Basic Study on Evaluation of Spatially Distributed Soil Property with Sparse Modeling

Abstract

Kriging, which uses theory of conditional Gaussian random field, has been widely used in geotechnical problems. Least square method and L2 norm plays an important role in the method. The concept of sparse modeling attracts much attention from various fields. It is reported that it is successfully applied to many problems in various fields such as signal processing, image processing, machine learning and so on. The representative formulation LASSO uses L1 norm instead of L2 norm in the formulation. After illustrating the concept and formulation of sparse modeling, application to evaluation of soil property from limited number of boring data is discussed. One dimensional and two dimensional cases are indicated with assumption of sparsity in first-order and second-order differentiation space. In one dimensional case, both assumptions, which are sparsity in first-order and second-order differentiation, give reasonable distribution. In two-dimensional case, however, the assumption of sparsity in first-order differentiation gives unnatural distribution in the numerical examples. In the evaluation of spatial distribution of geotechnical problems, assumption of sparsity in second-order differentiation space seems reasonable.