Weighted bi-domain sparse decomposition for encoder-signal-based planetary gearbox fault diagnosis

Abstract

As key transmission components in mechanical systems, gearboxes often operate under harsh environments and heavy-load conditions, making them susceptible to various types of damage. In recent years, built-in encoder signals have attracted increasing attention for rotating machinery health monitoring due to their low cost, ease of acquisition, and direct correlation with rotational motion. However, fault-related features in encoder signals are usually weak and easily submerged by strong harmonic interference and noise, posing significant challenges for accurate fault identification and feature extraction. To address this issue, this article proposes a weighted bi-domain sparse decomposition (WBSD) model for encoder signal analysis and fault diagnosis of gearboxes. The proposed WBSD model exploits the distinct morphological characteristics of fault-induced impulses and interference components in both the time and frequency domains. Specifically, two dedicated nonconvex regularization terms are constructed to enforce periodic group sparsity of fault impulses in the time domain and spectral sparsity of harmonic interference in the frequency domain by introducing weighted coefficients, periodic binary vectors, and nonconvex penalty functions, thereby enabling accurate separation and sparse representation of fault features. Furthermore, an efficient iterative solving algorithm is developed for the WBSD model by integrating the alternating direction method of multipliers with the majorization–minimization method. Experimental results obtained from both simulated signals and real encoder signals collected from a planetary gearbox test platform demonstrate that the proposed WBSD model consistently outperforms comparative methods in extracting weak fault impulses under strong noise and interference, confirming its effectiveness and practical applicability for fault diagnosis of gearboxes.