Multivariate Adaptive Regression Splines Application for Multivariate Geotechnical Problems with Big Data

Despite the rapid increases in processing speed and memory of low-cost computers, the enormous computational costs of running complicated numerical analyses such as finite element simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization since many geotechnical problems are highly nonlinear and multivariate. To reduce the cost, surrogate models, also known as meta-models, are constructed and then used in place of the actual numerical simulation models. To ensure the surrogate model is more reliable, the ranges of the design variables should be as wide as possible. Thus meta-modeling techniques capable of analyzing multivariate problems are desirable. This paper explores the use of a fairly simple nonparametric regression procedure known as multivariate adaptive regression splines (MARS) in approximating the relationship between the inputs and outputs with a big data. First the basis of the MARS methodology and its associated procedures are explained in detail. Then two complicated geotechnical problems are presented to demonstrate the function approximating capabilities of MARS and its efficiency in dealing with multivariate problems involving large amounts of data. This paper demonstrates that the MARS algorithm is capable of producing simple, accurate and easy-to-interpret models and estimating the contributions of the input variables.