基于Copula函数的水平和竖向地震动强度参数相关性分析  

CORRELATION ANALYSIS OF INTENSITY MEASURES OFHORIZONTAL AND VERTICAL GROUND MOTIONS BASED ONCOPULA FUNCTION

作　　者：王晓磊 王浠铭 阎卫东 吕大刚[3] 包旭 WANG Xiao-lei;WANG Xi-ming;YAN Wei-dong;LYU Da-gang;BAO Xu(School of Civil Engineering,Shenyang Jianzhu University,Shenyang 110168,China;Hebei Key Laboratory of Earthquake Disaster Prevention and Risk Assessment,Sanhe 065201,China;School of Civil Engineering,Harbin Institute of Technology,Harbin 150090,China)

机构地区：[1]沈阳建筑大学土木工程学院,沈阳110168 [2]河北省地震灾害防御与风险评价重点实验室,三河065201 [3]哈尔滨工业大学土木工程学院,哈尔滨150090

出　　处：《工程力学》2023年第5期79-92,共14页Engineering Mechanics

基　　金：国家自然科学基金项目(51908379);河北省地震灾害防御与风险评价重点实验室开放基金项目(FZ213206);辽宁省科技厅科研项目(2019JH2/10300054);沈阳市科技局科研项目(1900329)。

摘　　要：水平和竖向地震动强度参数的相关性是水平和竖向地震动选取等研究的重要基础。该文从PEER NGA-West2数据库中选取了975组地震动记录,基于水平向地震动四种合成方法,计算合成后的水平向地震动强度参数和竖向地震动强度参数。利用K-S检验、AIC和BIC准则,确定了水平和竖向地震动强度参数的最优边缘分布。采用Pearson线性相关系数、Kendall秩相关系数和Spearman秩相关系数,分别计算了水平和竖向地震动强度参数相关性度量指标。利用AIC和BIC准则,确定了水平和竖向地震动强度参数最优Copula函数。综合最优边缘分布和最优Copula函数,建立了水平和竖向地震动强度参数联合分布模型,给出了以水平向地震动强度参数为条件的竖向地震动强度参数预测均值,并且研究了不同场地类别对其相关性结果的影响。研究表明:水平和竖向地震动强度参数的边缘分布以广义极值分布为主;在四类地震动强度参数中,与时程相关的地震动强度参数相关性最高;Copula函数是一个建立水平和竖向地震动强度参数的联合分布模型的有效工具;基于四种方法合成的水平地震动强度参数与竖向地震动强度参数间的相关性基本相同;不同场地类别下水平和竖向地震动强度参数间的相关性差别不大。The correlation of horizontal and vertical ground motion intensity measures(GMIMs)is an important basis for some researches such as the selection of horizontal and vertical ground motions,etc.Thusly,975 groups of ground motions are selected from the PEER NGA-West2 database and combined horizontal GMIMs via four combination methods and vertical GMIMs are calculated.The optimal marginal probability distributions of horizontal and vertical GMIMs are respectively determined via the K-S test,AIC criterion and BIC criterion.The correlation coefficients between horizontal and vertical GMIMs are respectively determined via Pearson linear correlation coefficient,Kendall’s rank correlation coefficient and Spearman’s rank correlation coefficient.Based on AIC criterion and BIC criterion,the optimal Copula function of horizontal and vertical GMIMs is determined.The joint probability model of horizontal and vertical GMIMs is established using the obtained optimal marginal probability distributions and optimal Copula function,and the predicted mean of vertical GMIMs conditional on horizontal GMIMs are obtained and the influences of different site types on their correlation are studied.The results reveal that:the generalized extreme-value distribution is more preferable for marginal probability distributions of horizontal and vertical GMIMs;the correlation of intensity measures related to time history is higher than those of three other intensity measures;the Copula function is a useful tool for modeling the joint probability distribution model of horizontal and vertical GMIMs;the correlation of horizontal GMIMs obtained via four combination methods and vertical GMIMs is almost identical;and there is little difference for the correlation between horizontal and vertical GMIMs under different site types.

关 键 词：水平和竖向地震动 相关性 COPULA函数 地震动强度参数 水平分量合成 联合分布 

分 类 号：P315.9[天文地球—地震学]