Ensemble Kalman Inversion method for an inverse problem in soilstructure interaction
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 illposedness of the inverse problem. It is a regularizing optimizer used in Bayesian inverse problems that samples particles in pseudotime 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.07560
 Bibcode:
 2022arXiv220507560S
 Keywords:

 Mathematics  Numerical Analysis;
 65N21;
 62F15;
 65N75;
 65M32