Fuzzy Dispersion Entropy and Its Application

doi:10.3778/j.issn.1002-8331.2208-0360

Abstract

Abstract: Dispersion entropy (DispEn) is a new dynamic index to measure the degree of signal irregularity. Compared with sample entropy, dispersion entropy can detect both amplitude and frequency changes at the same time and shorten the calculation time greatly. However, DispEn is sensitive to parameter selection, especially the number of classes (quantization level). Since the dispersion entropy is set based on the round function (step function), in some cases a small change in signal amplitude due to noise will alter the quantization sequence, thus changing the entropy value. In order to solve these limitations, fuzzy dispersion entropy (FuzzyDispEn) is proposed by combining fuzzy membership function and dispersion entropy. In FuzzyDispEn, fuzzy membership between embedding vector and quantization level is realized based on Euclidean distance. The advantages of FuzzyDispEn are tested using different synthetic time series signals. The results show that compared with DispEn, FuzzyDispEn has lower sensitivity to signal length and parameter selection, and better anti-noise performance. FuzzyDispEn is also used in completely analysis of EEG and bearing signal. Experimental results show that FuzzyDispEn also performs better than DispEn in real physical signal analysis. The results show that fuzzy dispersion entropy can provide a new method for signal complexity measurement.

Key words: fuzzy dispersion entropy, fuzzy membership functions, complexity, EEG signal, bearing signal

摘要： 散布熵（dispersion entropy，DispEn）是近期提出的一种衡量信号不规则程度的动力学指标。相比于样本熵，散布熵可同时检测信号幅度和频率的变化，计算时间也大大缩短。然而，由于散布熵是基于取整函数（阶跃函数）设置的，对数据长度和参数选择较敏感，特别是类的数量（量化级别），某些情况下由噪声引起的信号幅值的微小变化会改变量化序列从而引起熵值剧烈波动。为解决这些局限性，结合模糊隶属度函数提出了模糊散布熵（fuzzy dispersion entropy，FuzzyDispEn）。在FuzzyDispEn中，基于欧式距离实现嵌入向量与量化级别的模糊化隶属。使用合成时间序列信号测试FuzzyDispEn相比DispEn的性能。结果表明，与DispEn相比，FuzzyDispEn对信号数据长度、参数选择的灵敏度更低，而且抗噪性更好。FuzzyDispEn还应用于脑电与轴承信号的复杂度检测，实验结果表明在真实物理信号分析方面FuzzyDispEn的性能表现同样优于DispEn。结果表明模糊散布熵可为信号复杂度测量提供一种新的方法。

关键词: 模糊散布熵, 模糊隶属度函数, 复杂性, 脑电信号, 轴承信号

HU Baohua, ZHU Zongjun, JIN Feixiang, LU Cuiping, XIU Lei, WANG Yong. Fuzzy Dispersion Entropy and Its Application[J]. Computer Engineering and Applications, 2024, 60(2): 326-336.

胡保华, 朱宗俊, 金飞翔, 鲁翠萍, 修磊, 王勇. 模糊散布熵及其应用[J]. 计算机工程与应用, 2024, 60(2): 326-336.

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