中文摘要：

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。

英文摘要：

The fractal dimension is an important parameter of detecting and characterizing chaos produced from a dynamical system. According to the relationship between time scale and multidimensional super-body’s volume, a method to compute the fractal dimension of multivariate time series is proposed. Numerical simulations show that the length of the time series is shorter, the method is more efficient and doesn’t need reconstructing phase space so as to avoid the infection from parameters determination such as delay time and embedding dimension. Furthermore, it can resist noise to a certain degree and can be used as an effective method to calculate the fractal dimension of multivariate time series in many areas.