文章提出基于贝叶斯推理的结构非线性概率模型参数估计方法,结合非线性参数的后验概率分布估计结果,实现结构在动力荷载作用下的失效概率预测.利用结构实测加速度响应作为输入,构建贝叶斯推理的似然函数,采用过渡马尔可夫蒙特卡洛(transitional Markov chain Monte Carlo,TMCMC)算法估计非线性概率模型参数的后验概率分布.当模型参数的后验概率分布被计算之后,利用更新后的参数后验概率分布作为输入,通过随机抽样算法预测结构在动力荷载作用下的失效概率.为验证方法的可行性,对地震荷载作用下的5层钢框架结构进行数值模拟,通过钢框架结构的缩尺振动台试验进一步验证该方法的有效性.研究结果表明:该方法能够准确实现非线性模型参数的后验概率密度计算,能够对结构在地震荷载下的失效概率进行有效预测.
Abstract
A Bayesian inference-based method was proposed for parameter estimation of structural nonlinear probabilistic model,and the estimated posterior probability distributions of nonlinear parameters were further used for structural failure probability prediction subjected to dynamic load.The measured accelerations were used as input to construct the likelihood function of Bayesian inference.The transitional Markov chain Monte Carlo(TMCMC)algorithm was performed to estimate the posterior probability distributions of structural non-linear probabilistic model parameters.Once the posterior probability distributions of the nonlinear parameters were calculated,the posterior distributions could then be further used as input to predict the failure probabili-ty of structures subjected to dynamic load by stochastic sampling algorithm.To validate the feasibility of the proposed method,the numerical simulation on a five-story steel frame structure under earthquake excitations was conducted.Then the proposed method was further verified through the scaled shaking table test of the steel frame structure.The results indicate that the proposed method can accurately estimate the posterior probability density of nonlinear model parameters and effectively predict the failure probability of structures due to dynamic load.
关键词
结构非线性/概率模型/贝叶斯推理/后验概率分布/失效概率
Key words
structural nonlinearity/probabilistic model/Bayesian inference/posterior probability dis-tribution/failure probability
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