## 5 Experiment Verification and Analysis
### Experiment on Datasets of Rolling Bearing in Case Western Reserve University
#### 5.1.2 Optimization Selection of the SR\(-\)1 DCNN Model  
(1) Sparse representation selection of related parameters  
In the process of sparse representation, the sparsity of the original vibration signal is determined by setting the parameter sparsity k in the OMP algorithm. If the parameter k is too large, the sparse component will contain too many signal features; while if the parameter k is too small, it will lead to the loss of some feature information. In addition, in the process of learning the construction of dictionary D, a small number of atoms will lead to fewer fault features in the reconstructed signal, while too many atoms will cause more noise interference in the reconstructed signal, which cannot achieve the effect of noise reduction. At the same time, in the process of adaptive dictionary training and learning, the selection of sample length W determines the number of training samples, which will also affect the impact feature information contained in the reconstructed signal. Therefore, the parameters are adjusted by reconstructing the relationship between the signal envelope kurtosis and the parameters. For example, Figure 6 shows the rolling body fault and the relationship between the sparsity and the reconstruction signal envelope kurtosis when the damage diameter is 0.007 inches. In order to ensure the maximum retention of the impact characteristic components of the reconstructed signal and highlight the characteristics of the impact fault, the sparse degree is finally selected. The same selection criteria select other sparse representation parameters in the fault state and finally choose the sample length Wend64; the number of atoms is 1024. The state of ten kinds of bearings are sparsely represented and reconstructed signals.  
(2) Parameter selection of 1 DCNN Network Model  
The structure of the 1 DCNN model used in this paper is modified based on WD-CNN [44]. The accuracy and loss are obtained by adjusting the number of network layers and the size, number, and step size of the convolution kernel, and the final selected network model parameters are shown in Table 2. The training and learning design of the 1 DCNN-based network model consists of five convolution stages for feature extraction; each convolution stage contains a set of one-dimensional convolution layers for learning  
Figure 5: Original vibration signal time-domain waveforms of the drive-end rolling bearing under the 0–3 hp load.  
important features from the input signal, and the batch normalization layer normalizes a batch output feature vector to an appropriate data distribution, which makes the value of the intermediate output of each layer more stable, thus accelerating the learning speed of the model. The nonlinear element activation function (Relu) is used for nonlinear transformation of the extracted features to overcome the problem of gradient disappearance and speed up the training speed, and the maximum pool layer is used to improve the local translation invariance of the input signal features. The first convolution layer in the network model uses a wide convolution core to suppress the high-frequency noise in the input signal and capture the correlation with the distance, while the other convolution layer uses a smaller convolution kernel to obtain a complex representation of the characteristics of the input signal. The output layer has 10 neurons to classify 10 health states of the bearing.