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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。
Determining the most probable failure point (MPPIR) of inverse reliability is the core issue in the structural inverse reliability analysis, and the most widely used is the modified mean method (AMV) and its improved method. However, when the non-linear function of the non-convex or non-concave non-concave function, AMV prone to periodic oscillation and other non-convergence problems. Based on the existing AMV improvement methods, an improved MPPIR search algorithm is proposed by controlling the search direction and the step length in the iterative process, and a specific calculation procedure is given in combination with the inaccurate one-dimensional search method. The numerical example shows that the proposed algorithm has better convergence than AMV, and does not need optimization method to determine the optimal step size compared with arc-length search method. For non-convex non-concave function and highly nonlinear function Functions have good convergence.