Abstract
Higuchi fractal dimension (HFD), as a classic nonlinear dynamic metric, which is commonly used to detect signal dynamic changes. However, it is difficult for HFD to process signal outliers. To address this issue, dispersion HFD (DHFD) is proposed, which improves the signal complexity representation ability of HFD by introducing the normal cumulative distribution function and round function in dispersion entropy. Nevertheless, the parameter selection of DHFD can affect the complexity value. Therefore, an optimized dispersion HFD (ODHFD) is proposed, which solves the threshold selection problem of DHFD and can more effectively reflect the complexity of the signal. In addition, an optimized refined composite DHFD (ORCMDHFD) has been proposed, which can more comprehensively reflect the complexity information for the signal at multiple scales. The simulation experiment results show that DHFD has a smaller standard deviation than HFD when calculating white noise signal complexity, and DHFD have the least dependence on signal length compared to other metrics, as well as RCMDHFD has the best separability for simulated noise signals. Actual experiments have shown that ODHFD and ORCMDHFD is superior to other entropy and fractal dimension metrics in distinguishing ship radiated noise and mechanical fault signals, and has broad application prospects in the field of signal analysis.
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