《Earthquake Engineering and Structural Dynamics》杂志刊登“基于演变谱的地震动空间变量的条件模拟”

作者：L.Hu,Y.L.Xu,Y.Zheng

刊物：《Earthquake Engineering and Structural Dynamics》，2012年， 41卷第15期，2125—2139页

关键词：条件模拟；地震动；非平稳；演变谱

摘要：本文为多支撑大跨度桥梁的地震动空间变量的条件模拟提供了一种计算程序。在一些支撑上测到了地震动的部分时程，这些时程是具有预定义演化功率谱密度特征的零均值非平稳随机过程。为了对其他支撑上的未知地震动时程进行条件模拟，Kriging方法首先对包含零均值高斯变量的随机向量进行简单条件模拟，并导出了具有演变功率谱密度矩阵特征的多振荡过程和多振荡过程的傅里叶系数，以及并衍生出的协方差矩阵。应用Kriging方法形成傅里叶系数的随机向量并进行傅里叶逆变换，可以模拟出未知的非平稳地震动时程。最后选用一个数值计算实例来验证该计算程序的功能，结果表明该程序能够确保形成无偏的时域相关性函数，尤其是未知时程和已知时程之间的互相关。该程序最终在香港青马大桥上成功利用有限的地震记录，生成了多支撑上的地面加速度时程。

Conditional simulation of spatially variable seismic ground motions based on evolutionary spectra

Authors: L. Hu, Y. L. Xu, Y. Zheng

Journal: Earthquake Engineering and Structural Dynamics，Volume 41, Issue 15,  pages 2125–2139, December 2012

Key words: conditional simulation; seismic ground motion;

nonstationary; evolutionary spectra

Abstract: This paper proposes a computational procedure for the conditional simulation of spatially variable seismic ground motions for long span bridges with multiple supports. The seismic ground motions, with part of their time histories measured at some supports, are regarded as zero-mean nonstationary random processes characterized by predefined evolutionary power spectral density. To conditionally simulate unknown seismic ground motion time histories at other supports, the Kriging method is first described briefly for the conditional simulation of a random vector comprised of zero-mean Gaussian variables. The multivariate oscillatory processes characterized by the evolutionary power spectral density matrix are then introduced, and the Fourier coefficients of the oscillatory processes and their covariance matrix are derived. By applying the Kriging method to the random vector of the Fourier coefficients and using the inverse Fourier transform, unknown nonstationary seismic ground motion time histories can be simulated. A numerical example is selected to demonstrate capabilities of the proposed simulation procedure, and the results show that the procedure can ensure unbiased time-varying correlation functions, especially the cross correlation between known and unknown time histories. The procedure is finally applied to the Tsing Ma suspension bridge in Hong Kong to generate ground accelerations at its multiple supports using limited seismic records.

原文链接：http://onlinelibrary.wiley.com/doi/10.1002/eqe.2178/abstract