滑动移除重标方差在动力学结构突变检验中的应用

孙东永; 张洪波; 黄强

doi:10.7498/aps.63.209203

摘要

标度指数是一个有效的非线性动力学指数，能够针对相关性时间序列动力学结构突变进行检测；通过滑动窗口技术和滑动移除窗口技术，重标极差对于相关时间序列动力学突变具有很好的检测能力，但由于重标极差方法本身的不完善，在滑动移除窗口较小时其检测结果出现一些虚假的突变点和突变区间. 鉴于此，本文提出了一种新的动力学检测方法——滑动移除重标方差. 理想序列数值试验表明，滑动移除重标方差具有很强的稳定性和准确性，在滑动窗口较小时其检测结果没有出现虚假的突变点和区间，实测资料的应用进一步验证了新方法的可靠性.

关键词:

Abstract

Scaling exponent is a valid nonlinear dynamics index, and can effectively detect the dynamic structure mutations in the correlation time series by means of moving a fixed widow and the moving cut a fixed window technique. When there is short-term correlation, sequence with short-term correlation and the calculation result of scaling exponent with rescaled range will be influenced to a certain degree, resulting in a certain deviation for the scaling exponent calculation of a moving cut window sequence, and some false mutations point and mutations range for abrupt change detection. In view of this, we present a new method of the dynamic structure mutation detection-moving cut data-rescaled variance analysis. The numerical testing of ideal time series shows that the moving cut data-rescaled variance analysis has strong stability and accuracy, which is much better than the moving rescaled variance and the moving approximate entropy. The test results have not false mutation point and interval when the moving window is small. The further application to practically measured data validates the reliability of the new method.

Keywords:

scaling exponent /
rescaled variance /
moving cut data-rescaled variance analysis /
mutations detection

作者及机构信息

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

基金项目: 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：51179148，51179149，51379014）、国家自然科学基金青年科学基金（批准号：51009009，51409005）和中国水利水电科学研究院流域水循环模拟与调控国家重点实验室开放研究基金（批准号：IWHR-SKL-201109）资助的课题.

Authors and contacts

1.
Key Laboratory of Subsurface Hydrology and Ecological Effect in Arid Region of Ministry of Education, School of Environmental Science and Engineering, Chang'an University, Xi'an 710054, China;

2.
Key Laboratory of Northwest Water Resources and Environment Ecology of Ministry of Education, Institute of Water Resources and Hydro-electric Engineering, Xi'an University of Technology, Xi'an 710048, China

Funds: Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 51190093), the National Natural Science Foundation of China (Grant Nos. 51179148, 51179149, 51379014), the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 51009009, 51409005), and the Open Research Fund of the State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (Grant No. IWHR-SKL-201109).

参考文献

[1]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Norlinear Theories and Methods on Spatial-Temporal Distribution of the Observational Data (Beijing: Metrological Press) p27 (in Chinese) [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法 (北京: 气象出版社) 第27页]
[2]	Alexi M G, Brook E J, Severinghaus J P 2007 Geophys. Res. Lett. 34 L20703
[3]	Yang P, Hou W, Feng G L 2012 Chin. Phys. B 21 019201
[4]	Wang X J, Zhi R, He W P, Gong Z Q 2012 Chin. Phys. B 21 029201
[5]	Tong J L, Wu H, Hou W, He W P, Zhou J 2014 Chin. Phys. B 23 049201
[6]	Wathen S F 2011 Clim. Change 108 333
[7]	Trewin B 2013 Int. J. Climatol. 33 1510
[8]	Lettenmaier D P, Wood E F, Wallis J R 1994 J. Climate 7 586
[9]	Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[10]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou University) p23 (in Chinese) [何文平 2008 博士学位论文 (兰州: 兰州大学) 第23页]
[11]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlinear Proc. Geoph. 15 601
[12]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[13]	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 59 8264]
[14]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 57 1976]
[15]	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 60 049202]
[16]	He W P, Wan S Q, Jiang Y D, Jin H M, Zhang W, Wu Q, He T 2013 Int. J. Climatol. 33 2713
[17]	Mandelbrot B B, Taqqu M S, Robust R S 1979 Bull. Int. Stat. Inst. 48 69
[18]	Lo A W 1991 Econometrica 59 1279
[19]	Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econometrics 112 265
[20]	Cajueiro D O, Tabak B M 2005 Math. Comp. Sim. 70 172
[21]	He X Q, Li Z F 2006 Syst. Engineer. Theory & Practice 12 47 (in Chinese) [何兴强, 李仲飞 2006 系统工程理论与实践 12 47]
[22]	Sun D Y, Huang Q, Wang Y M 2011 Journal of Hydroelectric Engineering 30 178 (in Chinese) [孙东永, 黄强, 王义民 2011 水力发电学报 30 178]
[23]	Wang C F, Zhang Q C, Li G 2003 Systems Engineering 21 22 (in Chinese) [王春峰, 张庆翠, 李刚 2003 系统工程 21 22]
[24]	Jin H M, He W P, Hou W, Zhang D Q 2012 Acta Phys. Sin. 61 069201 (in Chinese) [金红梅, 何文平, 侯威, 章大全 2012 61 069201]
[25]	Bai C Y 2008 M. S. Dissertation (Yangling: Northwest A&F University) p43 (in Chinese) [拜存有 2008 硕士学位论文 (杨凌: 西北农林科技大学) (第43页)]
[26]	Hou Q L, Bai H Y, Ren Y Y, He Y N, Ma X P 2011 Resour. Sci. 33 1505 (in Chinese) [侯钦磊, 白红英, 任园园, 贺映娜, 马新萍 2011 资源科学 33 1505]
[27]	Xie P, Chen G C, Li D, Zhu Y 2005 Water Resources and Power 23 11 (in Chinese) [谢平, 陈广才, 李德, 朱勇 2005 水电能源科学 23 11]
[28]	Xie P, Xu B, Zhang S A, Yang G L, Dou M, Chen G C, Liu Y, Liu J J 2006 Study of Regional Water Resources Variation in Change Environment (Beijing: Science Press) p32 (in Chinese) [谢平, 许斌, 章树安, 杨桂莲, 窦明, 陈广才, 刘媛, 刘静君 2012 变化环境下区域水资源变异问题研究 (北京: 科学出版社) 第32页]

