结构逆可靠度最可能失效点的改进搜索算法

IMPROVED SEARCH ALGORITHM FOR MOST PROBABLE POINT OF STRUCTURAL INVERSE RELIABILITY

确定逆可靠度最可能失效点(MPPIR)是结构逆可靠度分析的核心问题,以改进均值法(AMV)及其改进方法应用最广泛。但当功能函数非线性程度较高或为非凸非凹函数时,AMV易出现周期振荡等不收敛问题。以现有的AMV改进方法为基础,通过迭代过程中控制搜索方向和步长,提出一种MPPIR的改进搜索算法,并结合不精确一维搜索方法给出了具体的计算流程。数值算例分析表明:提出的算法与AMV相比具有更好的收敛性,与弧长搜索法相比不需要采用优化方法确定最优步长,且对于非凸非凹功能函数以及高度非线性功能函数都具有良好的收敛性。

Identifying the most probable point of inverse reliability （MPPIR） is the principle problem in structural inverse reliability analysis. The advanced mean value method （AMV） is widely used in the MPPIR search. However, the AMV method may fail to converge for non-concave and non-convex or high nonlinear performance functions. Based on several improved methods of the AMV, a new MPPIR search algorithm by controlling the search direction and step size during the iteration is proposed in this paper. The calculation procedure combined with inexact one-dimensional search method is also demonstrated. Numerical results show that the proposed algorithm has better convergence compared with the AMV. Further, the proposed algorithm is much easier than the arc search method because the optimization process for step size is not needed.