Balanced Generalised Tailored Approximation Point Algorithm for Solving Convex Optimisation Mathematical Problems in Bearing Vibration Signal Compressive Sensing

Abstract

With the continuous progress of science and technology, the transformation of compressive sensing problems into convex optimization problems has become a hot research topic. In this study, a novel algorithm, the balanced generalized customized proximal point algorithm, is proposed, which integrates the generalized customized proximal point algorithm with the balanced-augmented lagrangian method. Based on this algorithm, a compressive sensing system for bearing fault signals is designed, and the bearing fault signals are compressed by the universal compressive sensing model and the K-singular value decomposition algorithm, Then, the signals are reconstructed using the BG-CPPA. The experimental results showed that the BG-CPPA had a lower number of iterations and computation time compared with the traditional algorithm at different sparsity conditions. The reconstruction effect of the bearing inner ring signal was the best. Specifically, the BG-CPPA reduced the reconstruction error by 33.33% and 20.00%, while reducing the reconstruction time by 32.46% and 52.64%. At compression ratios of 0.3, 0.4, and 0.5, the proposed compressive sensing system reduced the reconstruction error by 35.39%, 44.06%, and 26.76% over the greedy algorithm, respectively. These results confirm the effectiveness of the BG-CPPA in improving the reconstruction accuracy and stability of bearing vibration signals, as well as the potential of the designed compressive sensing system in enhancing the observation efficiency of bearing fault vibration signals.