施引文献

[1]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Norlinear Theories and Methods on Spatial-Temporal Distribution of the Observational Data (Beijing: Metrological Press) p27 (in Chinese) [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法 (北京: 气象出版社) 第27页]
[2]	Alexi M G, Brook E J, Severinghaus J P 2007 Geophys. Res. Lett. 34 L20703
[3]	Yang P, Hou W, Feng G L 2012 Chin. Phys. B 21 019201
[4]	Wang X J, Zhi R, He W P, Gong Z Q 2012 Chin. Phys. B 21 029201
[5]	Tong J L, Wu H, Hou W, He W P, Zhou J 2014 Chin. Phys. B 23 049201
[6]	Wathen S F 2011 Clim. Change 108 333
[7]	Trewin B 2013 Int. J. Climatol. 33 1510
[8]	Lettenmaier D P, Wood E F, Wallis J R 1994 J. Climate 7 586
[9]	Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[10]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou University) p23 (in Chinese) [何文平 2008 博士学位论文 (兰州: 兰州大学) 第23页]
[11]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlinear Proc. Geoph. 15 601
[12]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[13]	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 59 8264]
[14]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 57 1976]
[15]	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 60 049202]
[16]	He W P, Wan S Q, Jiang Y D, Jin H M, Zhang W, Wu Q, He T 2013 Int. J. Climatol. 33 2713
[17]	Mandelbrot B B, Taqqu M S, Robust R S 1979 Bull. Int. Stat. Inst. 48 69
[18]	Lo A W 1991 Econometrica 59 1279
[19]	Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econometrics 112 265
[20]	Cajueiro D O, Tabak B M 2005 Math. Comp. Sim. 70 172
[21]	He X Q, Li Z F 2006 Syst. Engineer. Theory & Practice 12 47 (in Chinese) [何兴强, 李仲飞 2006 系统工程理论与实践 12 47]
[22]	Sun D Y, Huang Q, Wang Y M 2011 Journal of Hydroelectric Engineering 30 178 (in Chinese) [孙东永, 黄强, 王义民 2011 水力发电学报 30 178]
[23]	Wang C F, Zhang Q C, Li G 2003 Systems Engineering 21 22 (in Chinese) [王春峰, 张庆翠, 李刚 2003 系统工程 21 22]
[24]	Jin H M, He W P, Hou W, Zhang D Q 2012 Acta Phys. Sin. 61 069201 (in Chinese) [金红梅, 何文平, 侯威, 章大全 2012 61 069201]
[25]	Bai C Y 2008 M. S. Dissertation (Yangling: Northwest A&F University) p43 (in Chinese) [拜存有 2008 硕士学位论文 (杨凌: 西北农林科技大学) (第43页)]
[26]	Hou Q L, Bai H Y, Ren Y Y, He Y N, Ma X P 2011 Resour. Sci. 33 1505 (in Chinese) [侯钦磊, 白红英, 任园园, 贺映娜, 马新萍 2011 资源科学 33 1505]
[27]	Xie P, Chen G C, Li D, Zhu Y 2005 Water Resources and Power 23 11 (in Chinese) [谢平, 陈广才, 李德, 朱勇 2005 水电能源科学 23 11]
[28]	Xie P, Xu B, Zhang S A, Yang G L, Dou M, Chen G C, Liu Y, Liu J J 2006 Study of Regional Water Resources Variation in Change Environment (Beijing: Science Press) p32 (in Chinese) [谢平, 许斌, 章树安, 杨桂莲, 窦明, 陈广才, 刘媛, 刘静君 2012 变化环境下区域水资源变异问题研究 (北京: 科学出版社) 第32页]

