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滑动移除小波分析法在动力学结构突变检验中的应用

孙东永 张洪波 王义民

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滑动移除小波分析法在动力学结构突变检验中的应用

孙东永, 张洪波, 王义民

Application of moving cut data-wavelet transformation analysis in dynamic structure mutation testing

Sun Dong-Yong, Zhang Hong-Bo, Wang Yi-Min
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  • 标度指数计算的即时性与准确性对相关时间序列的动力学结构突变分析至关重要,然而现有方法在即时性与准确性上一直无法兼顾.将小波分析方法与滑动移除窗口技术相融合,提出一种新的动力学结构突变检测方法滑动移除小波分析法.通过选取不同的滑动移除窗口,分别对构建的线性、非线性理想时间序列进行动力学结构突变分析,结果表明不论是线性时间序列还是非线性时间序列,滑动移除小波分析能够准确地检测到序列的动力学结构突变点及突变区间,对于滑动移除窗口长度依赖性较小,具有很强的稳定性,而且在计算速度上明显优于滑动移除重标极差和滑动移除方差分析方法,将在大数据处理中具有一定的优势.同时分别对线性、非线性理想时间序列添加高斯白噪声,结果表明滑动移除小波分析具有很强的抗噪能力,能够准确地检测到加噪后序列的突变点.对佛坪站日最高温度实测资料的动力学结构突变的准确检测进一步验证了该方法的有效性.滑动移除小波分析法可为具有相关性的系统动力学结构突变的快速、准确检测提供一种途径.
    The scaling exponent is an effective nonlinear dynamic index, which can be used to detect the dynamic structure mutations of the correlation time series by the moving cut a fixed window technology. The immediacy and accuracy of scaling exponent is very important for detecting the series change points, however, some of the existing scale index calculation methods (such as rescaled range analysis and rescaled variance analysis) take none of these into account. Wavelet transform analysis can quickly decompose the sequence on different scales, and then the scaling index can be calculated by analyzing the scaling relation of wavelet coefficients on different scales, which has the characteristics of fast calculation speed and good convergence and memory saving. By moving cut window technology, in the present paper we put forward a new method, i. e., the moving cut data-wavelet transformation for detecting a series of dynamic structure mutations. The principle is that the removal of the data has little effect on the estimation of the scaling exponents of the correlation time series with the same dynamical properties. In order to test the performance of the method, first of all, the dynamic structure mutation analyses of linear ideal time series and nonlinear ideal time series are carried out by selecting different moving cut fixed windows. The test results show that the method can quickly and accurately detect the dynamic structure change points and intervals both in linear time series and nonlinear time series, besides, its calculation speed is obviously better than the moving cut data-rescaled range analysis and the moving cut data-rescaled variance analysis. It has strong stability, and depends less on the moving cut window length, which will have some advantages in the large data processing. At the same time, in order to detect the influence of noise on the method, the linear and nonlinear ideal time series are added to the white Gaussian noise (SNR=20, 25, 30 dB), respectively, and the results show that the method has a strong anti-noise ability with different moving cut window lengths, can still quickly and accurately detect the mutation point or interval in different noise additions. Finally, the method is used to detect the dynamic structure mutation of measured daily maximum temperature data of Foping station in Wei basin, the experimental results indicate that the mutation interval is consistent with the abrupt change in 1970's on a global scale, which further verifies the validity of the method.
      通信作者: 张洪波, honeber@126.com
    • 基金项目: 国家自然科学基金青年科学基金(批准号:51409005)、国家自然科学基金重大项目(批准号:51190093)、国家自然科学基金(批准号:51379014)和中央高校基本科研业务费专项资金(批准号:310829161008)资助的课题.
      Corresponding author: Zhang Hong-Bo, honeber@126.com
    • Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51409005), the Major Program of the National Natural Science Foundation of China (Grant No. 51190093), the National Natural Science Foundation of China (Grant No. 51379014) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 310829161008).
    [1]

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    He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese)[何文平, 吴琼, 张文, 王启光, 张勇2009物理学报58 2862]

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    Simonsen I, Hansen A, Nes O M 1998 Phys. Rev. E 58 2779

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    Veitch D, Abry P C 1999 IEEE Trans. Inf. Theory 45 878

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    Jones C L, Lonergan G T, Mainwaring D E 1996 J. Phys. A:Math. Gen. 29 2509

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    Hu K, Ivanov P C, Chen Z, Carpena P, Stanley H E 2001 Phys. Rev. E 64 011114

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    Gloter A, Hoffmann M 2007 Ann. Stat. 35 1947

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    Manimaran P, Panigrahi P K, Parikh J C 2005 Phys. Rev. E 72 046120

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    Ciftlikli C, Gezer A 2010 Turk. J. Elec. Eng. Comp. Sci. 18 117

    [15]

