摘要
主成分分析在一定程度上可以解决大坝变形监测回归模型因子间的复共线性,然而当提取的主成分信息不充分时,主成分回归用于大坝安全预测可能失效。提出以主成分分析提取的主成分作为半参数回归的参数分量,剩余成分和模型误差作为未知的非参数分量对主成分回归进行补偿,建立一种基于主成分和半参数的大坝变形监测混合回归模型。利用某大坝实测资料进行建模分析,结果表明该混合模型能克服回归因子间的复共线性,避免半参数回归补偿最小二乘估计中法矩阵的病态性,比传统的主成分回归和逐步回归模型具有更好的拟合和预报精度。
Principal component analysis（PCA） is a solution to the multicollinearity problem of dam regression models.However,uninformative principal components（PCs） may lead to the failure prediction of dam deformation.Thus a hybrid regression model using semi-parametric regression and PCA is proposed,where the PCs with the highest variance are treated as the semi-parametric component;the remaining PCs and model errors are treated as the non-parametric component to be estimated.The hybrid model is tested using the field observations of a dam in China.The result shows the hybrid model can circumvent the multicollinearity of dam causative effects and the ill-conditioned problem in semi-parametric penalized least squares regression.A comparative study with traditional PC regression and stepwise regression demonstrate the superior performance for dam deformation prediction.
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2011年第12期3738-3742,共5页
Rock and Soil Mechanics
基金
浙江省水利厅科技计划项目(No.RB1010)
关键词
大坝
复共线性
主成分分析
半参数回归
补偿最小二乘
dam
multicollinearity
principal component analysis
semi-parametric regression
compensated least squares
