基于杂交粒子群响应面的边坡稳定可靠性算法

针对可靠度指标β数学优化模型的理论不足,以及常规数学优化方法易陷入于局部最优解的问题,提出了基于杂交粒子群响应面的边坡可靠性算法。新方法以β的几何意义为基础,在对正值物理量、非正态、非独立随机变量预处理的基础上,补齐了附加约束条件,完整地给出了可靠性求解的数学优化模型,并澄清了β的正负取值问题。采用二次响应面法构造极限状态方程,并基于杂交粒子群算法搜索β的全局最优解。3个代表性案例结果证明:完善后的可靠性数学优化模型理论正确,对从数学优化角度求解可靠性问题进行了有效补充;基于杂交粒子群响应面的可靠性算法具有较好的全局搜索能力和较高的精度,与蒙特卡洛法的计算结果接近,但迭代次数明显减少,计算效率更高。

Study on reliability algorithm of slope stability based on response surface methodology and hybrid particle swarm optimization

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.