基于高斯混合模型和极限状态阈值随机性的概率地震需求分析

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (20) : 225-234.

论文

贾大卫，吴子燕，何乡

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Probabilistic seismic demand analysis based on a Gaussian mixture model and limit state threshold randomness

JIA Dawei,WU Ziyan,HE Xiang

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文章历史 +

摘要

传统概率地震需求分析普遍采用对数正态分布假定，且大多基于固定阈值衡量结构性能极限状态，这些简化方法很多时候与实际存在较大偏差。本文提出基于高斯混合模型(Gaussian mixture model ,GMM)的概率地震需求分析法。利用多维性能极限状态方程衡量结构破坏程度。基于增量动力分析法(increment dynamic analysis ,IDA)计算结构工程需求参数(engineering demand parameter ，EDP)，基于IDA曲线斜率划分结构阈值。不采用对数正态分布假定，利用GMM分别建立EDP和阈值的概率密度函数，将传统概率地震需求分析的三重积分拓展到五重积分，充分考虑阈值的随机性。利用蒙特卡洛(Monte Carlo ,MC)法求解，得到结构需求年平均超越概率。分别建立某钢筋混凝土框剪和框架结构作为研究对象，以最大层间位移角(MIDR)、最大层加速度(peak floor acceleration,PFA)作为EDP。研究表明：阈值具有较强的随机性，并且会随着破坏程度的提高而提高，忽略阈值随机性会导致结果出现较大偏差；与传统对数正态分布假定相比，基于GMM所得结构需求年平均超越概率偏小，对数正态分布假定会得到不准确的评估结果。
关键词：概率地震需求分析；多维性能极限状态；高斯混合模型；阈值随机性；增量动力分析

Abstract

Traditional probabilistic seismic demand analysis generally adopts the assumption of lognormal distribution, and most researchers adopt fixed threshold for limit state definition. These simplified strategies often deviate from the reality. This paper presents a probabilistic seismic demand analysis method based on Gaussian mixture model (GMM). Multi-dimensional performance limit state equation is used to measure the structure damage degree. Engineering demand parameter (EDP) is calculated based on the increment dynamic analysis (IDA). Structure thresholds under different seismic waves are obtained based on the slope of IDA curves. The probability density functions of EDP and threshold are established by GMM respectively without lognormal assumption. Traditional triple integral of probabilistic seismic demand analysis is extended to the quintuple integral, and the randomness of threshold is fully considered. Monte Carlo (MC) method is adopted, and the annual average exceeding probability of structural demand is obtained. A reinforced concrete (RC) frame-shear wall structure and a frame structure are established respectively as research objects. Maximum story displacement angle and maximum story acceleration are selected as two EDPs. The results show that: the randomness of the threshold is strong, and it will increase with the increase of the damage degree. Ignoring the threshold randomness will lead to large deviation of the results. The annual average exceeding probability of structural demand based on GMM is smaller, which indicates that the lognormal distribution assumption will get inaccurate evaluation results.
Key words: probabilistic seismic demand analysis; multi-dimensional performance limit state; Gaussian mixture model; threshold randomness; increment dynamic analysis

导出引用

贾大卫，吴子燕，何乡. 基于高斯混合模型和极限状态阈值随机性的概率地震需求分析[J]. 振动与冲击, 2022, 41(20): 225-234

JIA Dawei,WU Ziyan,HE Xiang. Probabilistic seismic demand analysis based on a Gaussian mixture model and limit state threshold randomness[J]. Journal of Vibration and Shock, 2022, 41(20): 225-234

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