A matching method of ground-motion response spectrum and the peak displacement based on the wavelet function
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摘要: 采用数值方法合成地震动时，除对反应谱拟合外，对峰值位移的拟合和天然地震动非平稳特性的模拟也具有重要的意义和工程应用前景。本文基于小波函数的拟合方法，提出了一种能够同时合成目标反应谱和峰值位移的地震动加速度时程。数值算例表明：该方法具有较快的收敛速度，可用较少的迭代运算实现对目标反应谱和目标峰值位移的较高精度拟合；相较于现有的其它拟合方法，由于所构造的小波函数具有时域局部特点，该方法合成的地震动能够较好地保留天然地震动的非平稳特性。Abstract: When using numerical methods to synthesize ground motions, in addition to fitting the response spectrum, the fitting of peak displacements and the simulation of the non-stationary characteristics of natural ground motions also have important significance and engineering application prospects. Based on the wavelet function fitting method, this paper proposes a ground motion acceleration time history that can synthesize the target response spectrum and peak displacement at the same time. Numerical calculation examples show that this method has a faster rate of convergence, and can achieve a higher precision fitting of the target response spectrum and target peak displacement through less iterative calculations. Moreover, compared with other existing methods, the ground motion synthesized by this method can retain the non-stationary characteristics of natural ground motion, due to the local characteristics of wavelet function in time domain.
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Keywords:
- ground motion /
- peak displacement /
- response spectrum /
- non-stationary characteristics /
- synthesize
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图 1 初始地震动加速度（a）、速度（b）及位移（c）时程
Figure 1. The initial ground-motion acceleration （a），velocity （b） and displacement （c） time histories
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图 2 用于调整初始地震动的增量小波函数
（a） 增量位移时程；（b） 增量速度时程；（c） 增量加速度时程
Figure 2. Incremental wavelet function for adjusting initial ground motion
（a） Incremental displacement time history；（b） Incremental velocity time history；（c） Incremental acceleration time history
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图 3 调整后的初始地震动时程
（a） 加速度时程；（b） 速度时程；（c） 位移时程.Dm 为调整后峰值位移，下同
Figure 3. Adjusted initial ground-motion time history
（a） Acceleration time history；（b） Velocity time history； （c） Displacement time history. Dm represents adjusted peak ground displacement，the same below
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图 4 初始地震动加速度（a）、位移（b）时程与调整后比较
Figure 4. Comparison of the initial ground-motion acceleration （a），displacement （b） time histories with the modified ones
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图 5 Maslak台站记录土耳其MW7.5地震的地震动加速度（a）、速度（b）和位移（c）时程
Figure 5. The ground-motion acceleration （a），velocity （b） and displacement （c） time histories of the MW7.5 earthquake in Turkey recorded by the station Maslak
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图 6 Maslak台站第一组（a）和第二组（b）设计地震动的加速度、速度和位移时程
Figure 6. Group 1 （a） and group 2 （b） design ground motion acceleration，velocity and displacement time histories curves of the station Maslak
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图 7 设计地震动加速度反应谱与目标谱的比较
（a） 加速度反应谱Sa；（b） Maslak台站记录的相对误差er
Figure 7. Comparison of target spectrum and design ground motion acceleration spectra
（a） Acceleration spectrum Sa；（b） Relative errorer er of the records by the station Maslak
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图 8 Maslak台站记录拟合精度与迭代次数的变化关系
Figure 8. Relationship between matching precision and iteration number of the records by the station Maslak
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图 9 CHY088台站记录到的集集MW6.2地震的地震动加速度（a）、速度（b）和位移（c）时程曲线
Figure 9. The ground-motion acceleration （a），velocity （b） and displacement （c） time histories of the MW6.2 Jiji earthquake recorded by the station CHY088
