基于三阶累积量的自适应多变量相空间重构

Adaptive Phase Space Reconstruction of Multivariate Based on Third-order Cumulant

利用三阶累积量反映多变量序列的高阶非线性相关性,建立了一种具有良好抗噪性的多变量相空间重构方法.将三阶累积量引入到序列局部本征维数(LID)的计算中,对不同相空间点构造新的三阶累积量相关矩阵;同时建立累积量切片评价函数,通过比较得到了对噪声及嵌入维数等重构参数变化鲁棒性强的累积量切片,然后确定序列的嵌入维数、嵌入延迟,重构多元变量相空间.仿真结果表明,建立的新方法对带噪声混沌序列具有较好的鲁棒性,多元变量奇异吸引子轨迹在重构相空间中得到了良好扩展.

This paper provided a multivariate phase space reconstruction method with good anti-noise per- formance by making use of the third-order cumulant which was used to reflect high-order nonlinear correla tion between multivariate series. First, the third-cumulant was introduced to calculate the local intrinsic dimension （LID） of series, and a new third order cumulant correlation matrix based on different phase points was constructed. An evaluation function was introduced to find an appropriate third-cumulant slice which possessed strong robustness property on the noise and the reconstruction parameters, like embed- ding dimension. Then, the embedding dimension and the embedding delay were calculated to reconstruct the phase space of multivariate series. Finally, simulation results were given to show that the approach proposed was more effective for noisy chaotic series, from which it could be clearly seen that the multivari- ate strange attractors got better extensions in the reconstructed phase space.