Multivariate adaptive regression splines for analysis of geotechnical engineering systems

Abstract

With the rapid increases in processing speed and memory of low-cost computers, it is not surprising that various advanced computational learning tools such as neural networks have been increasingly used for analyzing or modeling highly nonlinear multivariate engineering problems. These algorithms are useful for analyzing many geotechnical problems, particularly those that lack a precise analytical theory or understanding of the phenomena involved. In situations where measured or numerical data are available, neural networks have been shown to offer great promise for mapping the nonlinear interactions (dependency) between the system’s inputs and outputs. Unlike most computational tools, in neural networks no predefined mathematical relationship between the dependent and independent variables is required. However, neural networks have been criticized for its long training process since the optimal configuration is not known a priori. This paper explores the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) which has the ability to approximate the relationship between the inputs and outputs, and express the relationship mathematically. The main advantages of MARS are its capacity to produce simple, easy-to-interpret models, its ability to estimate the contributions of the input variables, and its computational efficiency. First the MARS algorithm is described. A number of examples are then presented that explore the generalization capabilities and accuracy of this approach in comparison to the back-propagation neural network algorithm.