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分形维数是描述混沌动力学系统的重要参数之一.根据时间尺度与多维超体体积之间的测度关系,提出一种多变量时间序列分形维数的计算方法.通过4种典型混沌动力学系统所产生的多变量时间序列及其相应不同信噪比混杂序列的仿真计算表明,所提出方法时间复杂度较低,所需序列长度较短,具有一定的抗噪能力,且无需进行相空间重构,避免了嵌入维数和延迟时间等参数选取对结果造成的影响,是计算多变量时间序列分形维数的一种有效途径.
Fractal dimension is one of the most important parameters to describe chaotic dynamical system.According to the relationship between time scale and multidimensional hypervolume volume, a method for calculating multivariate time series fractal dimension is proposed.Through four typical chaotic dynamics The simulation results of the multivariate time series generated by the system and their corresponding mixed sequences with different SNR show that the proposed method has the advantages of low time complexity, short sequence length, certain anti-noise ability and no phase space Reconstruction, which avoids the influence of parameters such as embedding dimension and delay time on the result, and is an effective way to calculate the fractal dimension of multivariate time series.