    Wu L, Ding Y M 2015 Int. J. Wavelets Multiresolut Inf. Process. 13 1550044

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    Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econom. 112 265

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    Clausel M, Roueff F, Taqqu M S, Tudor C 2014 Esaim Probab. Stat. 18 42

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    Taqqu M S, Teverovsky V 1997 Comm. Stat. Stoch. Model 13 723

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    Cajueiro D O, Tabak B M 2005 Math. Comp. Sim. 70 172

    [20]

    Kantelhardt J W, Koscielny-Bunde E, Rego H H A, Havlin S, Bunde A 2001 Physica A 295 441

    [21]

    Matos J A O, Gama S M A, Ruskin H J, Sharkasi A A, Crane M 2008 Physica A 387 3910

    [22]

    Mielniczuk J, Wojdyllo P 2007 Comput. Stat. Data Anal. 51 4510

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    Zhao Y Z, Wu L W 2014 Comput. Eng. Appl. 50 154 (in Chinese)[赵彦仲, 吴立文2014计算机工程与应用50 154]

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    Dang T D, Molnar S 1999 Period. Polytech, Electr. Eng. 43 227

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    Giordano S, Miduri S, Pagano M, Russo F, Tartarelli S 1997 Proceedings of 13th International Conference on Digital Signal Processing Santorini, Greece, July 2-4, 1997 p479

    [26]

    Li X B, Ding J, Li H Q 1999 Adv. Water Sci. 10 144 (in Chinese)[李贤彬, 丁晶, 李后强 1999 水科学进展 10 144]

    [27]

    Li X B, Ding J, Li H Q 1998 J. Hydraul. Eng. 8 21 (in Chinese)[李贤彬, 丁晶, 李后强 1998 水利学报 8 21]

    [28]

    Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese)[王启光, 张增平 2008 物理学报 57 1976]

    [29]

    He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese)[何文平, 何涛, 成海英, 张文, 吴琼2011物理学报60 049202]

    [30]

    Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese)[金红梅, 何文平, 张文, 冯爱霞, 侯威2012物理学报61 129202]

    [31]

    He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205

    [32]

    Powell A M, Xu J J 2011 Theor. Appl. Climatol. 104 443

    [33]

    Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese)[封国林, 龚志强, 支蓉2008气象学报66 892]

    [34]

    Shi N, Chen J Q, Tu Q P 1995 Acta Meteor. Sin. 53 431 (in Chinese)[施能, 陈家其, 屠其璞1995气象学报53 431]

    [35]

    Tong J L, Wu H, Hou W, He W P, Zhou J 2014 Chin. Phys. B 23 049201

    [36]

    Wu H, Hou W, Yan P C, Zhang Z S, Wang K 2015 Chin. Phys. B 24 089201

    [37]

    Zhang M L, Qu H, Xie X R, Kurths J 2017 Neurocomputing 219 333

    [38]

    Wan L, Zhang Y, Lin J, Jiang C D, Lin T T 2016 Chin. J. Geophys. 59 2290 (in Chinese)[万玲, 张扬, 林君, 蒋川东, 林婷婷2016地球物理学报59 2290]

  • [1]

    Rehman S, Siddiqi A H 2009 Chaos Soliton. Fract. 40 1081

    [2]

    He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604

    [3]

    He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese)[何文平, 吴琼, 张文, 王启光, 张勇2009物理学报58 2862]

    [4]

    He W P, Deng B S, Wu Q, Zhang W, Cheng H Y 2010 Acta Phys. Sin. 59 8264 (in Chinese)[何文平, 邓北胜, 吴琼, 张文, 成海英2010物理学报59 8264]

    [5]

    Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese)[孙东永, 张洪波, 黄强 2014 物理学报 63 209203]

    [6]

    Hurst H E 1951 Trans. Am. Soc. Civ. Eng. 116 770

    [7]

    Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685

    [8]

    Simonsen I, Hansen A, Nes O M 1998 Phys. Rev. E 58 2779

    [9]

    Veitch D, Abry P C 1999 IEEE Trans. Inf. Theory 45 878

    [10]

    Jones C L, Lonergan G T, Mainwaring D E 1996 J. Phys. A:Math. Gen. 29 2509

    [11]

    Hu K, Ivanov P C, Chen Z, Carpena P, Stanley H E 2001 Phys. Rev. E 64 011114

    [12]

    Gloter A, Hoffmann M 2007 Ann. Stat. 35 1947

    [13]

    Manimaran P, Panigrahi P K, Parikh J C 2005 Phys. Rev. E 72 046120

    [14]

    Ciftlikli C, Gezer A 2010 Turk. J. Elec. Eng. Comp. Sci. 18 117

    [15]

    Wu L, Ding Y M 2015 Int. J. Wavelets Multiresolut Inf. Process. 13 1550044

    [16]

    Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econom. 112 265

    [17]

    Clausel M, Roueff F, Taqqu M S, Tudor C 2014 Esaim Probab. Stat. 18 42

    [18]

