Discretize-Then-Optimize Modeling for Dynamic Force Inversion Based on Runge–Kutta Explicit Time Integration

Abstract

This paper presents a new discretize-then-optimize (DTO) method for dynamic force inversion in a two-dimensional (2D) linear elastic, damped solid based on Runge–Kutta (RK) explicit time integration. Previous literature on DTO modeling for force or material inversion has predominantly focused on inversion methods based on Newmark implicit time integration. However, because implicit time integration may not be suitable for a problem with a large number of degrees of freedom [e.g., third-dimensional (3D) wave problems], there is a need to study an alternative DTO force-inversion formulation that centers around the RK explicit time integration, leveraged by a diagonal mass matrix. This paper attempts to fill this gap and present the full detail of the new RK-DTO formulation for dynamic force inversion. Our computational examples demonstrate that the new RK-DTO inversion simulator effectively reconstructs moving dynamic forces on the upper surface of the solid. It excels in efficiency when dealing with a higher number of degrees of freedom (DOFs) and maintains accuracy even with increased DOFs and observation durations. A smaller sensor spacing enhances the accuracy of the inverted force profile in the RK-based inversion. The presented inversion method can effectively identify the profiles of dynamic moving loads even when measurement data include noise or when the values of material properties are not deterministic.