一种实用的混沌信号相关维的提取算法

分形维是混沌信号的一个重要参数,在确定分形维时,通常需要确定线性尺度区,然而线性尺度区的确定仍然是分形维提取算法中的一个富有挑战性的问题,线性尺度区的准确性,将直接影响分形维的准确性.本文对此问题进行了比较深入的研究,较好地解决了线性尺度区的选择问题,并基于GP算法给出了一套完整的相关维提取算法.该算法不仅运算量小、精度高、抗噪声干扰的能力较强,而且完全实现了对相关维的自动提取.

A Practical Algorithm for Extracting the Correlation Dimension from a Chaotic Signal

Fractal dimension is an important parameter of a chaotic signal.It is usually to determine a linear scaling region when evaluating fractal dimension,however,determining the linear scaling region is still a challenging problem.The accuracy of the fractal dimension estimated will be directly affected by the accuracy of the linear scaling region.This problem is deeply developed here and solved better.Based on the GP method,a series of algorithm for computing the correlation dimension D 2 is proposed.This new algorithm needs only a little computational time,has high accuracy and stronger ability of resisting noise and it can automatically calculate the correlation dimension.