# A Deep Learning Method for Bearing Fault Diagnosis through Stacked Residual Dilated Convolutions
## 3 Validation of Proposed SRDCNN Model
### Case Study I: Comparison with Traditional Deep Convolutional Neural Networks  
To evaluate the performance of the proposed SRDCNN model, a set of comparative experiments are performed on dataset A, which is collected under load of 0 hp and suffers small effects of environmental fluctuations. All the tested algorithms are coded in Python, and executed on a computer with an Intel Core i7-7700 CPU and 16 GB RAM (Dell, Xiamen, China, 2017). The structure parameters and performance indicators of these models are listed in Table 2.  
The first convolutional layer in 1d-DCNN has 16 filters of size \(32\times 1\) and the stride is 1, while the second convolutional layer has 32 filters with the size \(3\times 1\). The filters size in pooling layers is all \(2\times 1\) and the stride is 2. The parameters of other layers in 1d-DCNN are detailed in Table 2. The parameter settings in 2d-DCNN is similar to that of 1d-DCNN. The first convolutional layer has 16 filters of size \(5\times 5\) and the stride is 1, while the second convolutional layer has 32 filters with the same size and stride. The filters size in pooling layers is \(2\times 2\) and the stride is 2. The first layer in the LSTM-CNN has 20 filters of size \(32\times 1\) and the stride is 1, and the second layer is pooling layer that have the filter of size \(2\times 2\) and 2 strides. The third layer in the LSTM-CNN is a LSTM layer that has 100 cells, and the last layer is a dense layer which determines classification results. The first layer in SRDCNN has 32 filters of size \(64\times 1\) and the stride is 2, and the 2 nd, 3 rd, and 4 th layer have the same structure but different parameter values. Although the convolution kernel, the channel and the stride size of the SRDCNN are similar to the 1d-DCNN, the convolution operations of them are different. There are 10 types of bearing vibration faults in the experiments, so the number of neurons in the output layer of all the three models is 10. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Fault Location**} & \multicolumn{1}{c}{**None**} & \multicolumn{1}{c}{**Ball**} & \multicolumn{3}{c}{**Inner Ring**} & \multicolumn{3}{c}{**Outer Ring**} & \multicolumn{1}{c}{**Load (np)**} & \multicolumn{1}{c}{**Speed (rpm)**} \\ \hline \multicolumn{2}{c}{**Fault diameter (mil)**} & 0 & 7 & 14 & 21 & 7 & 14 & 21 & 7 & 14 & 21 & \\ \hline \multirow{2}{*}{**Dataset A**} & Train & 500 & 500 & 500 & 500 & 500 & 500 & 500 & 500 & 500 & \multirow{2}{*}{0} & \multirow{2}{*}{1797} \\  & Test & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & \\ \hline \multirow{2}{*}{**Dataset B**} & Train & 500 & 500 & 500 & 500 & 500 & 500 & 500 & 500 & \multirow{2}{*}{1} & \multirow{2}{*}{1772} \\  & Test & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & \\ \hline \multirow{2}{*}{**Dataset C**} & Train & 500 & 500 & 500 & 500 & 500 & 500 & 500 & 500 & \multirow{2}{*}{2} & \multirow{2}{*}{1750} \\  & Test & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & \\ \hline \multirow{2}{*}{**Dataset D**} & Train & 500 & 500 & 500 & 500 & 500 & 500 & 500 & 500 & \multirow{2}{*}{3} & \multirow{2}{*}{1730} \\  & Test & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of all experimental datasets.