Easier Computational Approach of Optimized Weights and Its Extensions for Learning Interpretable Machine Fault Features

Fault feature extraction is extremely important for machine condition monitoring (MCM). Recently, the proposed machine learning-based optimized weights have been proven to own fully physical interpretability to learn informative fault features for MCM. Nevertheless, machine learning algorithms-based optimized weights still can not be intuitively understood, which restricts the utilization of optimization weights for MCM. In this article, we first propose an equivalent and easier computational approach to intuitively calculate the aforementioned interpretable optimized weights, i.e., the optimized weights could be regarded as a subtraction result between a mean spectrum of faulty signals and a mean spectrum of healthy signals. Here, it is necessary to emphasize that the functions of subtraction operation and mean operation can be regarded as relieving an influence of random noise and fundamental healthy components, which provides a more intuitive understanding of the optimized weights. Next, the idea of the easier computational approach is extended to spectral correlation to construct 2-D optimized weights for simultaneously enhancing fault features in the envelope spectrum and Fourier spectrum. Moreover, based on the optimized weights, we further construct a health index that highly focuses on degradation-related fault frequency components, and it has a monotonic degradation assessment ability. Experimental run-to-failure datasets verified the effectiveness of these new ideas for MCM.