基于Copula模型的多维地震动参数相关性分析

Correlation Analysis of Multi-dimensional Ground Motion Intensity Parameters Based on Copula Theory

地震动常被拆解为两个水平向分量(x、y)和一个竖向分量(z)。为探寻Copula模型在多维地震动参数相关性分析中的应用可行性,从太平洋工程抗震研究中心选取1500组实测地震动,并从强度、持时和频谱3个方面筛选出12组地震动参数用于表征分析地震动不同向分量间的相关性。首先,计算得到u-v(u、v为地震动两个水平向分量和一个竖向分量中的任意两个分量,u、v=x,y,z)向分量间12组地震动参数的Pearson线性相关系数、Kendall秩相关系数和Spearman秩相关系数。其次,结合柯尔莫哥洛夫-斯米尔诺夫(Kolmogorov-Smirnov,K-S)检验和贝叶斯信息准则(the Bayesian information criteria,BIC)建立了12组地震动参数在x、y、z向分量上的最优概率模型。最后,利用BIC准则确定了u-v向分量间地震动参数的最优Copula函数,建立了u-v向分量间12组地震动参数的联合概率函数。结果表明:12组地震动参数相关性较好,但反应谱峰值对应周期参数在u-v向分量间的相关性和阿里亚斯强度参数在x-z向、y-z向分量间的相关性较低;通过Copula理论可以较为精准的建立u-v向分量间地震动参数的联合概率函数;在给定u向分量地震动参数条件下,得到的Copula条件均值和条件随机数能够用于v向分量地震动参数预测。

Ground motion is often broken down into two horizontal components(x,y)and one vertical component(z).In order to explore the feasibility of the application of Copula model in the correlation analysis of multi-dimensional ground motion parameters,1500 sets of measured ground motions were selected from the Pacific Engineering Seismic Research Center and 12 groups of ground motion parameters were selected from intensity,duration and spectrum to characterize and analyze the correlation between different directional components of ground motion.Firstly,Pearson linear correlation coefficients,Kendall rank correlation coefficients and Spearman rank correlation coefficients of 12 groups of ground motion parameters in the u-v(u and v are any two components of two horizontal components and one vertical component of ground motion,u,v=x,y,z)direction were calculated.Secondly,the optimal probability models of 12 groups of ground motion parameters in x-direction,y-direction and z-direction were established based on Kolmogorov-Smirnov(K-S)test and the Bayesian information criteria(BIC).Finally,the optimal Copula function of ground motion parameters between u-v components was determined by BIC criterion,and the joint probability function of 12 groups of ground motion parameters between u-v components was established.The results show that the correlation of ground motion parameters in the 12 groups is good,but the correlation of peak response spectrum corresponding period parameters in the u-v direction and the correlation of arias intensity parameters in the x-z direction and y-z direction is low.The joint probability function of ground motion parameters between u-v direction components can be established accurately by Copula theory.Given the ground motion parameters of u-direction component,the Copula conditional mean and conditional random number obtained can be used to predict the ground motion parameters of v-direction component.