Predictions of Geological Interface Using Relevant Vector Machine with Borehole Data

Abstract

Due to the discreteness, sparsity, multidimensionality, and incompleteness of geotechnical investigation data, traditional methods cannot reasonably predict complex stratigraphic profiles, thus hindering the three-dimensional (3D) reconstruction of geological formation that is vital to the visualization and digitization of geotechnical engineering. The machine learning method of relevant vector machine (RVM) is employed in this work to predict the 3D stratigraphic profile based on limited geotechnical borehole data. The hyper-parameters of kernel functions are determined by maximizing the marginal likelihood using the particle swarm optimization algorithm. Three kinds of kernel functions are employed to investigate the prediction performance of the proposed method in both 2D analysis and 3D analysis. The 2D analysis shows that the Gauss kernel function is more suitable to deal with nonlinear problems but is more sensitive to the number of training data and it is better to use spline kernel functions for RVM model trainings when there are few geotechnical investigation data. In the 3D analysis, it is found that the prediction result of the spline kernel function is the best and the relevant vector machine model with a spline kernel function performs better in the area with a fast change in geological formation. In general, the RVM model can be used to achieve the purpose of 3D stratigraphic reconstruction.