基于排列熵理论的非线性系统特征提取研究

Feature extraction for nonlinear systems based on permutation entropy theory

提出一种基于排列熵及其改进理论的伪相平面法,从而可以提取非线性系统中的微弱周期信号特征。通过选择合理的时间延迟和嵌入维数,对Duffing系统的响应信号进行相空间重构,得到一次排列熵和二次排列熵。随后将位移激励、一次排列熵和二次排列熵作为数据集,组成位移激励-一次排列熵和位移激励-二次排列熵两种伪相平面。通过将这两种方法与传统的相平面法、频谱分析和排列熵、排列熵谱、二次排列熵、二次排列熵谱的提取效果进行对比,验证了该方法的合理性。研究表明该方法能够对非线性系统中的微弱周期信号特征进行提取,取得了较好效果。

A pseudo phase plane method based on permutation entropy and its improved theory was proposed to extract weak periodic signal’s features in a nonlinear system.Through choosing a reasonable time delay and embedding dimension,the phase space of a Duffing system’s response signal was reconstructed to obtain primary permutation entropy and quadratic one.Then,displacement excitation,primary permutation entropy and quadratic one were taken as data sets to form two pseudo phase planes of displacement excitation-primary permutation entropy and displacement excitation-quadratic one.The proposed method’s extracting effect was compared with those of traditional methods including phase plane method,spectral analysis,permutation entropy,permutation entropy spectrum,quadratic permutation entropy and quadratic permutation entropy spectrum to verify the rationality of the proposed method.The study showed that the proposed method can extract characteristics of weak periodic signal in nonlinear systems,and achieve better effect.