## 3 Fault Diagnosis Method Based on 1 DCNN and INPSO-SVM
### Feature Extraction Based on 1 DCNN  
The training process of the convolutional neural network can be divided into a forward propagation stage and a backward propagation stage. In the process of forward propagation, the network firstly  
Figure 1: The framework of the proposed one-dimensional convolutional neural network improved novel particle swarm optimization support vector machine (1 DCNN-INPSO-SVM) intelligent fault diagnosis method.  
initializes the weights, and then convolution kernels filter each small region of the data to obtain the eigenvalues of the small region. The features obtained from the convolution layer are passed into the lower sampling layer, where the dimension and quantity of trainable parameters are reduced to avoid overfitting by pooling. Finally, the features extracted from the lower sampling layer are transferred to the fully connected layer and the softmax layer for classification, and the classification model is obtained to get the final fault diagnosis results. When the output results of the convolutional neural network are inconsistent with the real labels, the errors are propagated from the high level to the low level in the backward propagation stage. According to the ratio of each layer of errors to the total errors, the weights of each layer are updated. In the training stage of CNN, dropout technology, data sliding window expansion technology and batch normalization technology are used to prevent over-fitting and speed up the training process. The structure of the proposed 1 DCNN network is shown in Figure 2.  
The overall structure of proposed 1 DCNN network is composed of four convolution layers, four maximum pooling layers and two fully connected layers. Details about the architecture of 1 DCNN can be found in Table 1. The input signals are the normalized time-domain signals. Features can be extracted directly from the raw time domain signals by using one-dimensional convolution kernel and pooling kernel, which reduces the work of signal preprocessing. Compared with traditional CNN structure, the main advantage is that the convolution kernel of the first layer is larger in size to better suppress the high-frequency noise, and the following convolutional kernels are small with \(3\times 1\), which is helpful to obtain a good representation of the input signals and improve the network performance.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Layer Type** & **Kernel Size** & **Strides** & **Kernel Number** & **Output Size (Width \(\times\) Depth)** \\ \hline
1 & Conv1 & \(64\times 1\) & \(16\times 1\) & \(16\) & \(128\times 16\) \\
2 & Pool1 & \(2\times 1\) & \(2\times 1\) & \(16\) & \(64\times 16\) \\
3 & Conv2 & \(3\times 1\) & \(1\times 1\) & \(32\) & \(64\times 32\) \\
4 & Pool2 & \(2\times 1\) & \(2\times 1\) & \(32\) & \(32\times 32\) \\
5 & Conv3 & \(3\times 1\) & \(1\times 1\) & \(64\) & \(32\times 64\) \\
6 & Pool3 & \(2\times 1\) & \(2\times 1\) & \(64\) & \(16\times 64\) \\
7 & Conv4 & \(3\times 1\) & \(1\times 1\) & \(64\) & \(16\times 64\) \\
8 & Pool4 & \(2\times 1\) & \(2\times 1\) & \(64\) & \(8\times 64\) \\
9 & F & 300 & & \(1\) & \(300\times 1\) \\
10 & F & 10 & & \(1\) & \(10\times 1\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of 1 DCNN algorithm applied in the experiments.  
Figure 2: Structure of the proposed 1 DCNN model.