高斯过程动态响应面法及其在悬索桥结构可靠度分析中的应用

Gaussian Process Based Dynamic Response Surface Method and Its Application in Reliability Analysis for Suspension Bridge

为解决复杂桥结构可靠度分析时存在的功能函数不能显式表达的问题,提出一种基于二次二阶矩法的的高斯过程动态响应面方法。该方法利用有限元分析程序构造少量训练样本,利用训练后的高斯过程回归模型构建响应面,实现小样本条件下功能函数及其导数的显式表达,通过构造合理的迭代方式,利用各迭代步的验算点信息不断修正响应面的拟合误差,动态提升响应面对失效概率贡献较大区域的重构精度,进而结合二次二阶矩法快速推求结构的可靠指标。利用数值算例与结构算例验证了该方法的有效性,在此基础上对鱼嘴长江大桥的静力可靠度进行了研究。研究结果表明:与传统响应面法相比较,该方法具有较高的计算精度与计算效率,且易与既有的有限元软件相结合。

Aimed at the problem that the performance function cannot be expressed by explicit formulation for structural reliability analysis of complex structure, a new reliability analysis method based on Gaussian process regression （GPR） dynamic response surface hybridized into the second-order second-moment method was presented. A small number of training samples were created using finite element method （FEM） code for building the GPR response surface. Thus, the implicit performance and its derivatives were approximated by GPR with explicit formulation. An iterative algorithm was presented to reduce the errors of GPR response surface with information of design point in order to constantly improve the reconstructing precision at the important region, which contributed to the failure probability significantly. The classical second- moment method （SORM） combined with the GRP response surface was applied to calculate the structural reliability indexes. The accuracy and feasibility of the presented method were demonstrated by numerical examples and practical engineering structure. The reliability of Yuzui Yangtze River Suspension Bridge was analyzed using the presented method. The results show that the proposed method response surface method, modification. has higher efficiency and higher accuracy compared with the traditional which can directly take advantage of existing FEM code without any modification.