# A Deep Learning Method for Bearing Fault Diagnosis through Stacked Residual Dilated Convolutions
## 3 Validation of Proposed SRDCNN Model  
### Data Description  
In order to investigate the effectiveness of the proposed SRDCNN model, experiments are designed using a bearing dataset from the Case Western Reserve University (CWRU) Bearing Data Center [36]. The original experimental data was collected from an accelerometer of a motor-driven mechanical system at a sampling frequency of 12 kHz, and the test stand is shown in Figure 6. The number of data points collected during one rotation of the bearing can be inferred from the rotating speed of the bearing and the sampling frequency of the sensor; and the functional relationship between them can be expressed as (4), where \(n\) is the number of the data points collected per circle,\(f\) is the sampling frequency, and \(v\) is the rotating speed (rpm):  
\[n=f*60/v, \tag{4}\]  
As shown in Figure 7, the damage of the bearings used in the experiment are seeded by electro-discharge machining (EDM). There are three possible locations for bearing failure, namely the inner ring, the outer ring and the rolling element. For the convenience of this study, only three fault sizes were collected for each location, which are 7 mils, 14 mils, and 21 mils, respectively. Therefore, there are 10 types of signals in our experiments, one of which is the normal signal, and the others are the fault signals.  
Figure 5: Diagram of residual dilated convolutional layer.  
Since the SRDCNN model has a large number of parameters to learn and will work only with sufficient samples with labels, it will easily fall into the trap of overfitting without sufficient training samples. Thus, the data augmentation technique is adopted, in which a new sample is generated by removing the previous \(n\) sampling points from the previous sample and adding the next \(n\) sampling points. As shown in Figure 8, when the length of the original signal is constant, the number of samples depends on the sliding stride and the length of each sample. If the sliding stride is too small, it will lead to a high information redundancy between samples. However, if the sliding stride is too large, the number of samples may not be sufficient to effectively train the network. Therefore, a compromise is required.  
It is all known that the rotating speed of the motor fluctuates as the motor load changes. When the motor load increases, the rotating speed decreases and the number of the data points collected during one rotation of the bearing increases, and vice versa. Therefore, the number of the data points collected per circle will fall into the interval: 12,000 \(\times\) 60/(1797\(\sim\)1730) = (400-416). Limited by the structure of existing deep learning models and the computing power, most of the existing deep learning based intelligent fault diagnosis models have an input layer of about 200 neurons, and a few exceptional  
Figure 8: Diagram of the data augmentation.  
Figure 6: Test stand for collecting vibration signals from REBs used by CWRU.  
Figure 7: Photographs of three kinds of damaged bearings.  
models take input of over 400 neurons. In our experiments, one sample consists of 1024 sampling points. When the length of one sample is fixed, the sliding stride depends on the total length of the vibration signal and the number of samples required. In subsequent experiments, datasets A, B, C and D are collected under loads of 0, 1, 2, and 3 hp, respectively. Additionally, each dataset consists of 10 types of data, each of which contains 500 training samples (10% for verification) and 50 test samples by taking the sliding stride of 135. The complete details of the experimental datasets are described in Table 1. Ten types of time domain waveforms of bearing vibration signals, including normal signal, B fault signals (7, 14, 21), IR fault signals (7, 14, 21), and OR fault signals (7, 14, 21), can be seen in Figure 9.  
Figure 9: Time domain waveforms of ten types of bearing vibration signals.