•Combining HFD and NCDF with round function, dispersion HFD (DHFD) was proposed, and the revised metric solved the problem of traditional HFD being unable to handle signal outliers.•ODHFD and ORCMHFD were proposed by using intelligent optimization algorithms and refine composite multi-scale processing to solve the problem of DHFD parameter selection and inability to represent signal information at multiple scales.•Experimental results have demonstrated the validity of this metrics, and the results show that ODHFD and ORCMDHFD have the best signal stability and optimal signal separation. 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.