Variable-Step Multiscale Katz Fractal Dimension: A New Nonlinear Dynamic Metric for Ship-Radiated Noise Analysis

The Katz fractal dimension (KFD) is an effective nonlinear dynamic metric that characterizes the complexity of time series by calculating the distance between two consecutive points and has seen widespread applications across numerous fields. However, KFD is limited to depicting the complexity of information from a single scale and ignores the information buried under different scales. To tackle this limitation, we proposed the variable-step multiscale KFD (VSMKFD) by introducing a variable-step multiscale process in KFD. The proposed VSMKFD overcomes the disadvantage that the traditional coarse-grained process will shorten the length of the time series by varying the step size to obtain more sub-series, thus fully reflecting the complexity of information. Three simulated experimental results show that the VSMKFD is the most sensitive to the frequency changes of a chirp signal and has the best classification effect on noise signals and chaotic signals. Moreover, the VSMKFD outperforms five other commonly used nonlinear dynamic metrics for ship-radiated noise classification from two different databases: the National Park Service and DeepShip.