## 5 Conclusions  
In this paper, a new CS signal reconstruction method based on ADMM and neural networks, called ADMM-1 DNet, is especially suitable for the demand for online monitoring of devices in outdoor high-noise environmental conditions. Taking bearing parts as an example, combined with modern sensor technology, a detailed implementation scheme for monitoring mechanical equipment parts is given in this paper. Through experiments on simulated signals and real bearing vibration signals, we first formulate the parameter setting guidelines for the ADMM-1 DNet network, then explore the relationship between the signal sparsity level and the reconstruction error, and finally examine the time-frequency domain quality of the reconstruction signals in a real data set. The experiments show that the proposed network outperforms other classical algorithms in terms of reconstruction accuracy and convergence speed, while the learning of redundant analysis operators enables the online monitoring scheme to adapt to signals with different sparsity levels, which can further satisfy the needs of different reconstruction tasks. The method in this paper provides strong theoretical and practical scheme support for practical engineering applications and is expected to play an important role in the field of monitoring parts of outdoor working machinery and equipment. In future work, we expect to develop a more powerful equipment monitoring system by fusing multimodal data on the basis of ADMM-1 DNet to provide more comprehensive and reliable information for monitoring signal fault identification.  
Conceptualization, [PERSON] and Z.W.; Writing--original draft, [PERSON]; Writing--review & editing, J.G. All authors have read and agreed to the published version of the manuscript. This research was funded by the Major Cultivation Project of Gansu Province University Research and Innovation Platform (2024 CXPT-04) and the National Natural Science Foundation of China (No. 52365063). Not applicable. Not applicable. Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{C\_R} & \multicolumn{3}{c}{**ISTA-Net**} & \multicolumn{3}{c}{**ADMM + K-SVD**} & \multicolumn{3}{c}{**ADMM-1 DNet**} \\ \cline{2-10}  & **PSNR (dB)** & **Time (S)** & \(T_{\text{gen}}\) & **PSNR (dB)** & **Time (S)** & \(T_{\text{gen}}\) & **PSNR (dB)** & **Time (S)** & \(T_{\text{gen}}\) \\ \hline
**10\%** & 18.1488 & 1.7350 & 0.0647 & 15.6798 & 3.7033 & **—** & 19.1659 & 0.7400 & 0.0150 \\
**15\%** & 18.5336 & 1.9292 & 0.0586 & 15.2853 & 3.6672 & **—** & 20.3437 & **0.6841** & 0.0021 \\
**20\%** & 19.0301 & 1.7533 & 0.0555 & 15.2113 & 3.6574 & **—** & 22.0323 & 0.7150 & 0.0036 \\
**25\%** & 7.8792 & 1.7575 & 0.0953 & 17.0009 & 3.6502 & **—** & 23.3325 & 0.7058 & 0.0024 \\
**30\%** & 8.8558 & 1.7358 & 0.1062 & 18.1672 & 3.5468 & **—** & 25.2719 & 0.7425 & 0.0017 \\
**40\%** & **19.0870** & 1.7275 & **0.0124** & 20.6455 & **3.5397** & **—** & 26.1580 & 0.7217 & 0.0021 \\
**50\%** & 16.6747 & **1.6250** & 0.0498 & **21.2260** & 3.5564 & **–** & **26.9997** & 0.7350 & **0.0011** \\ \hline \end{tabular}
\end{table}
Table 5: Comparison of PSNR (dB), Time, and \(T_{\text{gen}}\) results for three algorithms reconstructing the MIX signal of the XJTU-SY dataset at different compression rates. The best performance is marked in bold, and the second-best performance is underlined. Time is a running time record for the three methods, showing the average time used for 100 iterations of 1024 samples.