瑞利复杂度-色散熵平面:一种新的水声信号非线性特征提取方法

Rényi Complexity-Dispersion Entropy Plane: A Novel Algorithm for Nonlinear Feature Extraction of Underwater Acoustic Signals

摘要:

针对传统熵特征提取算法无法全面表征信号复杂度的问题，提出一种瑞利复杂度-色散熵平面（Rényi Complexity-Dispersion Entropy Plane，RCDEP）特征提取方法。首先，在瑞利熵框架下重新定义色散熵。接着，将瑞利色散熵引入到统计复杂度框架中，通过定义概率密度分布的失衡度并使之与瑞利色散熵相乘得到瑞利复杂度。最后，将瑞利复杂度与瑞利色散熵组成二维特征平面。仿真分析结果表明，RCDEP能同时量化时间序列的随机性和相关结构的存在性。实验分析结果表明，水声目标在特征平面的起点、收敛斜率、终点均可作为分类的显著特征，通过多尺度分析，货船、游船、拖船的RCDEP特征差异明显，可分性强。

Abstract:

To address the limitation of traditional entropy feature extraction algorithms in comprehensively characterizing signal complexity, this paper proposes a feature extraction method called the Rényi Complexity-Dispersion Entropy Plane (RCDEP). First, dispersion entropy is redefined within the framework of Rényi entropy. Next, Rényi dispersion entropy is incorporated into the statistical complexity framework, where Rényi complexity is derived by defining the imbalance degree of the probability density distribution and multiplying it with Rényi dispersion entropy. Finally, a two-dimensional feature plane is constructed by combining Rényi complexity and Rényi dispersion entropy. Simulation results demonstrate that the starting point, convergence slope, and endpoint of RCDEP can serve as discriminative features for signals, enabling simultaneous quantification of the randomness of time series and the presence of correlation structures. Experimental analysis reveals distinct RCDEP features among cargo ships, tankers, and tugboats, exhibiting strong separability.