基于高斯过程回归的有限元应力解的改善研究
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摘要
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.
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.
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.
引文
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[15]张云鹏,李利平,贺鹏,等.隧道围岩大变形高斯过程回归预测模型及其工程应用[J].科学技术与工程,2018,1:122-127.
[16]王鑫,李红丽.台风最大风速预测的高斯过程回归模型[J].计算机应用研究,2015,32(1):59-62.
[17]钟美,赵兵涛,黄朔.基于高斯过程回归的燃煤烟气汞排放预测[J].动力工程学报,2016,36(12):987-992.
[18]王芳黎.基于高斯过程回归方法的研究及应用[J].工业控制计算机,2015,11:76-78.
[19]刘开云,方昱,刘保国.基于进化高斯过程回归算法的隧道工程弹塑性模型参数反演[J].岩土工程学报,2011,6:883-889.
[20]何志昆,刘光斌,赵曦晶,等.高斯过程回归方法综述[J].控制与决策,2013,8:1121-1129.
[2]FEARN T.Gaussian process regression[J].Journal of Near Infrared Spectroscopy,2013,24(6):23-24.
[3]PACIOREK C J,SCHERVISH M J.Nonstationary covariance functions for Gaussian process regression[C]//International Conference on Neural Information Processing Systems,MIT Press,2003,273-280.
[4]李振刚.基于高斯过程回归的网络流量预测模型[J].计算机应用,2014,34(5):1251-1254.
[5]孙斌,姚海涛,刘婷.基于高斯过程回归的短期风速预测[J].中国电机工程学报,2012,32(29):104-109.
[6]康军,段宗涛,唐蕾,等.高斯过程回归短时交通流预测方法[J].交通运输系统工程与信息,2015,15(4):51-56.
[7]ITO K,XIONG K.Gaussian filters for nonlinear filtering problems[J].IEEE Transactions on Automatic Control,2000,45(5):910-927.
[8]HONG S,ZHOU Z,LU C,et al.Bearing remaining life prediction using Gaussian process regression with composite kernel functions[J].Journal of Vibroengineering,2015,17(2):695-704.
[9]DI SCIASCIO F,AMICARELLI A N.Biomass estimation in batch biotechnological processes by Bayesian Gaussian process regression[J].Computers and Chemical Engineering,2008,32(12):3264-3273.
[10]ROHMER J,FOERSTER E.Global sensitivity analysis of large-scale numerical landslide models based on Gaussian-Process meta-modeling[J].Computers and Geosciences,2011,37(7):917-927.
[11]ROSTAMI H,MANSHAD A K.Application of evolutionary Gaussian processes regression by particle swarm optimization for prediction of dew point pressure in gas condensate reservoirs[J].Neural Computing and Applications,2014,24(3-4):705-713.
[12]杨振舰,夏克文.基于高斯过程回归的上市股价预测模型[J].计算机仿真,2013,30(1):293-296.
[13]万华平,任伟新,魏锦辉.基于高斯过程响应面的结构有限元模型修正方法[J].振动与冲击,2012,31(24):82-87.
[14]宗文婷,卫志农,孙国强,等.基于改进高斯过程回归模型的短期负荷区间预测[J].电力系统及其自动化学报,2017,29(8):22-28.
[15]张云鹏,李利平,贺鹏,等.隧道围岩大变形高斯过程回归预测模型及其工程应用[J].科学技术与工程,2018,1:122-127.
[16]王鑫,李红丽.台风最大风速预测的高斯过程回归模型[J].计算机应用研究,2015,32(1):59-62.
[17]钟美,赵兵涛,黄朔.基于高斯过程回归的燃煤烟气汞排放预测[J].动力工程学报,2016,36(12):987-992.
[18]王芳黎.基于高斯过程回归方法的研究及应用[J].工业控制计算机,2015,11:76-78.
[19]刘开云,方昱,刘保国.基于进化高斯过程回归算法的隧道工程弹塑性模型参数反演[J].岩土工程学报,2011,6:883-889.
[20]何志昆,刘光斌,赵曦晶,等.高斯过程回归方法综述[J].控制与决策,2013,8:1121-1129.