基于拒绝抽样算法的结构体系可靠度更新  

SYSTEM RELIABILITY UPDATING BASED ON THE REJECTION SAMPLING ALGORITHM

作　　者：马君明 李惠 兰成明[3] 刘彩平 MA Jun-ming;LI Hui;LAN Cheng-ming;LIU Cai-ping(National Center for Materials Service Safety,University of Science and Technology Beijing,Beijing 100083,China;School of Civil Engineering,Harbin Institute of Technology,Harbin,Heilongjiang 150090,China;School of Civil and Resource Engineering,University of Science and Technology Beijing,Beijing 100083,China)

机构地区：[1]北京科技大学国家材料服役安全科学中心,北京100083 [2]哈尔滨工业大学土木工程学院,黑龙江哈尔滨150090 [3]北京科技大学土木与资源工程学院,北京100083

出　　处：《工程力学》2022年第3期11-22,63,共13页Engineering Mechanics

基　　金：国家重点研发计划项目(2017YFC0806100);国家自然科学基金项目(51878044)。

摘　　要：该文着重研究基于观测信息的结构体系可靠度更新模型及其拒绝抽样算法。基于Bayesian理论建立考虑观测信息的结构体系失效概率更新模型,根据观测信息事件类型建立不等式和等式观测信息条件下随机变量的似然函数并推导其后验概率密度函数;基于观测信息域确定随机变量后验样本的拒绝抽样策略,探究拒绝抽样算法的抽样效率,推导更新后结构体系失效概率估计值及其标准差的计算公式;将上述方法应用于刚架结构发生塑性失效时体系可靠度更新计算。研究表明:考虑观测信息的结构体系条件失效概率更新模型可转化为随机变量后验概率密度在失效域上的积分,构造满足观测信息域的先验样本作为随机变量后验样本的抽样策略是可行的,该抽样策略可以处理多随机变量、多观测信息条件下结构体系可靠度更新;与抗力相关随机变量检测值增大及验证荷载值提高均可以降低更新后结构体系的失效概率,与抗力相关的随机变量还需控制其检测误差的标准差,以降低观测信息的不确定性。It studies the updating model of the reliability for structural systems considering the observation information and the corresponding rejection sampling strategy.The updating model of failure probabilities for structural systems is established based on the Bayesian theory.According to the type of observation information(i.e.,inequality observation information and equality observation information),the likelihood function and the posterior probability density function for random variables are derived.The rejection sampling strategy of posterior samples for random variables is determined based on the observation information domain,and the efficiency of the rejection sampling strategy is illustrated.The estimated value and its standard deviation of updated failure probabilities for structural systems are formulated.To verify the availability of the proposed method,the failure probabilities of plane frames are updated based on the plastic theory considering various observation information.The results indicate that the conditional failure probability of the structural systems considering the observation information is the integral of the posterior joint probability density of random variables in the failure domain.The strategy is feasible for selecting the prior samples which satisfy the constructed observation information domain as the posterior samples for random variables.The proposed sampling strategy can be used to update the reliability of structural systems with multiple random variables and multiple types observation information.The updated failure probabilities of structural systems decrease as the detection values of the resistance-related random variables increase or as the proofed loads increase.To reduce the uncertainties of the observation information,standard derivations of detection error for resistance-related random variables should be well controlled.

关 键 词：结构体系 可靠度更新 拒绝抽样 Bayesian理论 观测信息 不确定性 

分 类 号：TU311.2[建筑科学—结构工程]