is generally time-domain features or frequency-domain features or both. In the current proposed capsule network for fault diagnosis, the input is generally a pre-processed time-frequency graph [25; 26]. These preprocessing operations rely on expert experience, which hinders the further promotion of the algorithm. In addition, many algorithms have poor generalization, which is manifested in the fact that when a classifier trained by data under one working condition is used to classify data under other working conditions, the accuracy rate drops significantly.