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

The finite element method (FEM) is a classical approach to simulate the surface settlements induced by a tunnel boring machine (TBM). Unfortunately, for this application, the FEM is also computationally demanding. In this case, it is often useful to build simplified models from a set of reference simulations to quickly predict quantities of interest (QoIs) and make decisions. Such simplified models are called metamodels. In this article, our objective is to use kriging metamodels, aka Gaussian process metamodels, to build an approximation of a parametric 2D finite element tunneling model implemented using Python and ABAQUS. Our methodology evaluates the performance of kriging metamodels when the number of reference simulations varies. The performances are evaluated using several comparison metrics. We also compare two open-source implementations for kriging, two different assumptions for the mean of the Gaussian process, and we also test kriging against several classical regression methods.