摘要
采用传统极限平衡法进行边坡可靠度分析时,不可避免会遇到一个问题,即边坡功能函数形式的高度非线性以及隐含性.对于隐式功能函数,传统的求解方法是通过对功能函数进行多次迭代,从而得到安全系数值.但是由于功能函数的形式较为复杂,导致迭代计算的过程变得尤为繁琐且效率低下.鉴于传统边坡可靠度分析中存在的安全系数计算繁琐耗时的问题,提出一种基于粒子群优化(PSO)算法的自动采样Kriging代理模型方法,该方法可以代替功能函数的作用进行安全系数的求解.首先用拉丁超立方抽样方法(LHS)选取少量土体参数组,并通过极限平衡法求出对应的安全系数,将土体参数组和安全系数作为初始样本建立Kriging模型;其次由粒子群优化算法将最有期望改善模型拟合精度的样本点添加到样本集合中,以逐步迭代提升Kriging模型的计算精度;最后集合经典蒙特卡洛模拟(MCS)获得边坡的破坏概率.通过一个双层的土质边坡算例分析,证明了该方法可以实现准确高效的安全系数计算,尤其是在安全系数计算量十分庞大的情况下可以大大节省计算时间,是一种有效的边坡工程稳定可靠度分析方法.
When the traditional limit equilibrium method is used to analyze the slope reliability,there is inevitably a problem,that is,the high nonlinearity and impliedness of the performance function.For the implicit slope performance function,the traditional solution method is to obtain the safety factor value by iterating the performance function multiple times.However,due to the complicated form of the performance function,the process of iterative calculation becomes particularly cumbersome and inefficient.In view of the cumbersome and time-consuming calculation of the safety factor in the traditional slope reliability analysis,an adaptive sampling Kriging model based on particle swarm optimization algorithm is proposed in this paper.This method can replace the performance function to solve the safety factor.Firstly,the Latino hypercube sampling method is used to select the appropriate number of geotechnical parameters and the corresponding safety factor is solved by the limit equilibrium method.The geotechnical parameters and safety factor are used as the initial samples to establish the Kriging model.Secondly,the particle swarm optimization algorithm adds the sample points that are most expected to improve the accuracy of the model fitting to the sample set,and gradually improves the calculation accuracy of the Kriging model step by step.Finally,the classical Monte Carlo simulation is used to obtain the probability of failure of the slope.The analysis of a double-layered soil slope shows that the method can achieve accurate and efficient safety factor calculation.Especially in the case that the calculation factor of the safety factor is very large,the calculation time can be greatly saved,and it is an effective analysis method for slope stability reliability.
作者
吴海波
刘海龙
魏丽君
WU Hai-bo;LIU Hai-long;WEI Li-jun(School of Intelligent Control,Hunan Railway Professional Technology College,Zhuzhou 412001,China)
出处
《数学的实践与认识》
2021年第2期120-128,共9页
Mathematics in Practice and Theory
基金
湖南省自然科学基金项目(2018JJ5042)。
