基于Kriging模型梯度解析解的改进一次二阶矩方法

改进一次二阶矩（AFOSM）法是一种基于功能函数梯度的结构可靠性分析方法，鉴于其对隐式函数的梯度较难求解，提出了一种基于Kriging模型梯度解析解的AFOSM方法，利用Kriging代理模型的解析表达式推导得到功能函数对输入变量的梯度解析解，为AFOSM中设计点的确定提供高精度的梯度信息。通过Kriging与AFOSM的结合，很好地解决了基于有限元模型的隐式情况下梯度计算量相当大、可靠性分析难的问题。数值与工程算例验证了所提Kriging梯度解析解的较高精确性，同时验证了所提基于Kriging解析解的AFOSM结构可靠性分析方法的正确性与较高精度。

An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model

The Advanced First Order and Second Moment (AFOSM) method is a structural reliability analysis method based on the gradient information of performance function. Since the gradient information of the implicit function is difficult to solve, an AFOSM method based on the gradient analytical solution of Kriging surrogate model is proposed, using the analytical expression of Kriging surrogate model to obtain gradient information of the performance function with respect to input variables, and providing a high-precision gradient information for the computation of the design point in the AFOSM method. By combining Kriging and AFOSM, the problem of gradient calculation and reliability analysis in the implicit situation based on the finite element model can be better solved. Numerical and engineering examples are introduced to verify the high precision of the proposed gradient solution based on Kriging; besides, the accuracy and precision of the proposed Kriging analytical solution based AFOSM reliability analysis method are also verified.