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综合考虑结构物理参数的随机性和响应的统计相关性,提出了基于对数回归模型的结构易损性分析方法。以蒙特卡罗模拟和随机时程分析法考虑物理参数的随机性,采用β-二项分布探讨响应统计相关性,并建立对数回归模型计算结构易损性。以某一钢筋混凝土两跨连续梁高速公路桥为算例,根据设计图获取其物理参数作为均值,选取合适的标准差做蒙特卡罗模拟,随机采样得到参数样本,通过随机时程分析获得最大响应样本,利用矩估计、最小二乘分别求得β-二项分布和对数回归模型未知参数,最终获得各等级破坏状态下的易损性曲线,并与提出的基于累积极限状态阈值的结构易损性相比较。结果表明:所提出的易损性分析方法,能够达到对结构易损性的保守估计,保证预测结果的合理性,为检测桥梁构件是否过度老化或意外损坏提供理论依据。
Considering the randomness of structural physical parameters and the statistical correlation of response, a structural vulnerability analysis method based on logarithm regression model is proposed. The randomness of physical parameters was considered by Monte Carlo simulation and stochastic time-history analysis. The β-binomial distribution was used to investigate the statistical correlation and the logarithmic regression model was used to calculate the structural vulnerability. Take a reinforced concrete two-span continuous beam freeway bridge as an example, according to the design drawings to obtain its physical parameters as the mean, select the appropriate standard deviation as Monte Carlo simulation, random sampling parameters, obtained by stochastic time-history analysis of the maximum Response samples, the unknown parameters of β-binomial distribution and logarithm regression model were obtained by moment estimation and least squares respectively, finally the vulnerability curves of each grade were obtained and compared with the proposed structure based on cumulative limit state threshold Vulnerability comparison. The results show that the proposed vulnerability analysis method can achieve a conservative estimate of the structural vulnerability and ensure the reasonableness of the prediction results, providing a theoretical basis for detecting whether the bridge components are overly aged or accidentally damaged.