Machine health monitoring (MHM) aims to timely detect incipient faults and monotonically assess machine degradation tendency for prediction of remaining useful life (RUL), which is the basis of condition-based maintenance. Construction of a health index (HI) is a core step to realize the aforementioned purposes. Among existing HIs, sparsity measures (SMs) including kurtosis, smoothness index, Gini index, and negative entropy, etc., have shown promising applications in fault diagnosis of rotating machines because they are widely used to quantify repetitive transients caused by rotating faults. However, drawbacks of SMs for MHM still exist and they are that: (1) SMs are too fluctuating to detect incipient faults; (2) SMs are prone to be affected by impulsive noise; (3) SMs might not exhibit monotonic degradation tendency. To enhance the abilities of SMs as HIs for MHM, some improvements on SMs, coined as an adaptive weighted signal preprocessing technique (AWSPT), are proposed in this paper. Subsequently, theoretical values of AWSPT based SMs under healthy states are investigated. Numerical experiments reveal that AWSPT based SMs can quantify cyclo-stationarity and they are robust to the effects of impulsive noise. Bearing and gear run-to-failure datasets are used to show that the proposed AWSPT based SMs can simultaneously detect early bearing and gear faults and provide monotonic degradation tendency. Moreover, AWSPT based SMs are more effective in selecting an optimal envelope demodulation frequency band than traditional SMs.

Machine condition monitoring (MCM) uses signal processing and machine learning methods to analyze monitoring data and perform timely condition-based maintenance. Since monitoring data usually have a sparsity property, sparsity measures (SMs) are naturally considered to quantify the sparsity of signals and they serve as the objective functions of many signal processing and machine learning methods. Although Gini index, kurtosis, smoothness index, negative entropy, and Lp / Lq norm have been considerably investigated for MCM, the design of new SMs for enhancing MCM is rarely reported. In this article, based on the ratio of different quasi-arithmetic means (RQAM), two new SMs, coined as Gini index Ⅱ (GI2) and Gini index Ⅲ (GI3), are designed. New proofs show that the GI2 and GI3 satisfy all six sparsity attributes. Subsequently, the GI2 and GI3 of the square envelope of Gaussian white noise are theoretically investigated and their theoretical values are, respectively, equal to 2/3 and 1/3, which can be used as baselines for machine abnormality detection. Once GI2 and GI3 exceed the baselines, abnormal health conditions can be detected without needing historical data and prior fault knowledge. Finally, simulated and experimental case studies showed that the proposed GI2 and GI3 have competitive performance with Gini index and that they are better than kurtosis, negative entropy, and smoothness index, in characterizing the sparsity of signals. This article demonstrates that the RQAM is a potential framework to design new SMs.