一种时间序列多重分形分析的改进方法及其应用

通过分析时间序列广义维数的不同计算方法,本文引入一种新的多重分形奇异测度概念,提出了一种时间序列多重分形分析的改进方法。该方法不仅计算量小,而且其得到的连续分段线性曲线序列的广义维数具有恒等于１ 的性质。由于现实中许多信号可以用连续分段线性曲线逼近,因此上述性质深入刻划了这类信号的一个共同特征。仿真结果表明,本文推导出的性质为信号奇异性检测开辟了一条新途径,利用本文方法还可以快速有效地提取实测舰船噪声的短时多重分维特征。

An Improved Algorithm of Discrete Time Series Multifractal Analysis and Its Application

After comparing some general dimension algorithms, a new definition of multifractal singularity measure is introduced and an improved algorithm of time series multifractal analysis proposed. The algorithm not only needs low computational complexity, but also possesses the property that the general dimension of conti nuous piecewise linear series is constantly equal to 1. Since many practical signals can be fitted with continuous piecewise linear series, the property describes a common fundamental feature of this kind of signals. Simulation results show that the property deduced in this paper opens up a novel way to signal singularity detection. And the short time multifractal dimensions of ship noise are fast and effective, extracted by the improved method.