去趋势波动分析方法中不重叠等长度子区间长度的确定

侯威; 章大全; 杨萍; 杨杰

doi:10.7498/aps.59.8986

摘要

针对去趋势波动分析方法中参数不重叠等长度子区间长度s的选取,基于信息论的基本原理,提出使用符号分析方法对原始数据进行符号编码,并使用不同的方式对符号序列进行分段、计算互信息函数. 细致描述了不同分段方式对原始混沌序列的信息编码能力,以此判断所采用的分段方式能否真实有效地还原原始序列所包含的全部信息. 给出了确定最优分段个数或各分段长度的具体方式,确定了不重叠等长度子区间长度s的选取算法,以及判断所研究序列是否适用于去趋势波动分析方法,避免了以往参数s选取中随机性和主观性给计算结果带来的错误信息. 进一步将该方法应用于实际温度资料,计算并分析中国1961—2000年逐日平均温度的去趋势波动分析指数分布状况.

关键词:

Abstract

We develop a method to compute the segment size in the detrended fluctuation analysis (DFA), which is based on the basic concept of the information theory, and verify the method effectiveness by numerical experiment. This method is freed from the problem of subjectivity in the former process to choose the segment size which usually leads to false result. We Change the length of sequence with dynamics being the same, the results remain stable. The results indicate that when the length of sequence is too short, even the optimal selection of segment size is not enough for the portrait of the overall dynamic system, thus the DFA cannot be used in this circumstance. The method we developed in this paper can enhance the reliability of DFA results by judging whether the sequences analyzed meet the requirements of DFA. We also obtain the DFA index from 1961 to 2000 of China through DFA method and analyze its spatial characteristics of distribution.

Keywords:

作者及机构信息

(1)国家气候中心,北京 100081;兰州大学大气科学学院,兰州 730000; (2)国家气候中心,北京 100081;中国科学院大气物理研究所东亚区域气候环境重点实验室,北京 100029; (3)中国气象局北京城市气象研究所,北京 100089

基金项目: 国家自然科学基金(批准号:40905034, 40775048)和国家科技支撑计划(批号:2007BAC29B01, 2009BAC51B04)资助的课题.

Authors and contacts

(1)Institute of Urban Meteorology of Beijing, China Meteorological Administration, Beijing 100089, China; (2)National Climate Center, Beijing 100081, China;College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000, China; (3)National Climate Center, Beijing 100081, China;Key Laboratory of Regional Climate Environment Research for Temperature East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

参考文献

[1]	Peng C K, Buldyrev S V, Havlin S 1994 Phys. Rev. E 49 1685
[2]	Lux T, Marehesi M 1999 Nature 397 498
[3]	Mantegna R N, Stanley H E 1995 Nature 376 46
[4]	Liu F, Shan X M, Ren Y, Zhang J, Ma Z X 2004 Acta Phys. Sin. 53 550 (in Chinese)[刘锋、山秀明、任勇、张军、马正新 2004 物理学报 53 550]
[5]	Sealas E 1998 Physica A 253 394
[6]	Janosi I M, Janeesko B, Kondor D 1999 Physica A 269 111
[7]	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 物理学报 58 2853] 〖8] Stanley H E, Amaral L A N, Canning D 1999 Physica A 269 156
[8]	Stanley H E, Afanasyevr V, Anlaral L A N 1996 Physica A 224 302
[9]	Wang Q G, Zhi R, Zhang Z P 2008 Acta Phys. Sin. 57 5343 (in Chinese) [王启光、支蓉、张增平 2008 物理学报 57 5343]
[10]	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] 〖12] Govindan R B, Vjushin D, Brenner S 2001 Physica A 294 239
[11]	Kantelhardta J W, Zschiegner S A, Bunde E K 2002 Physica A 316 87
[12]	Bernaola G P 2001 Phys. Rev. Lett. 87 168
[13]	Wang Q G, Hou W, Zheng Z H, Gao R 2009 Acta Phys. Sin. 58 6640 (in Chinese)[王启光、侯威、郑志海、高荣 2009 物理学报 58 6640]
[14]	Panlov A N, Sosnovtseva O V, Ziganshin A R 2002 Physica A 316 233
[15]	Lee J M, Kin D J, Kim I Y 2002 Comp. Bio. Med. 32 37
[16]	Ott E 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press) pp305—333
[17]	Yang X L, Xu W 2008 Chin. Phys. B 17 2004
[18]	Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中 2007 物理学报 56 3152]
[19]	Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese) [肖方红、阎桂荣、韩宇航 2005 物理学报 54 550]
[20]	Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[21]	Yang Z A, Wang G R, Chen S G 1995 Chin. J. Comp. Phys. 12 442 (in Chinese)[杨志安、王光瑞、陈式刚 1995 计算物理 12 442]
[22]	Nichols J M, Nichols J D 2001 Math. Biosci. 171 21
[23]	Rechester A B, White R B 1991 Phys. Lett. A 156 419
[24]	Rechester A B, White R B 1997 Phys. Rev. Lett. 78 54
[25]	Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164
[26]	Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297
[27]	Azad R K, Rao J S, Ramaswamy R 2002 Chaos Solitions Fract. 14 633
[28]	Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese)[肖方红、阎桂荣、韩宇航 2004 物理学报 53 2877]
[29]	Zheng Z H, Ren H L, Huang J P 2009 Acta Phys. Sin. 58 7359 (in Chinese)[郑志海、任宏利、黄建平 2009 物理学报 58 7359]
[30]	Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164501
[31]	Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297

