[2A4] Gaussian assumptions free interpretable linear discriminant analysis for machine condition monitoring
Y Chen and D Wang
Shanghai Jiao Tong University, China
Bearings and gears are important parts of rotating machinery. Due to the load and the harsh operating environment, the degradation of bearings and gears can deteriorate sharply over time. With the development of information technology and sensor technology, it is possible to collect more and more data, so that condition monitoring with statistical learning and machine learning is more attractive. Compared with traditional signal processing algorithms, interpretable learning models could generate interpretable learnable weights/parameters as advanced physically interpretable fault features for both 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 the derivations and parameter estimations. This paper explores the feasibility of the Gaussian assumptions-free interpretable LDA to provide physically learnable model weights/parameters for supporting machine condition monitoring and fault diagnostic results. 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 accordingly given to support this Gaussian assumptions-free interpretable LDA. The benefit of Gaussian assumptions-free interpretable LDA is that Gaussian assumptions and their associated parameter estimations are not considered any more for the use of LDA. Finally, linear regression analysis with a sparse Lp-norm regularisation term is introduced as a feasible solution to practical implementation of the proposed Gaussian assumptions-free interpretable LDA to physically locate informative frequency bands and fault characteristic frequencies for condition monitoring and fault diagnosis. 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.
