结构失效面上的复合蒙特卡罗方法

Composite Monte-Carlo method on structural failure hyperplane

为了提高采用蒙特卡罗方法计算结构可靠度的效率和精度,提出了一种部分解析的失效面上的复合蒙特卡罗方法.通过对结构极限状态方程中某一变量或变量表达式的解析求解,将抽样点投影到结构失效面上.结合重要抽样方法,分别导出了原始空间(X空间)和旋转的正交正态空间(V空间)的算法.将抽样点投影到失效面上,不仅保证了抽样的有效性,而且使算法对高度非线性失效面具有更强的适应性.解析解的引入,降低了抽样维数,减小了计算结果的随机性,提高了计算精度.理论推导和数值计算证明了该方法的有效性.

A partly analytical composite Monte-Carlo method on structural failure hyperplane was proposed to efficiently and accurately calculate structural reliability. Samples were mapped into the structural failure hyperplane by separating and evaluating a random variable or an expression of the limit state function ana- lytically, and then structural failure probability was estimated in combination with importance sampling method. Approaches for the original X-space and the rotated orthogonal normal V-space were presented re- spectively. The projection of samples into the structural failure hyperplane guarantees the sampling availability and makes the proposed method more suitable for highly nonlinear limit state function. The adoption of analytical resolution reduces the sampling dimension and makes the result more accurate and stable. Theoretical analysis and numerical examples proved the efficiency of the method.