基于概率密度演化的基础隔震结构随机响应分析

针对抗震结构和基础隔震结构，应用概率密度演化方法对其进行多遇地震作用下的线性随机响应分析。通过引入工程地震动物理随机函数模型，采用数论选点法对多维外荷载随机变量进行离散代表点的生成并求得其赋得概率，利用离散代表点合成地震动加速度时程样本作为输入结构的随机激励，对于每条地震波，相当于对结构进行确定性动力反应分析。在求得结构响应及其相关导数后，应用TVD差分格式求解广义概率密度演化方程即可得到所求响应的时变概率密度及其演化。结果表明：基础隔震结构在随机地震作用下相比抗震结构具有良好的减震性能，隔震层的设置能够减小结构位移响应的标准差，减少了结构响应的离散型；概率密度演化方法不仅能够给出结构响应的二阶统计矩，还能全面地反映结构响应的时变概率信息，位移响应的概率密度函数分布不服从正态分布或其他常用分布，且随着时间演化。

Random response analysis of base-isolated structures based on probability density evolution

The probability density evolution method was used to analyze the linear random responses of seismic structures and base-isolated structures under frequent earthquakes. The physical random function model was introduced to select disperse representative points from multi-dimensional random variables by utilizing the number theory collocation method. Then the discrete representative points were used to synthesize seismic acceleration time-history samples as random excitation. After obtaining the structural response and its related derivatives, the TVD difference scheme was applied to solve the generalized probability density evolution equation, thus obtaining the time-varying probability density of the solved response and its evolution. The results showed that the base-isolated structure has better shock absorption performance than the anti-seismic structure under random earthquakes. The isolation layer can reduce the standard deviation of structural displacement response and the discretization of structural response. The probability density evolution method can not only give the second-order statistical moment of structural response, but also fully reflect the time-varying probability information of structural response. The probability density function distribution of displacement response, which evolves with time, does not obey normal distribution or other common distribution.