Gaussian assumptions-free interpretable linear discriminant analysis for locating informative frequency bands for machine condition monitoring

Interpretable learning models become an emerging topic in the domain of machine condition monitoring to connect signal processing algorithms with statistical learning and machine learning. Compared with traditional signal processing algorithms that show strong ability in data analysis, signal-processing-related interpretable learning models could generate interpretable learnable weights/parameters as advanced physically interpretable fault features for both machine condition monitoring and fault diagnosis. It is well-known that linear discriminant analysis (LDA) is one of the most popular and interpretable algorithms for machine condition monitoring. However, this popular algorithm needs Gaussian assumptions in their derivations and parameter estimations. In this paper, Gaussian assumptions-free interpretable LDA is proposed as an interpretable learning model to physically locate informative frequency bands and fault characteristic frequencies for machine condition monitoring. Firstly, statistical decision theory is introduced to connect the nature of regression with that of classification, which poses a foundation for the Gaussian assumptions-free interpretable LDA for machine condition monitoring. Secondly, two propositions are given to mathematically show that LDA can be realized by an equivalent linear regression analysis, which provides a perspective for the Gaussian assumptions-free interpretable LDA for simultaneous machine condition monitoring and fault diagnosis. Finally, linear regression analysis with a sparse Lp-norm regularization term is introduced to realize the Gaussian assumptions-free interpretable LDA for physically locating informative frequency bands and fault characteristic frequencies for machine condition monitoring. Two case studies are provided as illustrative examples to experimentally demonstrate that the Gaussian assumptions-free interpretable LDA is capable of indicating informative frequency bands and fault characteristic frequencies.