Optimal design of robust sensing matrix and its application in mechanical fault diagnosis

The application of compressed sensing (CS) in mechanical equipment fault diagnosis system can effectively alleviate the pressure of data transmission and storage in fault diagnosis system. The optimal design method of sensing matrix is introduced into mechanical fault diagnosis system for the first time. Considering the characteristics of low signal-to-noise ratio (SNR) of mechanical signals, a robust sensing matrix optimization framework suitable for mechanical signals is proposed based on the analysis of the robustness of different optimization frameworks of sensing matrix. A new closed-form algorithm with lower computational complexity is derived for the proposed optimization framework. Numerical simulations and experiments are carried out and the results show that the optimal sensing matrix obtained by the proposed method is robust and computationally efficient. Compared with the existing optimal sensing matrix and the commonly used random matrix, the proposed method can effectively reconstruct the mechanical fault signals at lower signal-to-noise ratio and compression ratio. © 2023 Nanjing University of Aeronautics an Astronautics. All rights reserved.