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.
翻译:为许多工程应用开发了基础结构和土壤之间的相互作用。为了确定基础结构中的压力,需要确定土壤僵硬对可变质板的迁移(直接问题)的影响,以及基础结构的僵硬对由此产生的下层(反向问题)的影响。在本文件中,我们处理温克勒数学模型,并提议使用高效的合成卡尔曼反向方案(EKI),使反向问题的不正确储存性迭接地规范。这是在巴耶斯反向问题中使用的一个常规化优化器,即模拟粒子在假时间采样粒子时根据这些粒子的移动而引入运动。EKI算法汇集到一个优化问题的解决办法,以尽量减少客观功能。在这方面,我们展示了如何通过使用有限差异方法结合EKI方法来重建装满现有建筑的长角薄板的温克勒亚等级反应系数,以将管理方程式的双声调操作器分解。