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图 10 CHY088台站第一组（a）和第二组（b）的设计地震动加速度、速度和位移时程
Figure 10. Group 1 （a） and group 2 （b） design ground motion acceleration，velocity，and displacement time histories curves of the station CHY088
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图 11 设计地震动加速度反应谱与目标谱的比较
（a） 加速度反应谱Sa；（b） CHY088台站记录的相对误差 er
Figure 11. Comparison of target spectrum and design ground motion acceleration spectra
（a） Acceleration spectrum Sa；（b） Relative errorer er of the records by the station CHY088
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图 12 CHY088台站记录的拟合精度与迭代次数的变化关系
Figure 12. Relationship between matching precision and iteration numbers of the records by the station CHY088
表 1 本文所用强震观测记录的基本信息
Table 1 Fundamental information on the strong-motion observation recordings used in this paper
发震日期 地震名称 台站名称 MW 震中距/km 分量 1999-08-17 土耳其地震 Maslak 7.5 90.74 EW 1999-09-20 中国台湾集集地震 CHY088 6.2 48.87 EW 
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表 2 以Maslak台站记录作为初始地震动的待拟合的目标参数
Table 2 The target parameters to be matched with the records of the station Maslak as the initial ground-motion
分组 PGA/g PGV/（m·s−1） PGD/m 第一组 0.22 0.04 0.06 第二组 0.22 0.04 0.03
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表 3 以CHY088台站记录作为初始地震动时程待拟合的目标参数
Table 3 The target parameters to be matched with the records of the station CHY088 as the initial ground-motion
分组 PGA/g PGV/（m·s−1） PGD/m 第一组 0.22 0.03 0.03 第二组 0.22 0.03 0.015
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蔡长青,沈建文. 1997. 人造地震动的时域叠加法和反应谱整体逼近技术[J]. 地震学报,19(1):71–78. Cai C Q,Shen J W. 1997. Time-domain superposition method and response spectrum overall approximation technology of artificial ground motion[J]. Acta Seismologica Sinica,19(1):71–78 (in Chinese).
郝明辉,王珊,张郁山. 2017. 峰值位移输入对单自由度体系地震反应的影响[J]. 建筑结构学报,38(1):85–92. Hao M H,Wang S,Zhang Y S. 2017. Influence of input ground-motion peak displacement on non-linear dynamic response of single-degree-of-freedom system[J]. Journal of Building Structures,38(1):85–92 (in Chinese).
胡灿阳,陈清军. 2008. 非平稳地震地面运动分析方法及模型综述[J]. 结构工程师,24(2):107–115. doi: 10.3969/j.issn.1005-0159.2008.02.022 Hu C Y,Chen Q J. 2008. State-of-the-art of analysis method and model of non-stationary earthquake ground motion[J]. Structural Engineers,24(2):107–115 (in Chinese).
胡聿贤,何训. 1986. 考虑相位谱的人造地震动反应谱拟合[J]. 地震工程与工程振动,6(2):37–51. Hu Y X,He X. 1986. Phase angle consideration in generating response spectrum- compatible ground motion[J]. Earthquake Engineering and Engineering Vibration,6(2):37–51 (in Chinese).
冀昆,温瑞智,任叶飞. 2016. 中国抗震规范强震记录选取的初选条件研究[J]. 防灾减灾工程学报,36(1):44–49. Ji K,Wen R Z,Ren Y F. 2016. Study on the initial of selection criteria strong motion records for Chinese Seismic Code[J]. Journal of Disaster Prevention and Mitigation Engineering,36(1):44–49 (in Chinese).
李琳,温瑞智,周宝峰,史大成. 2013. 基于条件均值反应谱的特大地震强震记录的选取及调整方法[J]. 地震学报,35(3):380–389. doi: 10.3969/j.issn.0253-3782.2013.03.009 Li L,Wen R Z,Zhou B F,Shi D C. 2013. Selection and scaling of ground motion records for great scenario earthquake based on the conditional mean spectrum[J]. Acta Seismologica Sinica,35(3):380–389 (in Chinese).
柳夏勃,俞瑞芳. 2016. 地震动强度非平稳特性参数与结构响应之间的近似定量关系分析[J]. 地震学报,38(6):924–933. doi: 10.11939/jass.2016.06.012 Liu X B,Yu R F. 2016. Approximate quantitative relationship between earthquake ground motion and structural responses[J]. Acta Seismologica Sinica,38(6):924–933 (in Chinese).
盛涛,施卫星,谢异同,袁俊. 2012. 拟合核电厂设计反应谱及峰值位移的地震动调整方法[J]. 核动力工程,33(1):4–8. doi: 10.3969/j.issn.0258-0926.2012.01.002 Sheng T,Shi W X,Xie Y T,Yuan J. 2012. A modifying method of recorded earthquake ground motion for matching design response spectrum and peak ground displacement in nuclear power plants[J]. Nuclear Power Engineering,33(1):4–8 (in Chinese).