施引文献

[1]	Peng C K, Buldyrev S V, Havlin S 1994 Phys. Rev. E 49 1685
[2]	Lux T, Marehesi M 1999 Nature 397 498
[3]	Mantegna R N, Stanley H E 1995 Nature 376 46
[4]	Liu F, Shan X M, Ren Y, Zhang J, Ma Z X 2004 Acta Phys. Sin. 53 550 (in Chinese)[刘锋、山秀明、任勇、张军、马正新 2004 物理学报 53 550]
[5]	Sealas E 1998 Physica A 253 394
[6]	Janosi I M, Janeesko B, Kondor D 1999 Physica A 269 111
[7]	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 物理学报 58 2853] 〖8] Stanley H E, Amaral L A N, Canning D 1999 Physica A 269 156
[8]	Stanley H E, Afanasyevr V, Anlaral L A N 1996 Physica A 224 302
[9]	Wang Q G, Zhi R, Zhang Z P 2008 Acta Phys. Sin. 57 5343 (in Chinese) [王启光、支蓉、张增平 2008 物理学报 57 5343]
[10]	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] 〖12] Govindan R B, Vjushin D, Brenner S 2001 Physica A 294 239
[11]	Kantelhardta J W, Zschiegner S A, Bunde E K 2002 Physica A 316 87
[12]	Bernaola G P 2001 Phys. Rev. Lett. 87 168
[13]	Wang Q G, Hou W, Zheng Z H, Gao R 2009 Acta Phys. Sin. 58 6640 (in Chinese)[王启光、侯威、郑志海、高荣 2009 物理学报 58 6640]
[14]	Panlov A N, Sosnovtseva O V, Ziganshin A R 2002 Physica A 316 233
[15]	Lee J M, Kin D J, Kim I Y 2002 Comp. Bio. Med. 32 37
[16]	Ott E 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press) pp305—333
[17]	Yang X L, Xu W 2008 Chin. Phys. B 17 2004
[18]	Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中 2007 物理学报 56 3152]
[19]	Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese) [肖方红、阎桂荣、韩宇航 2005 物理学报 54 550]
[20]	Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[21]	Yang Z A, Wang G R, Chen S G 1995 Chin. J. Comp. Phys. 12 442 (in Chinese)[杨志安、王光瑞、陈式刚 1995 计算物理 12 442]
[22]	Nichols J M, Nichols J D 2001 Math. Biosci. 171 21
[23]	Rechester A B, White R B 1991 Phys. Lett. A 156 419
[24]	Rechester A B, White R B 1997 Phys. Rev. Lett. 78 54
[25]	Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164
[26]	Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297
[27]	Azad R K, Rao J S, Ramaswamy R 2002 Chaos Solitions Fract. 14 633
[28]	Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese)[肖方红、阎桂荣、韩宇航 2004 物理学报 53 2877]
[29]	Zheng Z H, Ren H L, Huang J P 2009 Acta Phys. Sin. 58 7359 (in Chinese)[郑志海、任宏利、黄建平 2009 物理学报 58 7359]
[30]	Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164501
[31]	Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297

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