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自然界许多复杂系统的动力学结构因其受外强迫的作用, 常常会发生与人类生活密切相关的突变. 对突变做出准确预测并采取相应对策的有效途径就是检测. Fisher信息(FI)是一种能够敏锐捕捉并刻画系统变量的概率密度分布发生微小变化的量; 而当系统的动力学结构发生突变时, 来自突变前后两种不同动力学结构的数据其概率密度分布肯定会发生不同程度的改变. 基于此，本文将它用于检测和识别系统动力学结构所发生的突变, 以一种全新的思路来解决突变检测问题. 首先通过理想数据序列展示了使用FI来表征各种不同类型理想信号突变的能力. 进而应用于中国气象局国家气象信息中心“西北地区地面气候资料日值数据集”兰州站1960–2008年日平均气温资料的实际检测中, 结果表明与已有历史记载相符合, 进一步验证了该方法的有效性和实用性.The dynamics structure of many complex system there often happens a suddenly change due to the effect of outside force in nature. This abrupt change is closely related to human life. In order to make an accurate prediction of abrupt change and take corresponding measures, abrupt change should be detected effectively. Fisher information (FI) can keenly catch and characterize a small change in probability density distribution (PDD) of a system variable. While there is a change in dynamic structure of a system, the PDD of the system variable will have some changes correspondingly. In view of this, in this paper we describe in detail that FI is used to detect and recognize the abrupt change of system dynamics structure, and it is a new method to solve the detection of abrupt change in dynamic structure of a system. First of all, this method is used to present the ability to detect abrupt change lying in ideal datasets of different types of ideal signals. Next, this method is used to analyze daily datasets of ground climate from national meteorological information center of China meteorological administration between 1960 and 2008 in Lanzhou meteorological observation station in Northwest area. The results show that the daily datasets are consistent with historical records, which further verifies that the method is effective and practical.
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Keywords:
- Fisher information /
- dynamics structure /
- abrupt change detection /
- probability density distribution
[1] Feng G L, Gong Z Q, Zhi R 2008 Acta Metrol. Sin. 66 892 (in Chinese) [封国林, 龚志强, 支蓉 2008 气象学报 66 892]
[2] Gong Z Q, Feng G L, Wan S Q, Li J P 2006 Acta Phys. Sin. 55 477 (in Chinese) [龚志强, 封国林, 万仕全, 李建平 2006 55 477]
[3] Feng G L, Gong Z Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial Temporal Distribution of the Observational Data (Beijing: China Meteorological Press) pp1-100 (in Chinese) [封国林, 龚志强, 支蓉 2006 观察数据时空分布的非线性理论和方法 (北京: 中国气象出版社)第1–100页]
[4] Gong Z Q, Feng G L, Dong W J 2006 Acta Phys. Sin. 55 3180 (in Chinese) [龚志强, 封国林, 董文杰 2006 55 3180]
[5] 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 58 2862]
[6] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯威, 封国林, 董文杰, 李建平 2006 55 2663]
[7] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 57 1976]
[8] 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]
[9] 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]
[10] Cheng H Y, He W P, He T, Wu Q 2012 Acta Phys. Sin. 61 039201 (in Chinese) [成海英, 何文平, 何涛, 吴琼 2012 61 039201]
[11] Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. Signal Processing 15 2295
[12] Abhisek U, Rastko Z 2006 Electric Power System Research 76 815
[13] Gong Z Q, Zou M W, Gao X Q, Dong W J 2005 Acta Phys. Sin. 54 3947 (in Chinese) [龚志强, 邹明玮, 高新全, 董文杰 2005 54 3947]
[14] Feng G L, Hou W, Dong W J 2006 Acta Phys. Sin. 55 962 (in Chinese) [封国林, 侯威, 董文杰 2006 55 962]
[15] Wan S Q, Feng G L, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰, 李建平 2005 54 5487]
[16] Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉2009 58 2853]
[17] Cabezas H, Fath B D 2002 Fluid Phase Equilibria 194-197 3
[18] Fath B, Cabezas H, Pawlowski C W 2003 J. Theor. Biol. 222-224 517
[19] Frieden B R 1998 Physics from Fisher Information: A Unification (Cambridge, UK: Cambridge University Press)
[20] Frieden B R 2001 Probability, Statistical Optics and Data Testing (3th Ed.) (New York: Springer-Verlag)
[21] Mayer A L, Pawlowski C W, Cabezas H 2006 Ecol. Model. 195 72
[22] Karunanithi A T, Cabezas H, Frieden B R, Pawlowski C W 2008 Ecol. Soc. 13 22
[23] Fath B D, Cabezas H 2004 Ecol. Model. 174 25
[24] Cabezas H, Pawlowski C W, Mayer A L, Hoagland N T 2005 J. Clean. Product. 13 455
