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研究了连续噪声和尖峰噪声对去趋势波动分析的影响,发现噪声的存在使得双对数曲线在尺度较小时发生了"转折"现象.针对这一问题,文中采用三种不同滤波方法对理想时间序列进行了实验,结果表明,多级Vondrak滤波得到的高频序列与真实噪声序列无论是在强度还是在演变趋势上都展现出惊人的一致性,低频滤波序列的去趋势波动分析结果与真实信号十分接近,多级Vondrak滤波基本上能够消除由于噪声所引起的"转折"现象,而且这一研究结果对于滤波周期阈值的依赖性并不太大.多点滑动加权平均滤波虽然能够在一定程度上减轻噪声对于去趋势波动的影响,但不能从根本上消除由于噪声所引起的"转折"现象.快速傅里叶滤波在选择合适的滤波周期阈值时,能够基本消除噪声对去趋势波动分析的影响,但是由于其滤波结果对于滤波周期阈值的依赖较大,在实际应用中滤波周期阈值的选取比较困难.因此,多级Vondrak滤波是消除噪声对去趋势波动分析结果影响的一种有效的途径.
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关键词:
- 多级Vondrak滤波 /
- 去趋势波动分析 /
- 多点滑动加权平均滤波 /
- 快速傅里叶滤波
We studied the effects of continuous noises and random spikes on detrended fluctuation analysis, and found that the noises lead to the appearance of crossovers in the double logarithm curves when the linear fitting scale was less than a characteristic scale s×. To solve this problem, we use three kinds of filter methods, multi-stage Vondrak filter, N-point weighted moving average filter and fast Fourier filter, to filter high frequency from the analyzed time series. The results indicate that the evolution trend and intensity of high frequency series by multi-stage Vondrak filter is almost identical to those of real noises. Further investigation showed that multi-stage Vondrak filter can eliminate the phenomenon of crossover, and the DFA results of lowpass filtering time series are less dependent on the threshold of the filter periods. To some extent, N-points weighted moving average filter can partly eliminate the effect of noises on DFA, but can not completely eliminate the phenomenon of crossover caused by noises. Fast Fourier filter can almost totally eliminate the effect of noises on DFA when the period of filter adopts an appropriate value, but the filtering results have a stronger dependence on the period of filter, so it is difficult to select the period of filter in practical application. Therefore, comparatively speaking, multi-stage Vondrak filter is an effective measure to alleviate the effects of noises on the DFA results.-
Keywords:
- multi-stage Vondrak filter /
- detrended fluctuation analysis /
- N-points weighted moving average filter /
- fast Fourier filter
[1] He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys.Sin. 55 969 (in Chinese) [何文平、封国林、董文杰、李建平 2006 55 969]
[2] Du J 2002 J. Appl. Meteo. Sin. 13 16 (in Chinese) [杜 均 2002 应用气象学报 13 16]
[3] 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)]
[4] Zuo H J 2001 Meteorology Journal of Hubei 4 29 (in Chinese) [左惠娟 2001 湖北气象 4 29]
[5] Peng C K, Havlin S, Schwartz M, Stanley H E 1991 Phys. Rev. A 44 R2239
[6] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685
[7] Peng C K, Havlin S, Goldberger A L 1995 Chaos 5 82
[8] 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]
[9] 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 58 6640]
[10] Caballero R, Jewson S, Brix A 2002 Clim. Res. 21 127
[11] Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 68 046133-1
[12] Fraedrich K, Blender R 2003 Phys. Rev. Lett. 90 108501
[13] Govindan R B, Vyushin D, Bunde A, Brenner S, Havlin S, Schellnhuber H J 2000 Phys. Rev. Lett. 89 028501
[14] Govindan R B, Vjushin D, Brenner S, Bunder A, Havlin S, Schellnhuber H J 2001 Physica A 294 239
[15] Cao H X, Zheng Z F, Zhang X L, Xie Z, Pan J H 2007 Chin. J. Geophys. 50 420 (in Chinese) [曹鸿兴、郑祚芳、张秀丽、谢 庄、潘家华2007地球 50 420]
[16] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601
[17] 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]
[18] Chen Z, Ivanov P, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107
[19] Vondrak J 1969 Bull. Astron. Inst. Czech. 20 349
