Applicability of the computation method for spatial coherence functions based on the multidimensional autoregressive (AR) model

PDF(3515 KB)

Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (2) : 140-150.

WEN Pan1,2，JI Kun1,2，WEN Ruizhi1,2，REN Yefei1,2

Author information +

History +

Abstract

The power spectrum need to be artificially smoothed when traditional periodic diagram method is used to compute the ground motion coherence function, in addition, only two recordings could be considered. Considering these limitations, the multi-dimensional auto-regressed (AR) model was introduced in this paper to calculate coherence function instead of periodic diagram method and evaluate its applicability at many occasions. Firstly, this study took China Taiwan SMART-1 array data as an example to compare the coherence function results using AR model and periodic diagram method respectively. Then the difference among results of multidimensional AR model was discussed considering the reconstruction performance of time-histories, power spectrum and coherence function. Finally, the spatial multi-point ground motion simulation was adopted to evaluate the performance of coherence function obtained by different dimensions AR models through comparing the simulated and target ground motion. It was found that accurate reconstruction of strong ground motion records can be achieved in different dimensions AR models. However influence of the transfer function matrix would further affect the calculation results of power spectrum and coherence function. For the case of stations with small distance, the power spectrum calculation results are significantly influenced by different dimensions. The simulated ground motion based on the coherence function of 3-dimensional AR model is closer to the target ground motion in terms of time history and power spectrum than periodic diagram method. The influence decreases with the increase of the spacing between the recording stations, which is resulted by the decreasing of correlation relationship between them. In this occasion, the spatial ground motions simulated using the multidimensional AR model are not better than the traditional periodic diagram method.

Key words

spatial coherency function / autoregressive model / power spectrum / periodogram method / China Taiwan SMART-1 stations / multi-point ground motion simulation;

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WEN Pan1,2，JI Kun1,2，WEN Ruizhi1,2，REN Yefei1,2. Applicability of the computation method for spatial coherence functions based on the multidimensional autoregressive (AR) model[J]. Journal of Vibration and Shock, 2022, 41(2): 140-150

References

[1] Abrahamson N A. Program on technology innovation: effects of spatial incoherence on seismic ground motions[R]. Technical Report 1015110, EPRI, Palo Alto, CA: 2007.
[2] 冯启民, 胡聿贤. 空间相关地面运动的数学模型[J]. 地震工程与工程振动, 1981,1(2): 1-8.
FENG Qimin, HU Yuxian. The mathematical model based on spatially corrected ground motion[J]. Earthquake Engineering and Engineering Dynamics, 1981, 1(2): 1-8.(in Chinese).
[3] Hao H, Oliveira C S, Penzien J. Multiple-station ground motion processing and simulation based on Smart-1 array data[J]. Nuclear Engineering and Design, 1989, 111(3): 293-310.
[4] Nazmy A S, Abdel-ghaffar A M. Effects of ground motion spatial variability on the response of cable-stayed bridges[J]. Earthquake Engineering and Structural Dynamics, 1992, 21(1): 1-20.
[5] Abrahamson N A, Schneider E, Stepp J C. Empirical spatial coherency functions for application to soil-structure interaction analyses[J]. Earthquake Spectra, 1991, 7(1): 1-27.
[6] Kiureghian A D. A coherency model for spatially varying gound motions[J]. Earthquake Engineering and Structural Dynamics, 1996, 25(1): 99-111.
[7] Harichandran R S. Estimating the spatial variation of earthquake ground motion from dense array recordings[J]. Structural Safety, 1991, 10(1-3): 219-233.
[8] Oliveira C S, Hao H, Penzien J. Ground motion modeling for multiple-input structural analysis[J]. Structural Safety, 1991, 10(3): 79-93.
[9] 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, 27(3): 1-11.
DING Haipin, 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): 1-11. (in Chinese).
[10] Zerva A. Spatial variation of seismic ground motions, modelling and engineering applications[M]. CRC Press, Taylor and Francis Group, Boca Raton, FL, 2009.
[11] Kay S M, Marple S L. Spectrum analysis—A modern perspective[R]. Proceedings of the IEEE, 1981, 69(11): 1380-1419.
[12] Beamish N, Priestley M B. A Study of Autoregressive and Window Spectral estimation[J]. Applied statistics, 1981, 30(1): 41-58.
[13] Box G, Jenkins G M. Time Series Analysis: Forecasting and Control, 4th edn[M]. John Wiley and Sons, New Jersey. 2008.
[14] 李英民, 吴哲骞, 陈辉国. 已知地震记录的多点地震动仿真[J]. 重庆大学学报, 2013, 36(8): 105-111.
LI Yingmin, WU Zheqian, CHEN Huiguo. A record-based simulation of spatially correlation ground motion[J]. Journal of Chongqing University, 2013, 36(8): 105-111.(in Chinese).
[15] Rupakhety R, Sigbjörnsson 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.
[16] 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(1): 30-38.
DING Haipin, ZHU Yue, Li Xin. Determination of effective frequency range for coherency function based on autoregressive model[J]. Earthquake Engineering and Engineering Dynamics, 2020, 40(1): 30-38. (in Chinese).
[17] Akaike H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974, 19(6): 716-723.
[18] 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)
[19] Imtiaz A, Cornou C, Bard P Y. Sensitivity of ground motion coherency to the choice of time windows from a dense seismic array in Argostoli, Greece[J]. Bulletin of Earthquake Engineering, 2018, 16(9): 3605-3625.
[20] 赵世伟, 罗奇峰. 集集地震与汶川地震、美国西部地震的近场区视波速比较[J]. 振动与冲击, 2013, 32(14): 192-195.
ZHAO Shiwei, LUO Qifeng. Apparent wave velocity comparison among near seismic zones of Chi-chi earthquake, Wenchuan earthquake, and earthquake of western area of US[J]. Journal of Vibration and Shock, 2013, 32(14):192-195. (in Chinese)
[21] 程乾生. 希尔伯特变换与信号的包络、瞬时相位和瞬时频率[J]. 石油地球物理勘探, 1979(03): 1-14.
CHENG Qiansheng. Hilbert transform and signal envelope, instantaneous phase and instantaneous frequency[J]. Petroleum Geophysical Exploration, 1979(03): 1-14.