Investigations on sample entropy and fuzzy entropy for machine condition monitoring: revisited

Abstract

Complexity measures typically represented by entropy are capable of detecting and characterizing underlying dynamic changes in a system and they have been considerably studied for machine condition monitoring and fault diagnosis. Various entropies have been developed based on Shannon entropy to meet actual demands. Nevertheless, currently existing research works about complexity measures mainly focus on experimental studies, and their theoretical studies are still going on and not fully explored. In previous studies, it was theoretically and experimentally proved that two complexity measures including correlation dimension and approximate entropy have a ‘‘bilateral reduction” effect. Since sample entropy and fuzzy entropy are two more advanced complexity measures that were developed based on the concept of correlation dimension and approximate entropy, this paper continues conducting theoretical and experimental investigations on sample entropy and fuzzy entropy and exploring their theoretical properties to enrich the domain of complexity measure analysis and its applications to machine condition monitoring. Specifically, this paper theoretically proves and verifies that sample entropy and fuzzy entropy still have a similar “bilateral reduction” effect with correlation dimension and approximate entropy, and they are indeed complexity measures. The relationships between sample entropy, fuzzy entropy, and their key parameters during their calculation are numerically and experimentally studied. Bearing and gear run-to-failure datasets are used to investigate the effectiveness of sample entropy and fuzzy entropy for bearing and gear condition monitoring, and experimental results of sample entropy and fuzzy entropy are well-matched with the theoretical “bilateral reduction” effect of sample entropy and fuzzy entropy. Overall, this paper will provide a guideline for correct uses of sample entropy and fuzzy entropy for engineering applications, especially for machine condition monitoring.

Bearing early fault identification and condition monitoring based on dynamic difference index

“…Miao et al analysed the performance of representative sparsity indexes such as Gini index, l 2 /l 1 norm, Hoyer measure and kurtosis in rotating machinery fault diagnosis and proposed three performance attributes, namely, data length independence, random pulse resistance and fault pulse discriminability, to quantitatively evaluate the sparsity indexes [15]. Wang and Wang contributed to the theoretical understanding of sample entropy and fuzzy entropy by proving their properties and demonstrating their 'bilateral reduction' effect with correlation dimension and approximate entropy, and experimental results using bearing and gear run-to-failure datasets support the theoretical findings, demonstrating the effectiveness of sample entropy and fuzzy entropy in machine condition monitoring [16]. However, for the methods based on statistical parameters, each statistical parameter has its own advantages and disadvantages, and is easily disturbed by noise.…”