基于主动学习Kriging模型的改进一次可靠度方法

IMPROVED FIRST ORDER RELIABILITY METHOD BASED ON ADAPTIVE KRIGING MODEL

结构可靠度分析的一次可靠度方法在每一迭代中均涉及迭代点的函数值及梯度值计算,但后续迭代过程不能充分利用前期迭代过程中迭代点的计算结果,因此计算效率有待于进一步提升。考虑到迭代后期迭代点在局部区域内波动,若以已有迭代结果为基础建立代理模型进行迭代后期迭代点的函数值及梯度值计算将有助于改善一次可靠度方法的计算效率。为此,该文在将一次可靠度方法的迭代过程分为全局搜索阶段与局部搜索阶段的基础上,针对两个阶段分别采用不同的计算策略,即全局搜索阶段沿用已有一次可靠度方法的迭代过程,在局部搜索阶段则基于全局搜索阶段的迭代结果建立Kriging模型,并引入可评估Kriging模型在迭代点处精度的学习函数,实现局部搜索阶段迭代点的高效率计算,从而提出了具有更高计算效率的改进一次可靠度方法。数值算例和工程算例的计算结果表明建议方法在保持精度不变的情况下,可显著提高一次可靠度方法的计算效率。

The First Order Reliability Method(FORM)of structural reliability analysis involves the calculation of the function value and gradient value of the iteration point in each iteration,but the subsequent iteration process cannot make full use of the calculation results of the iteration point in the previous iteration process,the calculation efficiency thusly needs to be further improved.Considering that the iteration points fluctuate in the local area in the later iteration,if the surrogate model is established upon the existing iteration results to calculate the function value and gradient value of the iteration point in the later iteration,it will help to improve the calculation efficiency of the FORM.To this end,the iterative process of FORM is divided into a global search stage and a local search stage,and they are applied in different calculation strategies.In the local search stage,a Kriging model is established upon the iteration results in the global search stage,and a learning function that can evaluate the accuracy of the Kriging model at the iterative points is introduced to realize the efficient calculation of the iterative points in the local search stage,and an improved FORM with high computational efficiency is proposed.The calculation results of numerical examples and engineering examples show that the method proposed can significantly improve the computational efficiency of the FORM just of keeping the accuracy unchanged.