[1]丁海平,朱越,李昕.基于AR模型的相干函数有效频段范围的确定[J].地震工程与工程振动,2020,40(01):030-38.[doi:10.13197/j.eeev.2020.01.30.dinghp.004]
 DING Haiping,ZHU Yue,LI Xin.Determination of effective frequency range for coherency function based on autoregressive model[J].EARTHQUAKE ENGINEERING AND ENGINEERING DYNAMICS,2020,40(01):030-38.[doi:10.13197/j.eeev.2020.01.30.dinghp.004]
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基于AR模型的相干函数有效频段范围的确定
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《地震工程与工程振动》[ISSN:/CN:]

卷:
40
期数:
2020年01
页码:
030-38
栏目:
论文
出版日期:
2020-05-30

文章信息/Info

Title:
Determination of effective frequency range for coherency function based on autoregressive model
作者:
丁海平12 朱越1 李昕1
1. 江苏省结构工程重点实验室(苏州科技大学), 江苏 苏州 215011;
2. 中国地震局 工程力学研究所, 黑龙江 哈尔滨 150080
Author(s):
DING Haiping12 ZHU Yue1 LI Xin1
1. Key Laboratory of Structural Engineening of Jiangsu Province(Suzhou University of Science and Technology), Suzhou 215011, China;
2. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
关键词:
相干函数频段范围SMART-1台阵自回归模型
Keywords:
coherence functionfrequency rangeSMART-1 arrayautoregressive model
分类号:
P315.9
DOI:
10.13197/j.eeev.2020.01.30.dinghp.004
摘要:
目前人们在进行地震动相干函数模型参数的拟合时,选取的频段范围存在很大差异,而确定有效的频段范围对相干函数模型拟合结果的合理性很重要。本文利用AR模型(Autoregressive Model,自回归模型)计算地震动的功率谱,提出了根据功率谱"信噪比(SNR)"确定相干函数有效频段范围的方法。本文的信噪比中的"噪",专指AR模型中的激励白噪声,用于衡量AR模型中某一频率地震动功率谱与激励白噪声功率谱之间的比例。定义信噪比SNR=0时对应的频率为有效频段的最高频率,大于最高频率的频率成分,被当作是地震波中的随机成分,可以不考虑地震动的相关性。采用这一方法,对SMART-1第45次地震记录的不同台站间距下的地震波进行了功率谱估计,根据信噪比确定出了有效频段范围,并计算了相应的相干函数,结果表明此方法是可行的。
Abstract:
At present, when fitting the parameters of coherence function model of ground motion, there are great differences in the selected frequency range. It is very important to determine the effective frequency range for the rationality of the fitting results of coherence function model. From the point of view of autoregressive model-signal-to-noise ratio (SNR), a method of obtaining power spectrum from autoregressive model, and then determining the effective frequency range of coherence function model based on signal-to-noise ratio is presented. The SNR introduced in this paper is only used to measure the ratio between the ground motion power spectrum and the excitation white noise power spectrum in the autoregressive model. It is found that when SNR=0, the corresponding frequency is the highest frequency in the effective frequency band, and the frequency component higher than the highest frequency is regarded as the random component in seismic wave and the correlation of seismic ground motion cannot be considered. This method is used to estimate the power spectrum and calculate the coherency function of S-wave in the EW and NS directions of the 45th SMART-1 seismic records. The range of effective frequency band is determined according to the SNR, and the attenuation trend of the coherence function curve shows that this method is feasible.

