Ensemble Kalman Inversion method for an inverse problem in soil-structure interaction

TL;DR

This paper introduces an Ensemble Kalman Inversion approach combined with finite difference methods to solve the inverse problem of soil-structure interaction, specifically reconstructing the Winkler subgrade reaction coefficient for a loaded foundation.

Contribution

It presents a novel application of the Ensemble Kalman Inversion scheme to soil-structure inverse problems, enhancing regularization and solution accuracy.

Findings

EKI effectively reconstructs the Winkler subgrade reaction coefficient.

The method demonstrates convergence to the true solution.

Finite difference discretization supports accurate numerical implementation.

Abstract

The interaction between the foundation structures and the soil has been developed for many engineering applications. For the determination of the stress in foundation structure it is needed to determine the influence of the stiffness of soil with respect to the displacement w of the deformable plate (direct problem), and viceversa, how the stiffness of the foundation structure affects the resulting subsidence (inverse problem). In this paper, we deal with the Winkler mathematical model and propose to use an efficient Ensemble Kalman Inversion scheme (EKI) that regularizes iteratively the ill-posedness of the inverse problem. It is a regularizing optimizer used in Bayesian inverse problems that samples particles in pseudo-time introducing a motion due to the movement of these particles. The EKI algorithm converges to the solution of an optimization problem that minimizes the objective function. In this context we show how to reconstruct the Winkler subgrade reaction coefficient of a rectangular thin plate loaded with an existing building by using the EKI methodology combined by the finite difference method (FDM) to discretize the biharmonic operator of the governing equations.