[1]	孙东永, 张洪波, 王义民. 滑动移除小波分析法在动力学结构突变检验中的应用. , 2017, 66(7): 079201. doi: 10.7498/aps.66.079201
[2]	赵珊珊, 何文平. 北京气候中心气候系统模式对中国四季日平均气温的模拟性能评估. , 2015, 64(4): 049201. doi: 10.7498/aps.64.049201
[3]	张勇, 李诗高. 交通流突变点的无标度特征分析. , 2014, 63(24): 240509. doi: 10.7498/aps.63.240509
[4]	赵珊珊, 何文平. 基于长程相关性特征的北京气候中心气候系统模式对中国气温的模拟性能评估. , 2014, 63(20): 209201. doi: 10.7498/aps.63.209201
[5]	吴浩, 侯威, 王文祥, 颜鹏程. 试用Lyapunov指数探讨气候突变及其前兆信号. , 2013, 62(12): 129204. doi: 10.7498/aps.62.129204
[6]	蔡舒平, 戴理, 倪淏. 基于Fisher信息理论的突变检测新方法. , 2013, 62(18): 189204. doi: 10.7498/aps.62.189204
[7]	成海英, 何文平, 何涛, 吴琼. 基于概率密度分布型变化的突变检测新途径. , 2012, 61(3): 039201. doi: 10.7498/aps.61.039201
[8]	金红梅, 何文平, 侯威, 章大全. 不同趋势对滑动移除近似熵的影响. , 2012, 61(6): 069201. doi: 10.7498/aps.61.069201
[9]	金红梅, 何文平, 张文, 冯爱霞, 侯威. 噪声对滑动移除近似熵的影响. , 2012, 61(12): 129202. doi: 10.7498/aps.61.129202
[10]	何文平, 何涛, 成海英, 张文, 吴琼. 基于近似熵的突变检测新方法. , 2011, 60(4): 049202. doi: 10.7498/aps.60.049202
[11]	何文平, 邓北胜, 吴琼, 张文, 成海英. 一种基于重标极差方法的动力学结构突变检测新方法. , 2010, 59(11): 8264-8271. doi: 10.7498/aps.59.8264
[12]	何文平, 王启光, 吴琼, 张文, 张勇. 滑动去趋势波动分析与近似熵在动力学结构突变检测中的性能比较. , 2009, 58(4): 2862-2871. doi: 10.7498/aps.58.2862
[13]	王启光, 张增平. 近似熵检测气候突变的研究. , 2008, 57(3): 1976-1983. doi: 10.7498/aps.57.1976
[14]	支蓉, 龚志强. 利用幂律尾指数的中国降水突变检测与归因. , 2008, 57(7): 4629-4633. doi: 10.7498/aps.57.4629
[15]	刘志峰, 赖远庭, 赵刚, 张有为, 刘正锋, 王晓宏. 随机多孔介质逾渗模型渗透率的临界标度性质. , 2008, 57(4): 2011-2015. doi: 10.7498/aps.57.2011
[16]	周守利, 黄辉, 黄永清, 任晓敏. 基区重掺杂突变HBT带阶的扰动对电流影响研究. , 2007, 56(5): 2890-2894. doi: 10.7498/aps.56.2890
[17]	封国林, 龚志强, 董文杰, 李建平. 基于启发式分割算法的气候突变检测研究. , 2005, 54(11): 5494-5499. doi: 10.7498/aps.54.5494
[18]	高永华, 何明中, 段春贵. 推广x重新标度模型重标度参数公式与轻子-核DIS过程的核效应. , 2003, 52(1): 39-41. doi: 10.7498/aps.52.39
[19]	高永华, 何祯民, 段春贵. 改进的双重Q2重标度模型. , 2001, 50(6): 1028-1034. doi: 10.7498/aps.50.1028
[20]	赖建文, 周世平, 李国辉, 徐得名. 非重正交的李雅普诺夫指数谱的计算方法. , 2000, 49(12): 2328-2332. doi: 10.7498/aps.49.2328

计量

文章访问数: 5776
PDF下载量: 551
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板