Investigations on quasi-arithmetic means for machine condition monitoring

Machine condition monitoring aims to use on-line sensor data to evaluate machine health conditions. One of the most crucial steps is construction of a health index for incipient fault detection and monotonic degradation assessment. Moreover, observations of a health index can be used as inputs to prognostic models for machine remaining useful life prediction. Even though significant outcomes about sparsity measures, such as kurtosis, the ratio of Lp to Lq norm, pq-mean, smoothness index, negative entropy, and Gini index, for machine health monitoring have been achieved during recent years, construction of a health index for simultaneously realizing incipient fault detection and monotonic degradation assessment is not fully explored due to unexpected variances of repetitive transients caused by rotating machine faults. To solve this problem, in this paper, quasi-arithmetic means (QAMs) are thoroughly investigated. Moreover, the aforementioned sparsity measures can be respectively reformulated as the ratios of different QAMs. Further, a generalized framework based on the ratio of different QAMs for machine health monitoring is proposed. Experimental results demonstrate that some special cases of the generalized framework can simultaneously detect incipient rotating faults, exhibit a monotonic degradation tendency and be robust to impulsive noises, and they are better than existing sparsity measures for machine health monitoring.