    Taqqu M S, Teverovsky V 1997 Comm. Stat. Stoch. Model 13 723

    [19]

    Cajueiro D O, Tabak B M 2005 Math. Comp. Sim. 70 172

    [20]

    Kantelhardt J W, Koscielny-Bunde E, Rego H H A, Havlin S, Bunde A 2001 Physica A 295 441

    [21]

    Matos J A O, Gama S M A, Ruskin H J, Sharkasi A A, Crane M 2008 Physica A 387 3910

    [22]

    Mielniczuk J, Wojdyllo P 2007 Comput. Stat. Data Anal. 51 4510

    [23]

    Zhao Y Z, Wu L W 2014 Comput. Eng. Appl. 50 154 (in Chinese)[赵彦仲, 吴立文2014计算机工程与应用50 154]

    [24]

    Dang T D, Molnar S 1999 Period. Polytech, Electr. Eng. 43 227

    [25]

    Giordano S, Miduri S, Pagano M, Russo F, Tartarelli S 1997 Proceedings of 13th International Conference on Digital Signal Processing Santorini, Greece, July 2-4, 1997 p479

    [26]

    Li X B, Ding J, Li H Q 1999 Adv. Water Sci. 10 144 (in Chinese)[李贤彬, 丁晶, 李后强 1999 水科学进展 10 144]

    [27]

    Li X B, Ding J, Li H Q 1998 J. Hydraul. Eng. 8 21 (in Chinese)[李贤彬, 丁晶, 李后强 1998 水利学报 8 21]

    [28]

    Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese)[王启光, 张增平 2008 物理学报 57 1976]

    [29]

    He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese)[何文平, 何涛, 成海英, 张文, 吴琼2011物理学报60 049202]

    [30]

    Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese)[金红梅, 何文平, 张文, 冯爱霞, 侯威2012物理学报61 129202]

    [31]

    He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205

    [32]

    Powell A M, Xu J J 2011 Theor. Appl. Climatol. 104 443

    [33]

    Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese)[封国林, 龚志强, 支蓉2008气象学报66 892]

    [34]

    Shi N, Chen J Q, Tu Q P 1995 Acta Meteor. Sin. 53 431 (in Chinese)[施能, 陈家其, 屠其璞1995气象学报53 431]

    [35]

    Tong J L, Wu H, Hou W, He W P, Zhou J 2014 Chin. Phys. B 23 049201

    [36]

    Wu H, Hou W, Yan P C, Zhang Z S, Wang K 2015 Chin. Phys. B 24 089201

    [37]

    Zhang M L, Qu H, Xie X R, Kurths J 2017 Neurocomputing 219 333

    [38]

    Wan L, Zhang Y, Lin J, Jiang C D, Lin T T 2016 Chin. J. Geophys. 59 2290 (in Chinese)[万玲, 张扬, 林君, 蒋川东, 林婷婷2016地球物理学报59 2290]

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出版历程
  • 收稿日期:  2016-11-28
  • 修回日期:  2016-12-20
  • 刊出日期:  2017-04-05

滑动移除小波分析法在动力学结构突变检验中的应用

  • 1. 长安大学环境科学与工程学院, 旱区地下水文与生态效应教育部重点实验室, 西安 710054;
  • 2. 西安理工大学水利水电学院, 西北旱区生态水利工程国家重点实验室培育基地, 西安 710048
  • 通信作者: 张洪波, honeber@126.com
    基金项目: 国家自然科学基金青年科学基金(批准号:51409005)、国家自然科学基金重大项目(批准号:51190093)、国家自然科学基金(批准号:51379014)和中央高校基本科研业务费专项资金(批准号:310829161008)资助的课题.

摘要: 标度指数计算的即时性与准确性对相关时间序列的动力学结构突变分析至关重要,然而现有方法在即时性与准确性上一直无法兼顾.将小波分析方法与滑动移除窗口技术相融合,提出一种新的动力学结构突变检测方法滑动移除小波分析法.通过选取不同的滑动移除窗口,分别对构建的线性、非线性理想时间序列进行动力学结构突变分析,结果表明不论是线性时间序列还是非线性时间序列,滑动移除小波分析能够准确地检测到序列的动力学结构突变点及突变区间,对于滑动移除窗口长度依赖性较小,具有很强的稳定性,而且在计算速度上明显优于滑动移除重标极差和滑动移除方差分析方法,将在大数据处理中具有一定的优势.同时分别对线性、非线性理想时间序列添加高斯白噪声,结果表明滑动移除小波分析具有很强的抗噪能力,能够准确地检测到加噪后序列的突变点.对佛坪站日最高温度实测资料的动力学结构突变的准确检测进一步验证了该方法的有效性.滑动移除小波分析法可为具有相关性的系统动力学结构突变的快速、准确检测提供一种途径.

English Abstract

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