多维性能极限状态下概率地震需求分析的多元相关核密度估计法  

Probabilistic seismic demand analysis based on multivariate correlated kernel density estimation under multidimensional performance limit states

作　　者：贾大卫 吴子燕[1] 何乡 JIA Da-wei;WU Zi-yan;HE Xiang(School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Xi'an 710129,China)

机构地区：[1]西北工业大学力学与土木建筑学院,陕西西安710129

出　　处：《振动工程学报》2022年第6期1299-1310,共12页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51278420,51708545);西北工业大学研究生创意创新种子基金项目(ZZ2019121)。

摘　　要：本文不对工程需求参数(EDP)的分布类型进行人为假定,提出基于多元相关核密度估计的概率地震需求分析法。在带宽矩阵和多元高斯核函数中分别引入相关系数,并分别采用三种相关系数描述相关性,将传统核密度估计拓展到可以考虑随机变量相关性的多元核密度估计。基于SAP2000建立某钢筋混凝土框剪结构,选择最大层间位移角、最大层加速度衡量多维性能极限状态。在不同峰值地面加速度(PGA)下建立基于多元相关核密度估计的概率地震需求模型,并给出基于蒙特卡洛(MC)模拟的地震需求公式,得到结构需求的年平均超越概率。采用传统基于多维对数正态分布假定的地震风险概率法和不考虑EDP相关性的核密度估计进行对比,研究表明:与传统的多维对数正态分布假定相比,基于相关多元核密度估计的结构需求年平均超越概率偏大,而不考虑相关性的多元核密度估计所得年平均超越概率偏小;不同相关系数会影响到年平均超越概率的大小,其中Pearson相关系数影响最大,Spearman相关系数次之,Kendall相关系数最小。A probabilistic seismic demand analysis method based on multivariate correlated kernel density estimation is proposed without any assumption on the distribution of engineering demand parameters(EDPs).Three different correlation coefficients are used to describe the correlation respectively,and the traditional kernel density estimation is extended to multivariate correlated kernel density estimation based on the bandwidth matrix and multivariate Gaussian kernel function.A reinforced concrete frame shear wall structure is established based on SAP2000.The maximum inter-story drift ration and peak floor acceleration are selected to measure the multidimensional performance limit states.The probabilistic seismic demand model based on multivariate correlated kernel density estimation is established,and the structural demand annual average exceeding probability is obtained through Monte Carlo(MC)simulation.Traditional method based on multidimensional lognormal distribution assumption and the uncorrelated kernel density estimation are adopted for comparison.The research shows that:comparing with the traditional lognormal distribution assumption,the structure demand annual average exceeding probability based on the multivariate correlated kernel density estimation is larger,and the result of uncorrelated multivariate density estimation is smaller.Different correlation coefficients will affect the annual average exceeding probability,among which Pearson correlation coefficient is the most influential,Spearman correlation coefficient is the second,and Kendall correlation coefficient is the least.

关 键 词：概率地震需求分析 多元相关核密度估计 多维性能极限状态 框架-剪力墙结构 

分 类 号：TU311.2[建筑科学—结构工程] O324[理学—一般力学与力学基础]