Power function-based Gini indices: New sparsity measures using power function-based quasi-arithmetic means for bearing condition monitoring

The Gini index (GI), GI II, and III are proven to be effective sparsity measures in the fields of machine condition monitoring fault diagnosis, they can reformulated as ratio different quasi-arithmetic means (RQAM). Under this framework, generalized indices (GGIs) have been developed for sparse quantification by applying nonlinear weights GI, another form referred here power function-based I (PFGI1s), has introduced using function generator means. GGIs with weight parameters exhibit reliable quantization capability repetitive transient features, while their discriminability is lower than kurtosis negentropy under noise contamination. PFGI1 achieves enhanced increasing exponent, showing advantage generalization approach. In paper, based on RQAM, a single-parameter method generating PFGI1s into II from perspective mean generator, which leads (PFGI2s PFGI3s) constructed III, respectively. Mathematical derivation proves that PFGI2s PFGI3s satisfy at least five six typical attributes two new families measures. Simulation analysis shows that, similar PFGI1s, monotonically estimate data sequence simultaneously achieve strong random resistibility high compared traditional experimental results bearing run-to-failure demonstrate PFGI2s, appropriate exponents effectively quantify features caused faults accurately characterize degradation status state-of-the-art