## 4 Experiment
### Simulated Signal Experiment  
#### 4.2.1 Network Parameters Setting Method  
To explore the method of setting ADMM-1 DNet network adaptation parameters and develop a more reasonable online monitoring implementation scheme, simulation signals were used for experimental research. The signal formula is defined as follows:  
\[S(t)=0.1\sin(100\pi t+0.2\cos(40\pi t))+0.2\cos(250\pi t)+\eta(t) \tag{33}\]  
The signal is formed by the superposition of the frequency modulation component and cosine component, where the fundamental frequency is 50 Hz, the modulation frequency is 20 Hz, the frequency of the cosine component is 125 Hz, \(\eta(t)\) is a white noise term complying with normal distribution, the intensity is 1, and the time domain waveform of some signals is shown in Figure 4. In practical application, we can directly obtain the measured value instead of the original data. Therefore, ADMM-1 DNet cannot acquire theprior knowledge from the test data, and another training set is required to provide the prior knowledge. To simulate this, 1024 sampling points in the experiment were defined as one signal unit and a training set containing 1200 signal units and a test set of 240 signal units were generated as experiment samples. The experiment \(r\) is now set to 20%. Firstly, we explore the initialization method of network redundancy analysis operator \(\mathbf{\Phi}\) and select three initialization methods, namely, discrete cosine transform (DCT dictionary), Fourier transform (FCT dictionary), and the He (normal) method for the experiment. Figure 5 shows the restructuring effect of the three initialization methods. It can be seen that the restructuring \(T_{\text{test}}\) obtained by using the He (normal) initialization method is the minimum, and the restructuring PSNR performance of the He (normal) method is significantly better than the other two methods. This indicates that when the He (normal) method is chosen to initialize \(\mathbf{\Phi}\), the noise level of the reconstructed signal is relatively reduced and closer to the original signal. The reconstruction accuracy is the primary index to judge the performance of the reconstruction algorithm, and then the reconstruction speed shall be considered. The experiment explores the relationship between the number of network expansion layers, signal reconstruction \(T_{\text{test}}\), and network convergence time, and the results are shown in Figure 6. Using three different color balls to represent the results of network iterations 80, 90, and 100, respectively, it can be observed that when the number of unfolding layers is 4 or more, the reconstruction \(T_{\text{test}}\) is the lowest and gradually converges, indicating that the setting of four layers is more effective in achieving higher reconstruction accuracy. The same results are obtained with both 90 and 100 iterations when the number of layers is  
Figure 4: Simulated signal time–domain diagram. Figure 5: Reconstruction effects of the three initialization methods. 4, but 90 iterations take less time. Experimentally setting the empirical network training parameters to 4 layers and 90 iterations is a better compromise scheme, as required by the actual situation. Through simulation experiments, the best reconstruction performance of the network can only be achieved when different types of signals are configured with appropriate parameters. When training the network in the local data center, the network parameters should be adjusted one by one according to the principle of control variables. The parameter configuration process can be done automatically by the embedded program, and then the error and time cost caused by manual adjustment can be avoided. This \"tailored\" approach to network parameter training is not only more reliable than traditional static or empirically based parameter configuration methods but also allows the network to be adapted for a wide range of specific vibration signal reconstruction tasks.