基于概率密度分布型变化的突变检测新途径

成海英; 何文平; 何涛; 吴琼

doi:10.7498/aps.61.039201

摘要

对于一个稳定的动力系统而言,系统变量的概率密度具有较为稳定的分布型,而当系统的动力学结构发生变化后可能会导致系统变量的分布型发生不同程度的变化.鉴于此,本文从识别系统变量的概率密度分布的微小变化角度出发,将描述时间序列概率分布特征的偏度系数和峰度系数应用于时间序列的突变检测中.数值试验结果表明,偏度系数和峰度系数对突变信号具有很好的识别能力,进而揭示了一条检测突变的新途径.进一步的研究表明,新方法的检测结果对于子序列长度的选择具有较小的依赖性.

关键词:

Abstract

For a stable dynamic system, probability density distribution (PDD) of a system variable is relatively stable, and if there is a change in dynamic structure of a system, the PDD of the system variable will have some change correspondingly. According to this characteristic of PDD of a dynamic system, in this paper we present two new methods, namely, skewness index and kurtosis index, to detect an abrupt change in a time series by means of identifying some small changes in PDD. Tests on model time series indicate that skewness index and kurtosis index can be used to identify an abrupt change, such as abrupt change in parameter of an equation and abrupt dynamic change. Thus, we provide a new approach to detecting abrupt change in time series based on PDD. Further studies show that the detected results of the skewness index and kurtosis index are almost independence of the length of a subseries.

Keywords:

作者及机构信息

1.
盐城工学院基础教学部, 盐城 224051;

2.
国家气候中心, 北京 100081;

3.
济南市环境监测中心站, 济南 250014;

4.
国家卫星气象中心, 北京 100081

基金项目: 国家自然科学基金(批准号: 40905034, 41175067, 40930952)和公益性行业(气象) 科研专项(批准号: GYHY201106015, GYHY201106016)资助的课题.

Authors and contacts

1.
Department of Fundamental Science Teaching, Yancheng Institute of Technology, Yancheng 224051, China;

2.
National Climate Center, China Meteorological Administration, Beijing 100081, China;

3.
Jinan Environmental Monitoring Center, Jinan 250014, China;

4.
National Satellite Meteorological Center, China Meteorological Administration, Beijing 100081, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 40905034, 41175067, 40930952) and the Special Scientific Research Fund of Meteorological Public Welfare Profession of China (Grant Nos. GYHY201106015, GYHY201106016).

参考文献

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[2]	Krishinamulti T N, Ramanathan Y 1982 J. Atmos. Sci. 39 1290
[3]	Marten S, Jordi B, William A B, Victor B, Stephen R C, Vasilis D, Hermann H, Egbert H V N, Max R, George S 2009 Nature 461 53
[4]	Li Y C, Yan W, Jiang C S, Zuo Y L 2009 Recent Developments inWorld Seismology 369 1 (in Chinese) [李迎春, 闫伟, 蒋长胜, 左玲玉 2009 国际地震动态 369 1]
[5]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou University)(in Chinese) [何文平 2008 博士学位论文 (兰州:兰州大学)]
[6]	Mann H B 1945 Econometrica 13 245
[7]	Kendall M G, Charles G 1975 Rank Correlation Methods (NewYork: Oxford University) p202
[8]	Yamamoto R, Iwashima T, Sanga N K 1985 J. Meteor. Soc. Japan.63 1157
[9]	Livina V N, Havlin S, Bunde A 2005 Phys. Rev. Lett. 95 208501
[10]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc.Geophys. 15 601
[11]	He W P, Wu Q, Zheng W, Cheng H Y 2010 Acta Phys. Sin. 598264 (in Chinese) [何文平, 吴琼, 张文, 成海英 2010 59 8264]
[12]	Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[13]	Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[14]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006Nonlinear Theories and Methods on Spatial-Temporal Distribu-tion of the Obserbational Data (Beijing: Metrological Press)pp27–89 (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——第89页]
[15]	He W P, Wu Q, Zheng 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 58 2862]
[16]	Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[17]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 57 1996]
[18]	He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin.60 813 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 60 813]
[19]	Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. SignalProcessing 15 2295
[20]	Abhisek U, Rastko Z 2006 Electric Power Systems Research 76815
[21]	May R 1976 Nature 261 459

施引文献

[1]	Ye D Z, Tao S Y, Li M C 1958 Acta Metro. Sin. 29 249 (in Chinese) [叶笃正, 陶诗言, 李麦春 1958 气象学报 29 249]
[2]	Krishinamulti T N, Ramanathan Y 1982 J. Atmos. Sci. 39 1290
[3]	Marten S, Jordi B, William A B, Victor B, Stephen R C, Vasilis D, Hermann H, Egbert H V N, Max R, George S 2009 Nature 461 53
[4]	Li Y C, Yan W, Jiang C S, Zuo Y L 2009 Recent Developments inWorld Seismology 369 1 (in Chinese) [李迎春, 闫伟, 蒋长胜, 左玲玉 2009 国际地震动态 369 1]
[5]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou University)(in Chinese) [何文平 2008 博士学位论文 (兰州:兰州大学)]
[6]	Mann H B 1945 Econometrica 13 245
[7]	Kendall M G, Charles G 1975 Rank Correlation Methods (NewYork: Oxford University) p202
[8]	Yamamoto R, Iwashima T, Sanga N K 1985 J. Meteor. Soc. Japan.63 1157
[9]	Livina V N, Havlin S, Bunde A 2005 Phys. Rev. Lett. 95 208501
[10]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc.Geophys. 15 601
[11]	He W P, Wu Q, Zheng W, Cheng H Y 2010 Acta Phys. Sin. 598264 (in Chinese) [何文平, 吴琼, 张文, 成海英 2010 59 8264]
[12]	Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[13]	Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[14]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006Nonlinear Theories and Methods on Spatial-Temporal Distribu-tion of the Obserbational Data (Beijing: Metrological Press)pp27–89 (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——第89页]
[15]	He W P, Wu Q, Zheng 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 58 2862]
[16]	Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[17]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 57 1996]
[18]	He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin.60 813 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 60 813]
[19]	Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. SignalProcessing 15 2295
[20]	Abhisek U, Rastko Z 2006 Electric Power Systems Research 76815
[21]	May R 1976 Nature 261 459

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