## 4 Experimental Analysis
### The Validity of MSCAE  
The specific structure of the MSCAE proposed in this paper is shown in Figure 7. As can be seen from Figure 7, MSCAE consists of three encoding blocks, three decoding blocks and one fully connected block. The number of convolutional kernels in the three coding blocks is 8, 16, 4, and the size of convolutional kernels in the three pathways is 3 \(\times\) 1, 7 \(\times\) 1 and 11 \(\times\) 1, respectively, and the size and stride of maximum pooling are 8. The number of convolutional kernels in the three decoding blocks is 16, 8, 1, and the size of convolutional kernels in the three pathways is the same as the decoder, and the size and stride of upsampling are 8. The Sigmoid activation function is used in the fully connected block when the second layer obtains HI. The activation function is not used when reconstructed data are obtained. All the remaining layers use the ReLU activation function, and each layer uses the BatchNormalization (BN) layer to improve the model generalization. The detailed hyperparameter settings of the model are shown in Table 2. Comparative experiments are conducted in this paper to choose the scale factor v of the composite loss function. In this paper, five values of 0.2, 0.4, 0.6, 0.8 and 1.0 are selected for comparison and validation. Ten experiments are conducted on four test bearings using these five values, respectively, and the final box line diagram is obtained, as shown in Figure 8. From Figure 8, it can be seen that \(v\) is taken as 0.6, 0.6 and 0.4, respectively, as the best choice for the three working conditions. After training the MSCAE using the training bearing data, the MSCAE was tested using testing bearings, and the HI extracted by four testing bearings is shown in Figure 9. In Figure 9, the green color indicates that the value of HI is closer to 1, and the blue color is closer to 0. The red curve is the HI trend curve fitted using polynomials. Four bearings \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Batch size & 128 \\ Epoch & 100 \\ Learning rate \(lr\) & Adam (0.0001) \\ Number of Encoding Block & 3 \\ Number of Decoding Block & 3 \\ Kernel size & \([3\times 1],[7\times 1],[11\times 1]\) \\ Pooling size & 8 \\ Upsampling size & 8 \\ Number of fully connected layer units & \([60,1,60]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter setting of the model. Figure 8: The results of the selection of different scale factors \(\
u\). (**a**) The result of Bearing1_1. (**b**) The result of Bearing1_3. (**c**) The result of Bearing2_6. (**d**) The result of Bearing3_3. Figure 7: The details of MSCAE. in Figure 9 have a clear downward trend in HI, and by the time sampling stops, the value of HI is close to 0. In order to verify the superiority of MSCAE, this paper sets up a comparison between MSCAE and three convolutional autoencoders (CAE) with constant convolutional kernel sizes of \(3\times 1\), \(7\times 1\) and \(11\times 1\), respectively. To ensure the completeness of the experiments, the structure of the CAE is the same as the structure of a pathway in MSCAE. Moreover, when the model is trained, the hyperparameters are set the same as MSCAE. The obtained results are shown in Figure 10. From Figure 10, it can be seen that MSCAE exceeds the other three models in CI for the tested bearings under each operating condition. It shows that MSCAE can combine the advantages of different convolutional kernel sizes to identify different time scale information and make full use of the local and global information of the original vibration signal to extract a more effective HI. To further verify the superiority of MSCAE, four models were used to extract the HI of Bearing2_6 bearing for analysis, as shown in Figure 11. When the convolution kernel size is set to 3, the final HI trend increases, which is against the degradation law of the real bearing. Moreover, when the convolution kernel size is 7 and 11, the final HI trend decreases to 0.