# 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
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **1d-DCNN** & **2d-DCNN** & **LSTM-CNN** & **SRDCNN** \\ \hline Input layer & \(1024\times 1\) & \(32\times 32\) & \(1024\times 1\) & \(1024\times 1\) \\ Layer-1 & Conv1d (\(16\times 1\), \(16\)) & Conv2d (\(5\times 5\), \(16\)) & Conv1d (\(32\times 1\), \(20\)) & RDConv1d (\(64\times 1\), \(32\)) \\ Layer-2 & Pooling (\(2\times 1\), \(2\)) & Pooling (\(2\times 2\), \(2\)) & Pooling (\(2\times 2\), \(2\)) & RDConv1d (\(32\times 1\), \(32\)) \\ Layer-3 & Conv1d (\(3\times 1\), \(32\)) & Conv2d (\(5\times 5\), \(32\)) & LSTM (100) & RDConv1d (\(16\times 1\), \(64\)) \\ Layer-4 & Pooling (\(2\times 1\), \(2\)) & Pooling (\(2\times 2\), \(2\)) & Dense (10) & RDConv1d (\(8\times 1\), \(64\)) \\ Layer-5 & Conv1d (\(3\times 1\), \(64\)) & Flatten & & Flatten \\ Layer-6 & Pooling (\(2\times 1\), \(2\)) & Dense (100) & & Dense (100) \\ Layer-7 & Conv1d (\(3\times 1\), \(64\)) & Dense (10) & & Dense (10) \\ Layer-8 & Pooling (\(2\times 1\), \(2\)) & & & & Dense (10) \\ Layer-9 & Conv1d (\(3\times 1\), \(64\)) & & & & \\ Layer-10 & Pooling (\(2\times 1\), \(2\)) & & & & \\ Layer-11 & Flatten & & & & \\ Layer-12 & Dense (100) & & & & \\ Layer-13 & Dense (10) & & & & & \\ Mean accuracy & 0.986 & 0.992 & 0.978 & 0.994 \\ Standard deviation & 0.0064 & 0.0043 & 0.0071 & 0.0015 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Structure parameters and performance indicators of models. The training process and the confusion matrix diagram of these four models are shown in Figures 10-13. It can be seen that compared with the 1d-DCNN model, the other three models present the more stable training process. After about 50 epochs of training, the classification accuracy of the SRDCNN model has almost converged. The intelligent fault diagnosis method based on SRDCNN not only achieves extremely high validation accuracy after 80 epochs, but also obtains the same high accuracy rate of 99.4% in the test set. Meanwhile, the intelligent fault diagnosis methods based on 1d-DCNN, 2d-DCNN, and LSTM-CNN achieve a little lower accuracy rate in the test set, i.e., 98.6%, 99.2%, and 97.8% respectively. The above fact illustrates that deep learning method is very effective in bearing fault diagnosis. From the above experimental results, it can be seen that these four methods all have a good performance in the specific operation. However, due to the inevitable noise in workshop processes, the vibration signal is easily disturbed by noise. It is crucial and arduous to diagnose the types of fault under the noisy environment. Additionally, as the workload may change continuously due to production requirements, it is unrealistic to collect and label enough training samples to adapt to all the workloads. Hence, it is important for the classifier to learn the essential features by training samples collected under different workload conditions. The rest of this section will investigate the performance of SRDCNN under different loads and different noises. Figure 11: Diagram of the 2d-DCNN model (**left**) the training process and (**right**) confusion matrix. Figure 10: Diagram of the 1d-DCNN model (**left**) the training process and (**right**) confusion matrix.