关键词: 可靠度指标, 数学优化, 二次响应面法, 杂交粒子群算法, 边坡

Abstract: To solve the theory deficiency of reliability index β in mathematical optimization model and the problem that the conventional mathematical optimization method is easily trapped in the local optimal solution, a slope reliability algorithm based on hybrid particle swarm optimization and response surface methodology is proposed. This algorithm is based on the geometric meaning of β. After preprocessing positive physical variables, non-normal variables and independent random variables, the additional constraints are added, and the mathematical optimization model for reliability solution is given. The positive and negative values of β are clarified. The quadratic response surface method is used to construct the limit state equation, and the global optimal solution of β is searched based on hybrid particle swarm optimization. The results of three representative cases prove that the theory of reliability mathematical optimization model is correct, which is an effective supplement to solve reliability problems. The algorithm can do better global search. Its calculation result is close to that of Monte Carlo method, but the iterative times are obviously less and the calculation efficiency is higher.

Key words: reliability index, mathematical optimization；quadratic response surface methodology；hybrid particle swarm optimization, slope