Computationally Efficient OMP for Rolling Bearing Fault Diagnosis: A Study on Orthogonal and Overcomplete Dictionaries

Orthogonal Matching Pursuit (OMP) is an extensively used method in bearing fault diagnosis due to its flexibility. However, its reliance on repeated projection operations and pseudo-inverse computation results in a high computational cost, especially for large-scale signals and high-iteration scenarios. This study explores sparse coefficient estimation within the OMP framework under diverse dictionary structures. For orthogonal dictionaries, we leverage the fact that sparse coefficients can be directly computed through a single inner product projection. Then, we propose the Orthogonal Dictionary Matching Pursuit (ODMP) algorithm to streamline the sparse coding process. The efficiency and feasibility of the proposed algorithm are validated through theoretical analysis, simulations, and experimental evaluation. Furthermore, for overcomplete dictionaries, we propose the Temporal OMP (TOMP) algorithm, which leverages the non-overlapping structure of fault-induced impulses to facilitate the efficient extraction of fault-related components. As validated through our results, these proposed algorithms significantly minimize computational overhead while maintaining excellent diagnostic accuracy.These improvements provide practical benefits for engineering applications, enabling faster and more reliable fault detection in industrial systems. Implementation of the proposed algorithms is available at: https://github.com/godshooter/ODMP-and-TOMP.