基于最小二乘法和灰色决策的隧道变形最优组合预测模型  

Optimal Combination Prediction Model of Tunnel Deformation Based on Least Square Method and Grey Decision-making

作　　者：陈凯军 陈成伟 钟海龙 茶建华 CHEN Kaijun;CHEN Chengwei;ZHONG Hailong;CHA Jianhua(Mountain Expressway Engineering Group Construction Co.,Ltd.,Ji′nan 250014)

机构地区：[1]山东高速工程建设集团有限公司,济南250014

出　　处：《公路交通技术》2025年第1期142-151,共10页Technology of Highway and Transport

基　　金：山东省工信厅技术创新项目(202060101409,202060103144)。

摘　　要：为提高监控量测数据的处理效果和预测精度,基于46组隧道变形实测数据,采用灰色决策理论和RMSE、MAE、MAPE、Adjusted R^(2)等误差评定指标,全面对比了12种回归模型的拟合效果和预测精度,并引入组合预测,结合最优加权法、熵权法、灰色决策理论和图解法分别构建了组合预测模型。研究结果表明:1)单项预测模型中,皮尔曲线模型对隧道变形观测数据的预测精度最高;2)组合预测模型中,由指数曲线和皮尔曲线构建的模型预测精度最高,最适合隧道变形预测;3)各组合方法的综合效果测度并无明显差距,在实际应用中,可选取较为简单和适用的方法进行单项预测模型的权重组合。To enhance the processing efficacy and predictive accuracy of monitoring and measurement data,this study leverages 46 sets of actual tunnel deformation data.Utilizing grey decision theory and error evaluation metrics such as RMSE,MAE,MAPE,and Adjusted R^(2),it comprehensively compares the fitting effects and predictive precision of 12 regression models.Furthermore,it introduces combined forecasting,constructing combined prediction models by integrating the optimal weighting method,entropy weight method,grey decision theory,and graphical method.The research findings reveal that:1)Among the single prediction models,the Pearl curve model exhibits the highest predictive accuracy for tunnel deformation observation data;2)In the realm of combined prediction models,the model constructed from the exponential curve and the Pearl curve boasts the highest predictive accuracy,making it the most suitable for tunnel deformation forecasting;3)There is no significant disparity in the comprehensive effectiveness measures among the various combination methods.Therefore,in practical applications,simpler and more applicable methods can be selected for the weight combination of single prediction models.

关 键 词：隧道变形监测 最小二乘法 灰色局势决策 预测精度 最优组合预测 

分 类 号：U456[建筑科学—桥梁与隧道工程]