Affiliation:
1. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China
2. Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an University of Technology, Xi’an 710048, China
Abstract
Fractal dimension, as a common nonlinear dynamics metric, is extensively applied in biomedicine, fault diagnosis, underwater acoustics, etc. However, traditional fractal dimension can only analyze the complexity of the time series given a single channel at a particular scale. To characterize the complexity of multichannel time series, multichannel information processing was introduced, and multivariate Higuchi fractal dimension (MvHFD) was proposed. To further analyze the complexity at multiple scales, multivariate multiscale Higuchi fractal dimension (MvmHFD) was proposed by introducing multiscale processing algorithms as a technology that not only improved the use of fractal dimension in the analysis of multichannel information, but also characterized the complexity of the time series at multiple scales in the studied time series data. The effectiveness and feasibility of MvHFD and MvmHFD were verified by simulated signal experiments and real signal experiments, in which the simulation experiments tested the stability, computational efficiency, and signal separation performance of MvHFD and MvmHFD, and the real signal experiments tested the effect of MvmHFD on the recognition of multi-channel mechanical signals. The experimental results show that compared to other indicators, A achieves a recognition rate of 100% for signals in three features, which is at least 17.2% higher than for other metrics.
Funder
Natural Science Foundation of Shaanxi Province
National Science Foundation of China
Xi’an University of Technology Excellent Seed Fund
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
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