Multivariate Variable-Step Multiscale Extended Dispersion Entropy-Based Lempel–Ziv Complexity and Its Application in Fault Diagnosis

Extended dispersion entropy-based Lempel-Ziv complexity (EDELZC) can measure the irregularity or chaos of single channel time series, which is one of the ideal tools for extracting fault features from rotating machinery. However, EDELZC is only suitable for single scale and single channel time series analysis, which affects the effective extraction of fault features. To solve this problem, the multivariate embedding and variable-step multiscale techniques are integrated, the multivariate variable-step multiscale EDELZC (MvVSMEDELZC) is developed, which achieves the characterization of multi-channel feature information at different time scales. Moreover, in order to improve the recognition accuracy, the crayfish optimization algorithm (COA) is applied to optimize the parameters of the kernel extreme learning machine (KELM), and a new fault diagnosis method is proposed in combination with MvVSMEDELZC. The simulated signal experiments verify the ability of MvVSMEDELZC to detect dynamic changes of complex signals. The practical rotating machinery fault diagnosis experiments show that compared with other methods, the proposed fault diagnosis method offers superior accuracy and efficiency in identifying the condition of bearings and gears, which indicates its superior performance in properties in diagnosing rotating machinery faults.