A Survey of Select Force Inversion Methods for Structural Dynamics

  • Pechac, Jack (Sandia National Laboratories)
  • Chen, Mark (Sandia National Laboratories)

Please login to view abstract download link

Given sufficient sensor measurements around a structure, force inversion or estimation methodologies aim to identify the loading conditions that produced the measurements. Many applications desire this capability, such as identification of shock profiles at mounts, determining inputs for resonant plate testing, or even digital twin calibration efforts for response prediction. Numerous methods have been proposed; however, applying these tools to experimental full systems or complex assemblies has yielded inconsistent results. The main reason is that inverse problems are mathematically ill-posed. Slight misfits, such as discrepancies between the model/unit-under-test, noisy data, or even minor sensor misplacement can render non-physical (and, hence, untrustworthy) results. Tracking down the cause of these instabilities in the recovered force profile often becomes a labor-intensive and iterative exercise. Moreover, this process produces expertise in the form of ad hoc heuristics, specific to the problem/model at hand. This survey aims to translate this acumen into digestible best practices. In the scope of this survey, three force inversion methods are examined: matrix-free, truncated randomized singular value decomposition [1], impulse/frequency response transfer matrix inversion [2], and the sum of weighted accelerations technique (SWAT) [3]. The survey evaluates the methods to identify robustness and strengths by examining a common assembly, namely the frame-plate-wing testbed [4]. By no means does this survey aim to solve the force inversion problem. Rather, it serves as a unified benchmark of the methods at their current maturation. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. [1] Smith, Chandler Baldwin, et al. Solving Transient MIMO Control Inverse Problems using Randomized Truncated Singular Value Decomposition. No. SAND2023-07051C. Sandia National Lab.(SNL-NM), Albuquerque, NM (United States), 2023. [2] Carter, Steven. “Thoughts on using Sparse Inverse Solutions in Transfer Path Analysis.” IMAC, A Conference and Exposition on Structural Dynamics. Cham: Springer Nature Switzerland, 2024. [3] Schoenherr, Tyler F. “Reconstructing forces from continuous connections using swat.” Topics in Modal Analysis I, Volume 7: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014. [4] “Round Robin Frame Structure.” Mar. 2025. https://wiki.sem.org/wiki/Round_Robin_Frame_Structure