[20] Vondrak J 1977 Bull. Astron. Inst. Czech. 28 84
[21] Yan H M, Zhong M, Zhu Y Z 2006 J. Geode. Geody. 26 109 (in Chinese) [闫昊明、钟 敏、朱耀仲 2006大地测量与地球动力学26 109]
[22] Zheng D W, Dong D N 1986 Acta Astro. Sin. 27 368 (in Chinese) [郑大伟、董大南 1986 天文学报 27 368]
[23] Huang K Y, Zhou X 1981 Acta Astro. Sin. 22 121 (in Chinese) [黄坤仪、周 雄 1981 天文学报 22 121]
[24] Wang X L, Ropelewshi C F 1995 J. Climate 8 1584
[25] Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[26] Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[27] Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[28] Lorenz E N 1963 J. Atmos. Sci. 20 130
[29] Feng G L, Dai X G, Wang A H 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧 2001 50 606]
[30] Feng G L, Dong W J, Jia X J 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静 2002 51 1181]
[31] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial-Temporal Distribution of the Obserbational Data (Beijing: Metrological Press) p17 (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17页]
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[1] He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys.Sin. 55 969 (in Chinese) [何文平、封国林、董文杰、李建平 2006 55 969]
[2] Du J 2002 J. Appl. Meteo. Sin. 13 16 (in Chinese) [杜 均 2002 应用气象学报 13 16]
[3] 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)]
[4] Zuo H J 2001 Meteorology Journal of Hubei 4 29 (in Chinese) [左惠娟 2001 湖北气象 4 29]
[5] Peng C K, Havlin S, Schwartz M, Stanley H E 1991 Phys. Rev. A 44 R2239
[6] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685
[7] Peng C K, Havlin S, Goldberger A L 1995 Chaos 5 82
[8] 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]
[9] 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 58 6640]
[10] Caballero R, Jewson S, Brix A 2002 Clim. Res. 21 127
[11] Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 68 046133-1
[12] Fraedrich K, Blender R 2003 Phys. Rev. Lett. 90 108501
[13] Govindan R B, Vyushin D, Bunde A, Brenner S, Havlin S, Schellnhuber H J 2000 Phys. Rev. Lett. 89 028501
[14] Govindan R B, Vjushin D, Brenner S, Bunder A, Havlin S, Schellnhuber H J 2001 Physica A 294 239
[15] Cao H X, Zheng Z F, Zhang X L, Xie Z, Pan J H 2007 Chin. J. Geophys. 50 420 (in Chinese) [曹鸿兴、郑祚芳、张秀丽、谢 庄、潘家华2007地球 50 420]
[16] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601
[17] 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]
[18] Chen Z, Ivanov P, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107
[19] Vondrak J 1969 Bull. Astron. Inst. Czech. 20 349
[20] Vondrak J 1977 Bull. Astron. Inst. Czech. 28 84
[21] Yan H M, Zhong M, Zhu Y Z 2006 J. Geode. Geody. 26 109 (in Chinese) [闫昊明、钟 敏、朱耀仲 2006大地测量与地球动力学26 109]
[22] Zheng D W, Dong D N 1986 Acta Astro. Sin. 27 368 (in Chinese) [郑大伟、董大南 1986 天文学报 27 368]
[23] Huang K Y, Zhou X 1981 Acta Astro. Sin. 22 121 (in Chinese) [黄坤仪、周 雄 1981 天文学报 22 121]
[24] Wang X L, Ropelewshi C F 1995 J. Climate 8 1584
[25] Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[26] Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[27] Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[28] Lorenz E N 1963 J. Atmos. Sci. 20 130
[29] Feng G L, Dai X G, Wang A H 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧 2001 50 606]
[30] Feng G L, Dong W J, Jia X J 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静 2002 51 1181]
[31] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial-Temporal Distribution of the Obserbational Data (Beijing: Metrological Press) p17 (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17页]
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