主余震型地震动过程的降维模拟

Dimension-reduction simulation of main aftershock type ground motion process

该研究建议了主余震型地震动过程的降维模拟方法。首先,在非平稳地震动的演变功率谱密度(evolutionary power spectrum density,EPSD)模型的基础上,提出了演变功率谱密度模型参数的识别方法,并针对实测主余震地震动记录对峰值加速度、场地土的卓越圆频率和阻尼比以及调制函数参数等模型参数进行了识别;其次,通过拟合优度检验,得到了这些参数的最优边缘分布。然后,利用Copula理论对主余震参数之间的相关结构进行分析,得到了主震参数条件下对应余震参数的条件均值,并通过多项式拟合建立了主余震参数之间的实用计算公式。最后,结合谱表示-随机函数方法,建立了主余震型地震动的降维模型,生成了主余震型地震动的代表性时程。此外,通过与实测主余震记录的反应谱和傅里叶幅值谱的对比分析,验证了该模型的工程适用性。该研究工作以期为主余震型地震动作用下工程结构的随机动力反应分析与可靠度评估提供合理基础。

In this paper,a dimension reduction method was proposed to simulate the main and aftershocks process.First,based on the evolutionary power spectrum density(EPSD)model of non-stationary ground motions,an identification method for the parameters of the EPSD model was proposed,and the predominant circular frequency and damping ratio of the site soil,the peak ground acceleration and modulation function parameters were identified according to the measured main and aftershock records.Then,the optimal marginal distributions of these parameters were obtained through the goodness of a fit test.Next,the correlation structure between the main and aftershock parameters was analyzed by utilizing the Copula theory,and the conditional mean of the aftershock parameters corresponding to that of main-shock was obtained,and the practical calculation formulas between the main shock parameters and the aftershock parameters was established by polynomial fitting.Finally,incorporating the spectral representation-random function method,the dimension reduction model of the main aftershock type ground motion was built,and the representative time histories of the main aftershock type ground motion were generated.In addition,the applicability of the model was verified by comparing with the response spectrum and Fourier amplitude spectrum of the measured main and aftershock records.This paper aims at providing a reasonable basis for the random dynamic response analysis and reliability evaluation of engineering structures under the main aftershock ground motions.