## 4 Results and Discussion
### Stepwise Intelligent Fault Diagnosis Based on SAE
#### 4.2.2 Process of SAE Learning  
The SAE learning is mainly divided into unsupervised feature extraction (information compression) stage and supervised state identification stage. Furthermore, there are totally four AEs, and each hidden layer of proposed method utilized in this case is consists of 4000, 2000, 500, and 30 neuroses, respectively. The learning rate and momentum of each AE are 0.9 and 0.5, respectively. The active function is the'sigmoid'. Moreover, the input layer consists of 8192 neuroses representing the 8192-dimension, and the output layer has one neuron representing bearing state (0 or 1). The detailed parameters of the proposed method are described in Table 3.  
There are five parts in the stepwise intelligent diagnosis of the sliding bearing for rotor system. Firstly, the train data \(X_{train}\) is sequentially assigned to the AEs (from AE-1 to AE-4) to complete the feature extraction. Secondly, the extracted feature is putted into the neural network, which includes the compressed feature in hidden layer and the weights of the four AEs. Thirdly, the gradient descent is utilized to globally fine-tune the weights between the layers according to the \(Y_{train}\). Finally, the \(X_{test}\) and \(Y_{test}\) are applied to verify the accuracy of the fault diagnosis. The pseudocode of the stepwise intelligent fault diagnosis is shown as Table 4.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Input:** & **The 5 Kinds of Sliding Bearing Signal** \\
**Output:** & **Bearing Fault Diagnosis Result** \\ \hline \hline \end{tabular} /*Raw signal preprocessed*/ The raw signal preprocessed with statistical filter and obtain new signal \(N^{\prime}\), \(C^{\prime}\), \(O^{\prime}\), \(SU^{\prime}\), \(DU^{\prime}\); /*SAE training process*/ Construct data according to Table 2 and obtain \(G^{1}\) and \(G^{2}\); Mark label data as [0,1] according to \(G^{1}\), \(G^{2}\); Divide the train data \(X_{train}\) and \(Y_{train}\); and test data \(X_{test}\), \(Y_{test}\); /**Auto-encoder (Unsupervised learning)** / Construct AE-1, AE-2, AE-3 and AE-4; Obtain \(H_{1}\) and \(W_{1}\) by inputting the train data (\(X_{train}\)) to AE-1(8192-4000-8192); Construct AE-1, AE-2, AE-3 and AE-4; Obtain \(H_{1}\) and \(W_{1}\) by inputting the train data (\(X_{train}\)) to AE-1(8192-4000-8192); Obtain \(H_{2}\) and \(W_{2}\) by inputting \(H_{1}\) to AE-2 (4000-2000-4000); Obtain \(H_{3}\) and \(W_{3}\) by inputting \(H_{2}\) to AE-3 (2000-500-2000); Obtain \(H_{4}\) and \(W_{4}\) by inputting \(H_{3}\) to AE-4 (500-30-500); /**Network classification process (supervised learning)**  Build a neural network architecture: 8192-4000-2000-500-30-1; Enter \(H_{1}\), \(H_{2}\), \(H_{3}\), \(H_{4}\) and \(W_{1}\), \(W_{2}\), \(W_{3}\), \(W_{4}\) into the network to initialize parameters; Assign output layer weight \(W_{5}\) randomly and obtain the actual output \(Y\); Perform the gradient descent to fine-tune the globally \(W_{1}\), \(W_{2}\), \(W_{3}\), \(W_{4}\), \(W_{5}\); Get SAE training model; /*SAE testing process*/ The test data \(X_{test}\) is substituted into the above-mentioned trained classification model for fault identification, and the identification results are outputted and compared with \(Y_{test}\).  
\end{table}
Table 3: Detailed information of SAE.