Distance similarity entropy: A sensitive nonlinear feature extraction method for rolling bearing fault diagnosis

Entropy-based methods are widely used in machinery fault diagnosis for characterizing system disorder and complexity. However, conventional entropy techniques often fail to capture local signal variations when analyzing relationships between vectors, especially in complex settings. This leads to incomplete representations of subtle features and dynamic behaviors, resulting in inaccurate estimations of system complexity and affecting diagnostic accuracy and reliability. To address these limitations, a novel distance similarity entropy (DSEn) is proposed in this paper: (1) It leverages element-wise distance to precisely capture local shifts and subtle distortions between subsequences. (2) It employs a Gaussian kernel function for vector similarity, enhancing signal pattern analysis by preserving subtle differences and mitigating the impact of outliers. (3) It uses probability density estimation of distance similarities between adjacent vectors to track changes in internal signal patterns, enabling more accurate and sensitive estimations of signal complexity. Synthetic signal experiments demonstrate that DSEn excels in detecting dynamic time series changes and characterizing signal complexity. Tests on two bearing datasets reveal that DSEn's extracted features show significant differences, highlighted by Hedges’ g effect size. Compared to other commonly used entropies (SampEn, PermEn, FuzzEn, DistEn, etc.), DSEn shows superior fault identification accuracy, computational efficiency, and noise resistance.