RCHIMRDE: Refined Composite Hermite Interpolation Multiscale Regularized Dispersion Entropy and Its Application to Mechanical Fault Diagnosis

The accurate measurement of complexity in nonlinear signals is crucial for the condition monitoring and fault diagnosis of mechanical systems. While Dispersion entropy (DE) and multiscale DE (MDE) are commonly used for time series complexity analysis. However, DE suffers from two inherent limitations: it requires manual selection of the category number and lacks robustness to noise-induced symbol fluctuations. To overcome these limitations, this work introduces regularized DE (RDE), which automatically optimizes the category number through the Akaike information criterion; and the symbol series regularization is introduced to effectively suppress noise-induced symbol mutation and improves the robustness of entropy estimation. And MDE gradually loses signal fidelity as the scale factor increases. To overcome these limitations, the refined composite Hermite interpolation multiscale RDE (RCHIMRDE) was proposed, which employs polynomial-based signal reconstruction to preserve signal fidelity across multiple scales, addressing the information loss issue in conventional multiscale measurement approaches. Simulated signal analysis demonstrated that RDE has stronger robustness, more accurate entropy estimation in noisy environments, has higher stability and confirms its computational efficiency. Three sets of real-world signal cases from different datasets show that RCHIMRDE method delivers the highest diagnostic measurement accuracy, outperforming existing entropy-based metrics.