基于BOX-COX变换的桥梁结构地震易损性分析

Seismic vulnerability analysis of bridge structure based on BOX-COX transformation

云图法作为理论易损性曲线计算的主要方法之一,其为简化计算所作的线性、正态性和同方差性假设很多时候与实际存在偏差。为此,引入BOX-COX变换,并结合蒙特卡洛抽样,提出了一种既不需增加非线性时程分析次数,又不受云图法三个基本假设限制的易损性分析方法。并以一座预应力混凝土三跨连续梁桥为例,分别以决定系数、核密度估计曲线以及等级相关系数的显著性水平为评价指标,对基于BOX-COX变换的地震易损性分析方法的计算结果与云图法进行了分析比较,验证了该方法的有效性。研究结果表明:引入BOX-COX变换可使概率地震需求模型的线性程度提高,正态性改善,异方差性消除,保证了易损性计算结果的准确性;当概率地震需求模型存在异方差性时,使用云图法将导致结构易损性曲线计算结果的失真,且极限状态对应的损伤程度越高,该极限状态下的易损性曲线偏离实际越明显。

The cloud chart method is one of the main methods for calculating theoretical vulnerability curves,but its assumptions of linearity,normality and homoscedasticity to simplify calculation often deviate from the reality.Here,in order to solve this problem,a new vulnerability analysis method was proposed by combining BOX-COX transformation and Monte Carlo sampling technique.It was shown that this method doesn’t increase the number of nonlinear time history analysis,and it doesn’t need to satisfy 3 basic assumptions of the cloud chart method.A 3-span pre-stressed concrete continuous girder bridge was taken as an example to verify the effectiveness of the proposed method.The calculation results obtained with the proposed method were compared to those with the cloud chart method taking significance levels of determination coefficient,kernel density estimation curve,and rank-correlation coefficient as the evaluation indexes.Results showed that BOX-COX transformation can improve linearity,normality and homoscedasticity of the probabilistic seismic demand model(PSDM)to ensure the correctness of vulnerability analysis results;when PSDM has heteroscedasticity,using the cloud chart method can cause distortion of structural vulnerability curve calculation results,and the higher the damage degree corresponding to the limit state,the more obvious the vulnerability curve deviates from the reality.