Multiscale integrated diversity entropy: A nonlinear measurement method integrating direction and amplitude information and its application in fault diagnosis of rotating machinery

Abstract

Diversity entropy (DE) is a novel effective measure to characterize the complexity of nonlinear time series. However, DE lacks the amplitude information of signals and struggles to distinguish features that exhibit the same similarity but possess different spatial distribution states, thereby reducing the accuracy of fault diagnosis in rotating machinery. To address the limitations of DE, this paper proposes Integrated Diversity Entropy (IDE), a novel approach that measures both amplitude and directional complexity in time series. IDE optimizes similarity measurement by fusing amplitude information and utilizes basis vector weighting calculation, thus achieving accurate capture of dynamic characteristics of time series in both signal direction and numerical dimensions. The signal complexity extraction capability of IDE was validated with simulation signals, outperforming traditional entropy methods in robustness, consistency, and efficiency. On this basis, this article extends IDE to multi-scale analysis, integrating it with a support vector machine optimized by African vulture optimization algorithm (AVOA-SVM) to form an intelligent fault diagnosis framework for rotating machinery. When applied to experimental data from rotating machinery under various fault conditions, the method exhibited exceptional performance in feature extraction. Specifically, the average diagnostic accuracy for gearbox and bearing failures exceeded 97%. Compared to five other entropy-based methods, it demonstrated significant advantages in terms of diagnostic accuracy, stability, and efficiency.