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 consider 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. First, the total of a weighted square envelope spectrum is used to represent a degradation feature. To simultaneously consider 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 considered 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. In addition, 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.