传统相似性查询的维数约简方法导致时间序列的非线性和分形这些重要特征消失,基于小波变换的匹配方法是通过某一分辨级的距离标准来度量相似性.但是,在未知非平稳时间序列分形维数的情况下,序列相似性匹配的局部误差就会增大,曲线形状的相似性查询过程在一定程度上也因此受到影响.鉴于随机非平稳时间序列在时空动力学演化过程中呈现出非线性特征和分形特征,提出了序列分形时变维数的概念,原始分数布朗运动模型被加以改造成为一个具有局部自相似性的随机过程.给出了时变Hurst指数的估计式和算法,提出了一种新的序列相似性判别标准.在某一分辨级水平上进行曲线形状的相似性查询和度量,同时,对于局部相似性的局部维数曲线进行匹配.最后,用仿真算例对方法的有效性加以验证.

Traditional dimension reduction methods about similarity query introduce the smoothness to data series in some degree, but lead to the disappearance of the important features of time series about non-linearity and fractal.The matching method based on wavelet transformation measures the similarity by using the distance standard at some resolution level. But in the case of an unknown fractal dimension of non-stationary time series, the local error of similarity matching of series increases. The process of querying the similarity of curve figures will be affected to a certain degree. Stochastic non-stationary time series show the non-linear and fractal characters in the process of time-space kinetics evolution. The concept of series fractal time-varying dimension is presented. The original Fractal Brownian Motion model is reconstructed to be a stochastic process with local self-similarity. The Daubechies wavelet is used to deal with the local self-similarity process. An evaluation formula of the time-varying Hurst index is established. The algorithm of time-varying index is presented, and a new determinant standard of series similarity is also introduced. Similarity of the basic curve figures is queried and measured at some resolution ratio level,in the meantime, the fractal dimension in local similarity is matched. The effectiveness of the method is validated by means of the simulation example in the end.

Supported by the National Natural Science Foundation of China underGrant Nos.69933010, 70371042 (国家自然科学基金);the China Post-Doctor Science Foundation under Grant No.2003033310 (中国博士后科学基金)