基于偏最小二乘法的黄土湿陷性评价模型

Evaluation Model of Loess Collapsibility Based on the Partial Least Squares Method

基于统计学相关理论的黄土湿陷系数预测及评价方法是简化其工程应用的重要途径。当前采用多元回归方法建立黄土湿陷系数预测模型过程中往往缺乏对自变量间多重相关性对预测精度影响的合理考量。基于上述考虑,该文分别采用普通多元线性回归方法和偏最小二乘回归方法建立了黄土湿陷系数的多因素(天然含水量、初始孔隙比和压缩系数)回归模型并对二者精度进行了对比验证。结果表明:偏最小二乘方法在消除自变量之间多重相关性对结果的扰动方面成效显著,采用偏最小二乘回归分析方法获取的回归模型预测效果明显优于普通多元线性回归方法获取的回归模型。黄土湿陷系数与天然含水量和初始孔隙比之间存在显著的正相关关系。压缩系数对湿陷系数的解释能力较差,即使通过偏最小二乘分析方法依然无法正确体现其对湿陷系数的微弱影响,在后续相关回归分析中不宜将压缩系数作为湿陷系数的自变量。

The prediction or evaluation of loess collapse coefficient based on the statistical theory is a significant way to simplify its application in engineering.However,there is a lack of the effect of multiple correlations between each variable on the prediction accuracy in the establishing of the prediction model of collapse coefficient.To this end,two prediction models of collapse coefficient are built using the ordinary multiple linear regression method and the partial least squares regression method,in which the natural moisture content,initial void ratio and compression coefficient are taken as the independent variables.Moreover,the accuracy of these two models is verified by comparison.The results indicate that the effect of multiple correlations between each independent variable on the prediction accuracy could be diminished significantly when the partial least squares regression method is adopted.The regression model obtained by the partial least squares regression method could predict the collapse coefficient of loess in a batter way compared with that by the ordinary multiple linear regression method.Furthermore,there is an evident positive relationship between the collapsibility coefficient and the natural moisture content or the initial void ratio.However,the compression coefficient had a very weak explanatory ability for the collapsibility coefficient of loess and the subtle effect could not be described properly through the partial least squares regression method.Therefore,the compression coefficient is not suggested as the independent variable of the collapsibility coefficient in the subsequent regression analysis.