关键词: 多维积分, 曲线拟合法, 加权余量法, 最大熵法, 非线性数值模拟, 可靠性分析, 参数随机变异

Abstract: A high efficient direct integration method is proposed for evaluating the variation effect of nonlinear numerical simulation results of geomechanics subject to multi-random parameters. In this method, taking the interested results as stochastic implicit response variables, firstly the integration points are determined by the multidimensional integration theory and direct integration reliability analysis method. Then the sample points are calculated by using the numerical simulation software; and then high order probability moments of response functions are evaluated by integration subroutine; at last the numerical probability density function of response variable then the confidence interval is obtained from several proposed method including curve fitting method, the weighted residual method and the maximum entropy distribution solver software developed by the authors. The numerical examples show that this method has higher accuracy and the computational efforts are reduced.

Key words: multidimensional integration, curve fitting, weighted residual method, maximum entropy method, nonlinear numerical simulation, reliability analysis, random variation of parameters