Fisher’s discriminant ratio based health indicator for locating informative frequency bands for machine performance degradation assessment

Abstract

A general tactic for machine performance degradation assessment (PDA) is to develop a health indicator (HI) to identify different degradation stages. A suitable HI is not only capable of distinguishing different machine degradation stages but also has an inherent characteristic of monotonicity because of irreversible machine degradation. Since informative frequency bands, such as resonance frequency bands, can indicate the occurrence of machine faults and fault levels, it is desirable to locate informative frequency bands and consider integrating informative frequency bands for machine PDA. In this paper, a Fisher’s discriminant ratio-based health indicator is proposed to fully consider the contributions of all spectrum amplitudes in the frequency domain to machine PDA. Firstly, locating informative frequency bands of non-process data, such as vibration and acoustic data, is formulated as a Fisher’s discriminant ratio based optimization problem. Once the optimization problem is solved, informative frequency bands, such as resonance frequency bands, can be automatically determined by observing optimized weights used in a designed HI. The larger an absolute optimized weight, the more informative a frequency is. Secondly, the sum of the multiplication of frequency amplitudes and optimized weights can be directly used as a HI for machine PDA. Unlike most existing feature-level fusion methods, the proposed method can directly realize data-level fusion, namely fusion of frequency amplitudes. Thirdly, the recovery of a Fourier spectrum by considering optimized weights can be further used for squared envelope analysis for machine fault diagnosis. Two case studies showed that the proposed HI can not only distinguish different degradation stages but also can monotonically assess degradation trends. More interestingly, optimized weights can automatically indicate the locations of informative frequency bands. Comparisons with some popular sparse measures, the fast Kurtogram and machine learning algorithms demonstrate the superiority of the proposed method.