信息熵和HQ准则在最大Lyapunov指数计算中的应用

王基1 杨琪斌1.2 刘树勇1 位秀雷1

振动与冲击 ›› 2017, Vol. 36 ›› Issue (1) : 129-134.

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (1) : 129-134.
论文

信息熵和HQ准则在最大Lyapunov指数计算中的应用

  • 王基1  杨琪斌1.2  刘树勇1  位秀雷1
作者信息 +

Application of information entropy and HQ rule in estimating largest Lyapunov exponent

  • WANG Ji1, YANG Qibin1,2, LIU Shuyong1, WEI Xiulei1
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文章历史 +

摘要

最大Lyapunov指数是判断时间序列是否为混沌的一个重要判据,目前应用比较广泛的是小数据量法。本文将信息熵和HQ准则应用在最大Lyapunov指数的算法中,改进了小数据量法。信息熵优化了相空间重构参数,克服了独立求解重构参数的不足;利用HQ准则确定邻近点个数增加了计算时的精度。仿真实验表明本文中改进的小数据量法在计算最大Lyapunov时具有良好的准确性,对噪声具有良好的鲁棒性。

Abstract

The largest Lyapunov exponent is an essential criterion to judge if a time series is chaos or not. The small-data method is widely used in chaotic characteristic extraction at present. Here, the information entropy and HQ rule were applied in estimating the largest Lyapunov exponent to improve the small-data method. The information entropy was applied to optimize parameters of phase space reconstruction, and disadvantages of traditional algorithms were overcome clearly. The computational accuracy of LE was improved greatly by using the HQ rule to calculate the number of neighbouring points. Simulation results showed that the improved small-data method here has good performances in estimating the largest Lyapunov exponent, and the algorithm is robust to noise.

关键词

信息熵 / HQ准则 / 小数据量法 / Lyapunov指数

Key words

information entropy / HQ rule / small-data method / Lyapunov exponent

引用本文

导出引用
王基1 杨琪斌1.2 刘树勇1 位秀雷1. 信息熵和HQ准则在最大Lyapunov指数计算中的应用[J]. 振动与冲击, 2017, 36(1): 129-134
WANG Ji1, YANG Qibin1,2, LIU Shuyong1, WEI Xiulei1. Application of information entropy and HQ rule in estimating largest Lyapunov exponent[J]. Journal of Vibration and Shock, 2017, 36(1): 129-134

参考文献

[1] Gencay,Dechert. An algorithm for the n-dimensional unknown dynamical system [J]. Physica D,1992,59:142-157.
[2] A Wolf,J B Swift,H L Swinney,J A Vastano. Determining Lyapunov exponents from a time series [J]. Physica D,1985,16:285-317.
[3] M T Ro senstein,J J Collins, C J De luca. A practical method for calculating largest Lyapunov exponents from small data sets[J]. Physica D,1993,65:117- 134.
[4] 蒋爱华,周璞,章艺等.相空间重构延迟时间互信息改进算法研究[J].振动与冲击,2015,14(2):71-74.
Jiang Aihua,Zhou Pu,Zhang Yi. Improved mutual information algorithm for phase space reconstruction[J]. Journal of Vibration and shock,2015,14(2):71-74.
[5] 杨爱波,王基,刘树勇等.基于空间栅格法的最大Lyapunov指数算法研究[J].电子学报,2012,40(9):1871-1875.
Yang Aibo,Wang Ji,Liu Shuyong. An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method[J]. Acta Electronica sinica,2012,40(9) :1871-1875.
[6] 刘树勇,杨庆超,位秀雷等.邻近点快速搜索方法在混沌识别中的应用[J].华中科技大学学报(自然科学版),2012,40(11):89-92.
Liu Shuyong,Yang Qingchao,Wei Xiulei.The application of fast searching nearest points methodto chaos identification[J].J.Huazhong Univ. of Sci.&Tech.(Natural Science Edition),2012,40(11):89-92.
[7] 杨永锋,仵敏娟,高喆等.小数据量法计算最大Lyapunov指数的参数选择[J].振动、测试与诊断,2012,32(3):371-374.
Yang Yongfeng, Wu Minjuan, Gao Zhe. Parameter selection of maximum Lyapunov exponent for small data volume method[J]. Journal of Vibration,Measurement &Diagnosis,2012,32(3):371-374.
[8] 李彬彬.非线性心音时间序列的最大Lyapunov指数[J]. 上海电机学院学报,2011,14(1):17-20.
Li Binbin. Largest Lyapunov Exponents of Nonlinear Heartbeat Time Series[J]. Journal of shanghai dianji university,2011,14(1):17-20.
[9] Takens F 1981 Dynamical Systems and Turbulence(Berlin:SpringVerlag) 366.
[10] Hannan E J,Quinn B G.The determination of the order of an autoregression [J].Journal of the Royal Statistical Society. SeriesB (Methodological),1979,190-195.
[11] Akaike H. Autoregressive model fitting for control [J]. Annals of the Institute of Statistical Mathematics,1971,23(1): 163-180.
[12] Akaike H. A new look at the statistical model identification [J]. Automatic Control,IEEE Transactions on,1974,19(6):716-723.
[13] Gao Jianbo,Zheng Zheming. Local exponential divergence plot and optimal embedding of a chaotic time series [J]. Physics Letters A.1993,(181):153-158.

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