Nonlinear weight learning model for incipient fault detection and degradation modelling and its interpretability for fault diagnosis

Optimization-based weight learning approaches that incorporate multiple sensor signals or vibration spectral components have demonstrated their effectiveness in monitoring mechanical systems. However, the current weight learning methods are limited by their reliance on linear fusion functions. The exploration of nonlinear link functions, particularly in the context of fusing spectral components in vibration spectra for health indices (HIs) construction, remains largely unexplored. Additionally, the development of formulas for interpreting HIs constructed using nonlinear fusion functions poses significant theoretical challenges. To address these limitations, this study proposes a novel nonlinear optimization-based weight learning model for constructing an HI that captures the nonlinear relationships among spectral components. This HI is designed to pinpoint fault characteristic frequencies while also highlighting other spectral lines associated with bearing degradation modelling. Furthermore, we derive formulas that enable the calculation of the contributions of frequency components to nonlinearly constructed HIs, thereby enhancing the interpretability of the model. By selecting an appropriate kernel function, subtle changes resulting from incipient faults and the underlying degradation process can be effectively captured. The effectiveness of the proposed model in detecting incipient faults, modelling degradation, and identifying fault types is validated through two run-to-failure case studies and a gearbox bearing experiment.