基于多元自适应回归样条的高维岩土工程问题分析

为解决岩土工程中多元变量间的非线性相关问题,采用一种非参数回归算法——多变量自适应回归样条建立对目标参数的预测模型。该算法基于大量可靠的岩土监测数据,运用简单线性样条函数的组合对输入、输出参数进行相关性拟合,生成显性表达式,同时得到各输入参数的相对重要性。通过桩的可贯入性、地下洞室稳定性分析2个实例,对该方法进行评估。2个实例中测试集的决定性系数R~2分别为0.921和0.986,最重要的输入参数分别是桩材料的弹性模量和围岩质量,表明该方法可较精确地拟合多元输入参数与输出参数间的相关性,可用于未知响应的预测。

Analysis of multi-dimensional geotechnical engineering problems based on multivariate adaptive regression splines

A nonparametric regression algorithm, called the multivariate adaptive regression splines(MARS), is adopted to establish a simple and interpretable model to approximate the nonlinear interactions between inputs and outputs. Based on well-documented case data, MARS is capable of producing explicit expressions using the combination of simple linear spline functions, as well as obtaining the relative importance of input parameters. The reliability and accuracy of MARS were validated via the geotechnical applications of pile drivability assessment and stability evaluation of underground caverns. The coefficients of determination for the testing set in the two examples are 0. 921 and 0. 986, respectively, indicating that MARS can effectively fit the correlation between input parameters and target outputs. As for the parametric relative importance, the elasticity modulus of pile and quality of surrounding rock are recognized as the two most influential factors. MARS method can accurately relate the target responses to nonlinear and multivariate inputs; thus, it is useful in the practical engineering construction.