基于改进加权响应面的结构可靠度计算方法

在结构可靠度分析中，响应面法由于具有良好的适用性和可操作性，是目前广泛使用的基于代理模型的分析方法。针对响应面法的计算效率和精度难以平衡兼顾等难点问题，提出一种基于改进加权响应面的结构可靠度计算方法。首先，在迭代过程中，同时考虑样本点与验算点距离、极限状态函数值、联合概率密度函数值3个权重因子对样本点进行赋权，采用加权回归并重复利用已有样本点更新不含交叉项的二次多项式响应面函数。其次，在迭代收敛后，选取已有样本点中权重较大的样本点加权拟合含有交叉项的二次多项式响应面函数。最后，结合数值算例和工程案例，通过与传统抽样方法和其他响应面法进行对比，验证了改进加权响应面法的可行性。结果表明所提方法具有较高效率的同时也保证了精度。 

Structural reliability calculation method based on improved weighted response surface

Response surface method is a widely used agent model analysis method for structural reliability analysis because of its good applicability and maneuverability. Aimed at the difficulties of the response surface method, such as balancing the efficiency and accuracy, a structural reliability calculation method based on improved weighted response surface is proposed. In the iterative process, three weighting factors, including the distance between the sample point and the design point, the absolute value of limit state function and the value of joint probability density function, are considered to weight the sample points. The quadratic polynomial response surface function without cross term is updated by weighted regression and reusing all known sample points. After the iterative convergence, the sample points with the larger weight among the existing sample points are selected to fit the quadratic polynomial response surface function with cross terms. Finally, with numerical examples and engineering cases, the feasibility of the proposed method is verified by comparing with traditional sampling methods and other response surface methods. The results show that the proposed method has higher efficiency and meanwhile guarantees accuracy.