## 3 Experiments and Analysis
### Experiment 1: Case Western Reserve University (CWRU) Bearing Dataset
#### 3.1.4 Validation Results  
As mentioned in Section 2.4.2, the proposed SSDAE contains two hidden layers. The neuron numbers of the first and second hidden layers were set to 100 and 60, respectively. The number of output layer neurons was four, which was determined by the number of bearing health conditions. The activation function was sigmoid, and the learning rates of the two hidden layers and the softmax layer were 0.1, 0.1, and 0.2, respectively. The sparsity parameter was 0.15, and the corruption level was 0.3. The detailed parameters of the SSDAE are listed in Table 3.  
Figure 12: MPE of intrinsic mode function 1 (IMF1) for four health conditions. Figure 13: MPE of IMF3 for four health conditions. The extracted feature vector was divided into training and testing data. The former was used to train the constructed network, and the latter was used to validate the performance of the diagnosis model. Four tests were carried out, with an average classification accuracy of 99.55%. One of the test classification results is shown in Figure 14. According to the classification result, 498 out of 500 test samples were identified accurately. All samples of N and IRF were identified accurately, and only two samples were misjudged: one BF sample was misjudged as an ORF, and one ORF sample was misjudged as an IRF. The classification accuracy rate was 99.6% (498/500 = 99.6%). The experimental result shows that the proposed method based on MPE and the SSDAE can effectively detect bearing faults, and the recognition and analysis effect in different working conditions is ideal. To further validate the superiority of the proposed SSDAE model structure, a comparative experiment of a different stack order, Scheme 1 (SAE + DAE), with Scheme 2 (DAE + SAE) was conducted. According to the training process of the SSDAE model, the experimental results of the two schemes were compared in the same experimental condition. Figure 15 shows that the reconstruction error of both schemes decreases as iterations increase. In Scheme 1, the reconstruction error is less than 0.05 after 100 iterations, and with the increase in iterations, the reconstruction error is stable at about 0.025. In Scheme 2, the reconstruction error is less than 0.25 after 100 iterations. With the increase in iterations, the reconstruction error decreases slowly. As the number of iterations reaches 200, the reconstruction error is still as high as 0.2. However, at the beginning of training, the reconstruction error of Scheme 1 is slightly larger than that of Scheme 2. With the increase in iterations, the reconstruction error of Scheme 1 decreases rapidly and is less than that of Scheme 2. Therefore, (the proposed) Scheme 1 is superior to Scheme 2 in terms of the real reconstruction error. One possible reason for this result is that when human visual systems process information, its mechanism is similar to sparse coding. That is, a single neuron only responds strongly to certain information. Most of the neurons in the hidden layer are suppressed, and input data are represented by sparse components. Therefore, the ability of the SAE to extract representative features is better than that of the DAE. The DAE model itself can erase the noise in the training data because the noise data is close to the test data, which can reduce the generation gap between the training and test data. Thus, in Scheme 1, the SAE is first  
Figure 14: Classification result of the proposed method for bearing dataset. \begin{table}
\begin{tabular}{c c c c c} \hline
**No. of Hidden** & **No. of Input Layer** & **No. of Hidden** & **No. of Output** & **Activation** \\
**Layers** & **Neurons** & **Layer Neurons** & **Layer Neurons** & **Function** \\ \hline
2 & 60 & 100,60 & 4 & sigmoid \\
**Epoch Number** & **Corruption Level** & **Learning Rate** & **Sparsity** & **Sparsity Penalty** \\
**Parameter** & **Term** & **Term** \\
100 & 0.3 & 0.1,0.1,0.2 & 0.15 & 3 \\ \hline \end{tabular}
\end{table} 
Table 3: The proposed stacked sparse denoising autoencoder (SSDAE) network parameters.