# A Deep Learning Method for Bearing Fault Diagnosis through Stacked Residual Dilated Convolutions
## 1 Introduction
Considering that deep learning models can directly work on the raw data without any data preprocessing, there have been some deep learning-based bearing fault diagnosis studies working directly on the raw vibration signal to improve the real-time performance of fault diagnosis. [PERSON] et al. [17] established a one-dimensional deep convolutional neural network (1d-DCNN), which adopted an end-to-end learning method and achieved satisfactory accuracy under a noisy environment. [PERSON] and [PERSON] [18] broaden and deepen the neural network and designed an end-to-end one-dimensional multi-scale deep convolutional neural network with few training parameters and a smooth training process. [PERSON] et al. [19] presented a two-dimensional deep convolutional neural network (2d-DCNN) by mapping the raw monitoring signal to feature maps. [PERSON] et al. [20] developed an effective data preprocessing method to convert the time-domain raw signals into images, and built a new CNN based on LeNet-5 to make full use of the experience related to CNN from image processing. Although there has been no agreement on the source of the generalization ability of deep learning, it is no denying that the deep learning method has better generalization performance than most machine learning methods [21; 22]. A large number of generalization experiments have been carried out, and the results show that the deep learning model has better generalization performance than the traditional machine learning algorithm [7; 14; 15; 17; 19]. From the previous literature, it can be concluded that the deep learning model has almost replaced the traditional feature extraction method and become the popular algorithm for bearing fault diagnosis. Although the fault diagnosis model based on deep learning can achieve satisfactory real-time and generalization performance, the model is prone to fall into the trap of local false features during the training process, which are greatly affected by the sample quality [23]. The sample quality can be improved to some extent by increasing the redundancy of the sample information by using more points in a sample [14], but the effects of random factors (such as ambient noise and working conditions fluctuation) can't be fundamentally eliminated. As the redundancy of sample information increases, the model will have a higher potential to resist random factors and avoid local false features. Besides, the detection device in reality has a higher sampling frequency to grasp more operating information and, therefore, the number of sampling points collected per revolution of the machine is increased. In conclusion, it is no longer satisfactory to take just 200-400 data points as one sample of the bearing fault diagnosis model. The number of input layer neurons in the fault diagnosis model needs to be expanded to avoid local false features and to adapt to high frequency dynamic detection. In order to address the problems above, in this paper, an intelligent fault diagnosis method based on stacked residual dilated convolutional neural network (SRDCNN) is proposed. The main novelties and contributions of this paper are summarized below:  
1. A novel effective deep learning framework is proposed, which subtly integrates the dilated convolution, the input gate structure of LSTM and the residual network. 2. The model works directly on raw noisy signals without any pre-denoisng methods, providing new solutions for some fields of signal analysis [24; 25]. 3. This algorithm performs pretty well under the noisy environment by effectively enlarging the receptive field and controlling the entry of information. 4. This algorithm keeps high diagnostic accuracy across different workloads due to the ability to automatically and efficiently extract essential features.