基于β-二项分布的结构易损性分析

易损性曲线建立过程中受激励不确定性和结构参数不确定性的影响,会引起结构或构件观测结果的统计相关性。为此,本文提出基于β-二项分布的结构易损性分析方法。该方法根据性能量化指标阈值和Monte Carlo模拟确定震后观测结果,采用β-二项分布探讨震后观测值的统计相关性;结合对数回归模型,推导了改进β-二项分布的累积分布函数,计算结构失效概率;通过累积对数正态分布拟合易损性曲线,比较了观测失效样本数与观测失效概率统计相关性对易损性的影响,并与未考虑统计相关性的传统易损性曲线作对比。某8层钢筋混凝土框架-剪力墙结构的算例表明,考虑统计相关性的易损性较传统易损性偏大,且结构遭受8度以上地震作用时,考虑失效样本数统计相关性的易损性使预测结果更为保守,利于工程安全。

Structural fragility estimation with beta-binomial distribution

The uncertainty of seismic excitation and structural parameters in the process of establishing fragility curves leads to statistical dependence among observations,which has been neglected in past applications.In this paper,a new methodology based on beta-binomial distribution to calculate structural fragility is presented.Observations indicating the states (failure or survival) are confirmed via quantitative indicators threshold as well as Monte Carlo after each earthquake.Beta-Binomial distribution is addressed to discuss the statistical dependence among observations.Improved cumulative beta-binomial distribution function is derivation to calculate failure probability combined with logistic regression model.Seismic vulnerability curve can be fitted by means of cumulative lognormal distribution,which is compared with traditional fragility that of neglecting statistical dependence among observations and fragility curve considering statistical dependence among observed failure rates.A seat eight floors reinforced concrete frame-shear structure is used as an example to illustrate the approach:fragility curve considered statistical dependence is larger than traditional fragility,and the proposed method taken into account statistical dependence among failures will be better conservative to ensure the safety of structures.