[25] Cabezas H, Pawlowski C W, Mayer A L, Hoagland N T 2005 Resources, Conservation and Recycling 44 279
[26] Shastri Y, Diwekar U, Cabezas H 2008 Environ. Sci. Technol. 42 5322
[27] Shastri Y, Diwekar U, Cabezas H, Williamson J 2008 Environ. Sci. Technol. 42 6710
[28] Rico-Ramirez V R, Qunitana-Hernandez P A, Ortiz-Cruz J A, Hernandez-Castro S 2008 Computer-Aided Chem. Engin. 25 1155
[29] Fisher R A 1922 Philosoph. Trans. Roy. Soc. London 222 309
[30] Eason T, Cabezas H 2012 J. Environ. Manage. 94 41
[31] Li Y Q 2001 Plateau Meteorol. 20 88 (in Chinese) [李跃清 2001 高原气象 20 88]
[32] Lorenz E N 1963 J. Atmos. 20 130
[33] Lorenz E N 1976 Quat. Res. 6 495
[34] Charney J G, Devore J G 1979 J. Atmos. Sci. 36 1205
[35] Wei F Y, Cao H X 1995 Sci. Atmos. Sin. 19 140 (in Chinese) [魏凤英, 曹鸿兴 1995大气科学 19 140]
[36] Zhao F F, Xu Z X 2006 Sci. Atmos. Sin. 64 246 (in Chinese) [赵芳芳, 徐宗学 2006气象学报 64 246]
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[1] Feng G L, Gong Z Q, Zhi R 2008 Acta Metrol. Sin. 66 892 (in Chinese) [封国林, 龚志强, 支蓉 2008 气象学报 66 892]
[2] Gong Z Q, Feng G L, Wan S Q, Li J P 2006 Acta Phys. Sin. 55 477 (in Chinese) [龚志强, 封国林, 万仕全, 李建平 2006 55 477]
[3] Feng G L, Gong Z Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial Temporal Distribution of the Observational Data (Beijing: China Meteorological Press) pp1-100 (in Chinese) [封国林, 龚志强, 支蓉 2006 观察数据时空分布的非线性理论和方法 (北京: 中国气象出版社)第1–100页]
[4] Gong Z Q, Feng G L, Dong W J 2006 Acta Phys. Sin. 55 3180 (in Chinese) [龚志强, 封国林, 董文杰 2006 55 3180]
[5] 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 58 2862]
[6] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯威, 封国林, 董文杰, 李建平 2006 55 2663]
[7] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 57 1976]
[8] 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]
[9] 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]
[10] Cheng H Y, He W P, He T, Wu Q 2012 Acta Phys. Sin. 61 039201 (in Chinese) [成海英, 何文平, 何涛, 吴琼 2012 61 039201]
[11] Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. Signal Processing 15 2295
[12] Abhisek U, Rastko Z 2006 Electric Power System Research 76 815
[13] Gong Z Q, Zou M W, Gao X Q, Dong W J 2005 Acta Phys. Sin. 54 3947 (in Chinese) [龚志强, 邹明玮, 高新全, 董文杰 2005 54 3947]
[14] Feng G L, Hou W, Dong W J 2006 Acta Phys. Sin. 55 962 (in Chinese) [封国林, 侯威, 董文杰 2006 55 962]
[15] Wan S Q, Feng G L, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰, 李建平 2005 54 5487]
[16] Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉2009 58 2853]
[17] Cabezas H, Fath B D 2002 Fluid Phase Equilibria 194-197 3
[18] Fath B, Cabezas H, Pawlowski C W 2003 J. Theor. Biol. 222-224 517
[19] Frieden B R 1998 Physics from Fisher Information: A Unification (Cambridge, UK: Cambridge University Press)
[20] Frieden B R 2001 Probability, Statistical Optics and Data Testing (3th Ed.) (New York: Springer-Verlag)
[21] Mayer A L, Pawlowski C W, Cabezas H 2006 Ecol. Model. 195 72
[22] Karunanithi A T, Cabezas H, Frieden B R, Pawlowski C W 2008 Ecol. Soc. 13 22
[23] Fath B D, Cabezas H 2004 Ecol. Model. 174 25
[24] Cabezas H, Pawlowski C W, Mayer A L, Hoagland N T 2005 J. Clean. Product. 13 455
[25] Cabezas H, Pawlowski C W, Mayer A L, Hoagland N T 2005 Resources, Conservation and Recycling 44 279
[26] Shastri Y, Diwekar U, Cabezas H 2008 Environ. Sci. Technol. 42 5322
[27] Shastri Y, Diwekar U, Cabezas H, Williamson J 2008 Environ. Sci. Technol. 42 6710
[28] Rico-Ramirez V R, Qunitana-Hernandez P A, Ortiz-Cruz J A, Hernandez-Castro S 2008 Computer-Aided Chem. Engin. 25 1155
[29] Fisher R A 1922 Philosoph. Trans. Roy. Soc. London 222 309
[30] Eason T, Cabezas H 2012 J. Environ. Manage. 94 41
[31] Li Y Q 2001 Plateau Meteorol. 20 88 (in Chinese) [李跃清 2001 高原气象 20 88]
[32] Lorenz E N 1963 J. Atmos. 20 130
[33] Lorenz E N 1976 Quat. Res. 6 495
[34] Charney J G, Devore J G 1979 J. Atmos. Sci. 36 1205
[35] Wei F Y, Cao H X 1995 Sci. Atmos. Sin. 19 140 (in Chinese) [魏凤英, 曹鸿兴 1995大气科学 19 140]
[36] Zhao F F, Xu Z X 2006 Sci. Atmos. Sin. 64 246 (in Chinese) [赵芳芳, 徐宗学 2006气象学报 64 246]
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