孙忠贤. 2009. 地震动特性对结构地震反应的影响分析[D]. 哈尔滨: 中国地震局工程力学研究所: 1–63. Sun Z X. 2009. The Influence of Ground Motion Characteristics on Response of Structures[D]. Harbin: Institute of Engineering Mechanics, China Earthquake Administration: 1–63 （in Chinese）.
王飞. 2016. 峰值速度和峰值位移对钢结构弹塑性地震反应影响研究[D]. 北京: 中国地震局地球物理研究所: 1–406. Wang F. 2016. Influence of PGV and PGD on Structural Nolinear Seismic Response of Steel Buildings[D]. Beijing: Institute of Geophysics, China Earthquake Administration: 1–406 （in Chinese）.
王珊,张郁山. 2017. 各类抗震设计规范对设计地震动时程规定的对比分析[J]. 中国地震,33(1):56–67. doi: 10.3969/j.issn.1001-4683.2017.01.006 Wang S,Zhang Y S. 2017. Comparison of various seismic design codes on design ground motion time history[J]. Earthquake Research in China,33(1):56–67 (in Chinese).
张翠然,陈厚群. 2008. 工程地震动模拟研究综述[J]. 世界地震工程,24(2):150–157. Zhang C R,Chen H Q. 2008. Review and prospects on the simulation research of engineering earthquake ground motion[J]. World Earthquake Engineering,24(2):150–157 (in Chinese).
张郁山,赵凤新. 2011. 地震动峰值位移对单自由度体系非线性动力反应的影响[J]. 工程力学,28(1):55–64. Zhang Y S,Zhao F X. 2011. Influence of ground-motion peak displacement on non-linear dynamic response of single-degree-of-freedom system[J]. Engineering Mechanics,28(1):55–64 (in Chinese).
张郁山,赵凤新. 2014. 基于小波函数的地震动反应谱拟合方法[J]. 土木工程学报,47(1):70–81. Zhang Y S,Zhao F X. 2014. Matching method of ground-motion response spectrum based on the wavelet function[J]. China Civil Engineering Journal,47(1):70–81 (in Chinese).
赵凤新,张郁山. 2006. 拟合峰值速度与目标反应谱的人造地震动[J]. 地震学报,28(4):429–437. doi: 10.3321/j.issn:0253-3782.2006.04.010 Zhao F X,Zhang Y S. 2006. Artificial ground motion compatible with specified peak velocity and target spectrum[J]. Acta Seismologica Sinica,28(4):429–437 (in Chinese).
赵凤新,张郁山. 2007. 拟合峰值位移与目标反应谱的人造地震动[J]. 核动力工程,28(2):38–41. doi: 10.3969/j.issn.0258-0926.2007.02.009 Zhao F X,Zhang Y S. 2007. Artificial ground motions compatible with both specified peak displacement and target response spectrum[J]. Nuclear Power Engineering,28(2):38–41 (in Chinese).
中华人民共和国住房和城乡建设部. 2010. GB 50011—2010 建筑抗震设计规范[S]. 北京: 中国建筑工业出版社: 1–34. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. 2010. GB 50011—2010 Code for Seismic Design of Buildings[S]. Beijing: China Architecture & Building Press: 1–34 （in Chinese）.
中华人民共和国住房和城乡建设部. 2014. GB 50909—2014 城市轨道交通结构抗震设计规范[S]. 北京: 中国计划出版社: 1–26. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. 2014. GB 50909—2014 Code for Seismic Design of Urban Rail Transit Structures[S]. Beijing: China Planning Press: 1–26 （in Chinese）.
周媛. 2006. 地震动速度与位移对大跨斜拉桥地震反应影响的研究[D]. 北京: 中国地震局地球物理研究所: 1–88. Zhou Y. 2006. Study on Effects of Ground Velocity and Ground Displacement on Seismic Responses of Long Span Cable-Stayed Bridge[D]. Beijing: Institute of Geophysics, China Earthquake Administration: 1–88 （in Chinese）.
U.S. Nuclear Regulatory Commission. 2007. Standard Review Plan: 3.7.1 Seismic Design Parameters[S]. Washington DC: 1–9.
U.S. Nuclear Regulatory Commission. 2014. Standard Review Plan: 3.7.1 Seismic Design Parameters[S]. Washington DC: 1–10.
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