Discrimination and Sparsity Driven Weight-oriented Optimization Model for Interpretable Initial Fault Detection and Fault Diagnosis

Currently, data-driven machine fault detection and diagnosis is one of the mainstream methodologies while most methods simply take into account discrimination ability of extracted features without considering their interpretability. Model decision-making procedures are opaque and unable to describe how they are related to the characteristics of physical faults. In this study, a novel weight-oriented optimization model is proposed for simultaneously interpretable initial fault detection and fault diagnosis. Firstly, the total of a weighted square envelope spectrum is used to represent a degradation feature. To simultaneously take into account its discrimination and sparsity, three properties of the degradation feature are identified and theoretically stated as an optimization model of a generalized Rayleigh quotient. Weight sparsity is taken into account in the proposed model to be connected with cyclic fault frequencies for interpretability enhancement. The described degradation feature can be viewed as a health indicator for incipient fault detection. Additionally, it is demonstrated how the defined degradation feature is successfully paired with a straightforward Euclidean distance for fault diagnosis. Moreover, their associated weights are all physics-informed fault characteristics.