数据标准化对Sevcik分形维数算法的性能影响

Influence of different data normalizing methods on the performance of Sevcik fractal dimension algorithm

在运用Sevcik方法计算一维时间序列分形维数时通常会涉及到数据标准化的问题。鉴于实测时间序列中不可避免的混有随机噪声,提出用零均值标准化方法来代替原Sevcik方法中极大极小值标准化法,得到Sevcik-Zscore方法。以两种典型的合成分形序列为对象,分析了Sevcik算法和Sevcik-Zscore算法在准确性、运算时间、对数据长度依赖性和抗噪性能4个方面的表现。仿真结果表明:Sevcik算法在时间序列分形维数较小时的计算精度高,而Sevcik-Zscore方法在时间序列分形维数较大时的计算精度高。Sevcik比Sevcik-Zscore方法的计算效率高,但Sevcik-Zscore方法在对数据长度依赖性方面要优于Sevcik方法。两种方法在抗噪性能分析中表现类似。在海杂波数据和轴承振动信号分析中的应用也表明Sevcik-Zscore方法要优于Sevcik方法。不同的数据标准化方式会对时间序列的Sevcik分形维数计算产生不同的影响,需要慎重选择。

Time series would be firstly normalized before calculating fractal dimension using Sevcik algorithm. To deal with unavoidable random noise in real time series,a new algorithm named Sevcik-Zscore was proposed in this paper. In Sevcik-Zscore algorithm,zeromean normalization method instead of original Min-max normalization was introduced into Sevcik algorithm. Aiming at exploring the influence of different normalizing methods on Sevcik fractal dimension algorithm,accuracy,running time,dependency on data length and the anti-noise performance of Sevcik and Sevcik-Zscore algorithms were compared by analyzing two typical synthetic fractal waveforms.Simulation results indicate that Sevcik algorithm can get higher accuracy with smaller fractal dimension compared to Sevcik-Zscore algorithm,and vise versa. Moreover,Sevcik algorithm is more computationally efficient than Sevcik-Zscore algorithm,but the later algorithm can get higher performance than the former one in the analysis of dependency on data length. These two algorithms got nearly the same performance in the aspect of tanti-noise. At last,applications in sea clutter time series and bearing vibration time series analysis show that Sevcik-Zscore performs better than Sevcik algorithm.