基于改进点估计法的结构随机动力地震反应概率密度演化

摘要

为了获得结构反应概率密度随时间的变化规律，将改进的点估计法、最大熵原理与随机动力学的概率密度演化理论相结合，提出了基于统计矩信息的结构非线性随机动力反应概率密度演化分析方法。以一栋按我国规范设计的钢筋混凝土框架结构为研究对象，选取结构在地震作用下的顶层位移和整体地震损伤指数作为反应参数，并考虑结构参数的不确定性，用本文提出的方法进行了地震作用下结构的非线性随机动力反应的概率密度演化分析及参数灵敏度分析，结果表明：钢筋屈服强度、结构的阻尼、混凝土容重对结构的位移反应影响较为明显，灵敏度超过10％。%In order to obtain the law of probability densities of structural responses varying with time, a new moment-based approach for analysis of probability density evolution of nonlinear stochastic dynamic responses of structures was developed,by combining an improved point estimation method (IPEM)with the maximum entropy theory and the probability density evolution theory for stochastic dynamics of structures. The proposed method was then used to perform probabilistic density evolution analysis and parameter sensitivity analysis of a reinforced concrete (RC ) frame structure designed according to Chinese codes,selecting the top displacement and global seismic damage index of the structure under earthquake as response parameters,and taking into account the uncertainty of structural parameters. The results show that the steel yield strength,the structural damping ratio,and concrete gravity density have dominant influences on structural displacement,with a sensitivity of more than 10%.