# A Deep Learning Method for Bearing Fault Diagnosis through Stacked Residual Dilated Convolutions
## 1 Introduction  
With the rapid development of manufacturing technology and the increasing complexity of manufacturing systems, the challenges of safety and reliability requirements for manufacturing equipment and mechanical products have become extremely important. Their failure will not only lead to production interruptions, but also increase the operating costs of the company. Rolling element bearing (REB) is one of the key components of industrial transmission systems and plays an extremely important role in supporting and transmitting power. Although bearings have already been widely used in aerospace, vehicles, ships, and other important fields, they are one of the vulnerable parts of rotating machinery in terms of the current manufacturing technology and actual working conditions. Research shows that an approximately 30% of failures in rotating machinery are caused by bearing damage. Therefore, it remains a challenge to ensure production safety, as well as to reduce production costs by monitoring and diagnosing the bearing state [1]. In the last two decades, bearing fault diagnosis has already attracted extensive attention [2]. Many monitoring techniques have been applied to the monitoring and diagnosis of bearings [3]. The most common solution is to analyze the bearing signals continuously collected by the vibration monitoring system installed on the rotating machines and provide real-time monitoring and warning [4]. The goal of bearing fault diagnosis is to establish an effective real-time condition monitoring and identification system to ensure continuous production through predictive maintenance. In order to achieve this goal, there are three main challenges to address:  
1. To meet the requirements of real-time fault diagnosis of rotating machinery, the fault diagnosis model needs to perform continuous and rapid diagnosis based on the vibration signal collected in real-time [5]. 2. To improve the effectiveness of the fault diagnosis model, the essential features need to be extracted to avoid local false features caused by ambient noise and fluctuations in working conditions [6]. 3. To keep good performance under different working conditions, the fault diagnosis model needs to have good generalization performance under different load and noise conditions [7]. Various methods have been developed for the fault diagnosis of bearings. [PERSON] and [PERSON] [8] designed the parameters for optimal resonance demodulation, using the fast kurtogram for initial estimates and the genetic algorithm for final optimization. [PERSON] et al. [9] combined the merits of ensemble local mean decomposition and fast kurtogram to detect the fault for rotating machinery. Nevertheless, traditional feature extraction methods require a great deal of domain expertise and prior knowledge, which limits the mining of new features. Previous studies have shown that the accuracy of classifying results is largely dependent on the extracted features. To automatically learn feature representations from raw data, [PERSON] et al. [10] drew on the hierarchical learning process of human brain and proposed a milestone deep learning model training paradigm. Deep learning has made breakthroughs in natural language processing [11], speech recognition [12], image recognition [13], and other fields. There have been some attempts on feeding the frequency data of vibration signals into deep learning model. [PERSON] et al. [14] carried out a detailed study of stacked denoising autoencoders for bearing fault diagnosis. [PERSON] et al. [15] presented a deep convolutional neural network with wide first-layer kernels, using the normalized 1025 Fourier coefficients transformed from the raw temporal signals as the input. [PERSON] et al. [16] developed a convolutional neural network (CNN) to learn features from raw data, frequency spectrum and combined time-frequency data, and demonstrated that feature learning with CNN could provide much better results than manual feature extraction.