Kriging metamodels for 2D finite element simulations of the settlements induced by TBM excavation in urban areas

Abstract

Finite element methods (FEM) are a classical approach to simulate the surface settlements induced by a tunnel boring machine (TBM). Unfortunately, for this application, FEM are also computationally demanding, and it is often useful to build simplified models from a set of reference simulations to quickly predict quantities of interest and make decisions. Such simplified models are called metamodels. In this article, our objective is to compare several approaches for building such metamodels. More precisely, we compare polynomial regression, neural networks, and kriging approaches, using standard open-source Python packages.
The test case is a parametric 2D finite element tunneling model. A Python script has been developed to build the whole model, from geometry to simulation, using the FE program ABAQUS. Our comparison methodology considers different types of models in each family of metamodels, several comparison metrics, several design types (choice of reference simulations), and design size (number of reference simulations).