Discretize-Then-Optimize Modeling for Dynamic Force Inversion Based on Runge–Kutta Explicit Time Integration
Publication: Journal of Engineering Mechanics
Volume 150, Issue 4
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.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the 626 corresponding author by request, including the MATLAB code (.m format) of the simulations and the MATLAB data sets (.mat format) of the simulation data.
Acknowledgments
This material is based upon work supported by the National Science Foundation under Awards CMMI-2044887 and CMMI-2053694. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors are also grateful for the support by the Faculty Research and Creative Endeavors (FRCE) Research Grant-48058 at Central Michigan University. The authors appreciate the reviewers for their reviews and insightful comments.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 4 • April 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Apr 24, 2023
Accepted: Nov 28, 2023
Published online: Feb 9, 2024
Published in print: Apr 1, 2024
Discussion open until: Jul 9, 2024
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