代表点数目对概率密度演化方法分析精度的影响

Effects of the Number of Representative Points on the Analysis Accuracy of the Probability Density Evolution Method

基于物理随机地震动模型和切球选点法生成3组不同容量地震动样本,以此作为外激励输入,采用概率密度演化方法分别对结构进行随机地震反应分析,并对分析结果进行比较,以研究代表点数目对分析精度的影响.数值分析结果表明,基于切球选点法生成的少量代表样本能够对目标总体的一、二阶统计特性进行较为准确地估计;当样本容量较小时,结构随机动力响应在各时刻的概率分布分析结果具有一定的误差.因此,应根据随机动力系统中随机变量的数目、所采用的选点方法以及预期的计算精度合理确定概率密度演化方法中样本的容量.

3 sets of random ground motions with different-size samples were generated based on a physical stochastic ground motion model and a strategy of selecting points via sphere of contact.Then the stochastic response analysis of a model structure subjected to the generated ground motions was carried out with the probability density evolution method（PDEM）.Through comparison of the results from the stochastic seismic response analysis,the effects of the number of representative points on the analysis accuracy of the PDEM were investigated.Numerical results show that a relatively small number of representative points selected under the strategy of sphere of contact yield fairly accurate results of the 1st-and 2nd-order statistical characteristics of structural responses.At the same time,it is pointed out that a small sample size may lead to a certain analytical errors of the response probability distribution at each time point.Therefore,the number of representative points in the PDEM should be reasonably determined according to the number of random variables of the related stochastic dynamic system,the method of selecting representative points and the expected calculation accuracy.