基于高斯过程回归的有限元应力解的改善研究

本文应用高斯过程回归方法对有限元应力解进行了改善研究.考题是一简化为平面应力问题的各向同性且受均布载荷的等截面悬臂深梁,应力考察量取Mises应力,高斯积分点为样本点,单元角结点为改善点.4结点单元有限元模型和8结点单元有限元模型的计算结果表明:(1)改善点的总体误差比样本点的总体误差都小,且4结点明显、8结点不明显;(2)边界结点的改善效果均较传统整体应力修匀的效果显著;(3)改善点应力具有置信区间;(4)较传统分片应力修匀方法,高斯过程回归方法可将所选取区域内的所有角结点的应力同时给予改善,且边界角结点改善效果好.

Improvement of Finite Element Stress Solution Based on Gauss Process Regression

The finite element stress solution is studied by Gaussian process regression in this paper. The test is an isotropic and uniform beam with uniformly distributed load. Mises stress is taken as the measured stress, the gauss integral point is taken as the sample point, and the element angle node is taken as the improvement point. The calculation results of finite element models using 4 node element and 8-node element show that: (1) the overall errors of the improvement points are smaller than the total error of the sample points. The effect is more obvious for the 4-node model and less obvious for the 8-node model; (2) the improvement effect for boundary nodes is better than that from traditional overall stress modification; (3) the improved point stress has a confidence interval; (4) compared with the traditional stress separation method, the Gaussian process regression method can simultaneously improve the stresses of all the angular nodes in the selected region, with particular good effect for the boundary angle joints.