基于高斯混合模型的非规则连续梁桥概率地震需求分析

Probabilistic seismic demand analysis of irregular continuous girder bridge based on Gaussian mixture modeling

摘要:

为真实反映结构地震需求均值及方差随地震动强度的非线性变化,提出了一种基于高斯混合模型(Gaussian mixture model,GMM)的概率地震需求模型。该模型基于统计学原理,对地震需求及地震动强度的联合概率密度分布和条件概率分布进行估计,然后采用高斯混合回归（Gaussian mixture regression,GMR）建立。以一座3跨30 m的连续T梁桥为例,对该模型的特点进行了分析研究,并与传统的对数线性回归需求模型进行对比。结果表明:地震荷载作用下,受桥台及挡块对梁体位移的限制作用、台后填土及墩柱屈服的影响,桥梁结构状态具有显著的阶段性特征,地震需求与地震动强度的联合分布也因此表现出明显的多峰特性,GMM可实现对该联合分布的较好拟合；相较于对数线性回归模型,基于GMM建立的概率地震需求模型反映了地震需求均值及方差的非线性变化,拟合更优,因而计算得到的易损性曲线与对数线性回归模型存在一定差异；地震需求及地震动强度的联合概率分布的混合成分、基于GMM的地震需求模型均值及方差与结构状态的阶段性特征有着紧密联系。

Abstract:

To capture nonlinear variations in the mean and variance of seismic demand relative to seismic intensity measures, this study proposes a probabilistic seismic demand model based on a Gaussian mixture model (GMM). Grounded in statistical principles, the model estimates the joint and conditional probability distributions of seismic demand and intensity, subsequently established via Gaussian mixture regression (GMR). Using a 3-span, 30-meter continuous T-beam bridge as a case study, we analyze the model′s characteristics and compare them with traditional log-linear regression approaches. Results indicate that structural states exhibit distinct stage-dependent characteristics due to constraints from abutments and shear keys on girder displacement, coupled with backfill soil effects and pier column yielding. Consequently, the joint distribution of seismic demand and intensity displays significant multimodality, which the GMM effectively captures. Owing to its capacity to characterize nonlinear variations in seismic demand statistics, the GMM-based model demonstrates superior fitting performance, yielding fragility curves that differ discernibly from those generated by log-linear regression. Furthermore, mixture components of the joint probability distribution—alongside the mean and variance of the GMM-based model—show strong correlations with the structure′s stage-dependent behavioral phases.