联合极限状态下基于最大熵可靠度的易损性分析

考虑工程需求参数(EDP)的前四阶矩,提出基于最大熵可靠度理论的地震易损性分析方法。基于SAP2000建立钢筋混凝土框剪模型,选择最大层间位移角和最大层加速度衡量结构的联合性能极限状态,建立极限状态方程。不对EDP的分布进行人为假定,在不同峰值加速度(PGA)下计算两种EDP的前四阶矩,并作为约束条件,建立极限状态方程的最大熵概率密度函数,将多维积分转化为一维积分,通过最大熵二次四阶矩法计算失效概率,得到易损性曲线。采用基于对数正态分布假定的蒙特卡洛(MC)法进行对比,研究表明,基于最大熵法得到的易损性曲线与传统方法得到的易损性曲线基本重合,验证了本文所提方法的精度;通过最大熵概率密度函数简化积分,计算效率较高;在联合极限状态下,忽略不同EDP极限状态的相关性不利于工程安全。

Fragility analysis based on maximum entropy reliability under joint limit state

A seismic fragility analysis method based on maximum entropy reliability theory is proposed considering the first four moments of the engineering demand parameter (EDP).A reinforced concrete frame structure model is established based on SAP2000, two EDPs are selected to measure the joint limit state, and the performance-based limit state equation is established.The first four moments of the two EDPs are calculated under different peak ground accelerations (PGA) without the log-normal assumption to establish the maximum entropy probability density function of the limit state equation, the multi-dimensional integral is transformed into a one-dimensional integral, and the failure probability is calculated by the maximum entropy quadratic fourth moment method.A traditional Monte Carlo (MC) method based on the assumption of lognormal distribution is used for comparison.The research shows that:The fragility curves obtained by the maximum entropy method coincide with traditional methods, which verifies the accuracy of the proposed method.The maximum entropy probability density function is used to simplify the integration and the calculation efficiency is high.In the joint limit state, ignoring the correlation of limit states under different EDPs is not conducive to engineering safety.