一种无偏差的多通道多尺度样本熵算法

Unbiased multivariate multiscale sample entropy

多通道数据采集技术的发展为复杂系统非线性动力学特性研究提供了更加丰富的先验信息.然而传统的非线性特征量只能处理单通道数据,无法直接提取多通道数据的非线性特征.近年来,有学者对多尺度样本熵算法进行了一般化处理,提出了多通道多尺度样本熵算法.该算法不仅可以对多通道数据整体的复杂度进行表征,还可以有效提取通道内和通道间隐含的相关性信息.但是,该算法缺乏相应的理论支撑,在实际应用中无法兼顾性能和稳定性.针对以上问题,本文提出了一种无偏差的多通道多尺度样本熵算法,并利用概率论从理论上分析了多通道多尺度样本熵算法不稳定以及性能差的原因.后续的仿真实验证明改进后的算法不但可以有效地提取通道内和通道间的相关性信息,同时在处理复杂数据时表现出了良好的稳定性.该算法为诸如模糊熵、排列熵等非线性特征量的算法一般化提供了思路和理论依据.

The development of multi-channel data acquisition techniques has provided richer prior information for studying the nonlinear dynamic characteristics of complex systems.However,conventional nonlinear feature extraction algorithms prove unsuitable in the context of multi-channel data.Previously,the multivariate multiscale sample entropy(MMSE)algorithm was introduced for multi-channel data analysis.Although the MMSE algorithm generalized the multiscale sample entropy algorithm,presenting a novel method for multidimensional data analysis,it remains deficient in theoretical underpinning and suffers from shortcomings,such as missing cross-channel correlation information and having biased estimation results.In this paper,unbiased multivariate multiscale sample entropy algorithm(UMMSE)is proposed.UMMSE increases the embedding dimension from M to M+p.This increasing strategy facilitates the reconstruction of a deterministic phase space.By virtue of theoretical scrutiny grounded in probability theory and subsequent experimental validation,this paper illustrates the algorithm's effectiveness in extracting inter-channel correlation information through the integration of cross-channel conditional probabilities.The computation of similarities between sample points across different channels is recognized as a potential source of bias and instability in algorithms.Through simulation experiments,this study delineates the parameter selection range for the UMMSE algorithm.Subsequently,diverse simulation signals are employed to showcase the UMMSE algorithm’s efficacy in extracting both within-channel and cross-channel correlation information.Ultimately,this paper demonstrates that the new algorithm has the lowest computational cost compared with traditional MMSE algorithms.