参考文献/References:

[1] BI K, HAO H, CHOUW N. 3D FEM analysis of pounding response of bridge structures at a canyon site to spatially varying ground motions[J]. Advances in Structural Engineering, 2013, 16(4):619-640.
[2] LI C, HAO H, LI H, et al. Modeling and simulation of spatially correlated ground motions at multiple onshore and offshore sites[J]. Journal of Earthquake Engineering, 2017, 21(3):359-383.
[3] LIU C, GAO R. Design method for steel restrainer bars on railway bridges subjected to spatially varying earthquakes[J]. Engineering Structures, 2018, 159:198-212.
[4] WU Y, GAO Y, ZHANG N, et al. Simulation of spatially varying ground motions in V-shaped symmetric canyons[J]. Journal of Earthquake Engineering, 2016, 20(6):992-1010.
[5] CHOPRA A K, WANG J T. Earthquake response of arch dams to spatially varying ground motion[J]. Earthquake Engineering & Structural Dynamics, 2010, 39(8):887-906.
[6] PARK D, SAGONG M, KWAK D Y, et al. Simulation of tunnel response under spatially varying ground motion[J]. Soil Dynamics & Earthquake Engineering, 2009, 29(11):1417-1424.
[7] HAO H. Effects of spatial variation of ground motions on large multiply-supported structures[R]. Report No. UCB-EERC-89-07, University of California, Berkeley, 1989.
[8] Loh C H, Lin S G. Directionality and simulation in spatial variation of seismic waves[J]. Engineering Structures, 1990,12(2):134-143.
[9] Abrahamson N A, Schneider J F, Stepp J C. Empirical spatial coherency functions for application to soil-structure interaction analyses[J]. Earthquake Spectra, 1991, 7(1) 1-27.
[10] 丁海平,罗翼, 等,截止频率的取值对地震动空间相干函数统计结果的影响[J].地震学报, 2018,40(5):1-9. DING Haiping, LUO Yi, et al. Influence of cut-off frequency on statistical results of spatial coherence function of ground motion[J]. Acta Seismologica Sinica, 2018,40(5):1-9. (in Chinese)
[11] 李英民, 吴哲骞, 陈辉国.地震动的空间变化特性分析与修正相干模型[J]. 振动与冲击, 2013,32(2):164-170. LI Yingmin, WU Zheqian, CHEN Huiguo. Analysis and modeling for characteristics of spatially varying ground motion[J]. Journal of Vibration and Shock, 2013,32(2):164-170. (in Chinese)
[12] 丁海平,朱越,于彦彦.基于能量的相干函数有效频段范围的选取[J].地震工程与工程振动,2019,39(2):035-45. DING Haiping, ZHU Yue, YU Yanyan. Selection of effective frequency range for coherency function based on energy method[J]. Earthquake Engineering and Engineering Dynamics,2019,39(2):035-45. (in Chinese)
[13] 丁海平, 袁莉莉, 刘成浩. 窗函数和带宽对地震动相干函数的影响[J]. 自然灾害学报, 2018, v.27(3):3-13. DING Haiping, YUAN Lili, LIU Chenghao. Effection of window function and bandwidth on the ground motion’s coherency function[J]. Journal of Natural Disasters, 2018, 27(3):3-13. (in Chinese)
[14] Akaike H. Power spectrum estimation through autoregressive model fitting[J]. Annals of the institute of Statistical Mathematics, 1969, 21(1) 407-419.
[15] 杨叔子,吴雅. 时间序列分析的工程应用下册[M]. 武汉:华中科技大学, 2007. YANG Shuzi, WU Ya. Time series analysis in engineering application (Second Edition)[M]. Wuhan:Huazhong University of Science and Technology Press. 2007. (in Chinese)
[16] Rupakhety R, Sigbj?rnsson R. Spatial variability of strong ground motion novel system-based technique applying parametric time series modelling[J]. Bulletin of Earthquake Engineering, 2012,10(4):1193-1204.
[17] Abrahamson N A, B A, Bolt, Darragh R B, et al. The SMART I accelerograph array (1980-1987):a review[J]. Earthquake Spectra, 2012, 3(2):263-287.

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备注/Memo

备注/Memo:
收稿日期:2019-04-12;改回日期:2019-07-23。
基金项目:国家自然科学基金项目(51678383)
作者简介:丁海平(1966-),男,教授,博士,主要从事地震工程和防灾减灾工程研究.E-mail:hpding@126.com
更新日期/Last Update: 1900-01-01