Advances in impact force identification: A comprehensive review of techniques and mathematical innovations

摘要

This review provides a comprehensive and critical synthesis of state-of-the-art methodologies for impact force identification, a pivotal inverse problem in aerospace, automotive, civil infrastructure, and robotics systems. A systematic taxonomy is established to evaluate impact force reconstruction techniques, including deconvolution, subspace state-space formulations, and data-driven models, as well as localization strategies, such as triangulation, similarity-based matching, and optimization-based algorithms. The comparative analysis underscores the trade-offs between model-based approaches, which offer high computational efficiency in linear regimes, and machine learning methods, which demonstrate robustness in capturing nonlinear and high-dimensional system behaviors. The paper delves into recent mathematical advancements aimed at mitigating the inherent ill-posedness of inverse problems, emphasizing the roles of advanced regularization schemes, compressed sensing, and sparsity-promoting techniques. Notable emerging directions include hybrid physics-informed machine learning frameworks, domain adaptation and transfer learning to alleviate data dependency, and incremental learning paradigms suited for real-time deployment. Unresolved challenges are also identified, particularly in scenarios involving multiple concurrent impacts, sparse sensor networks, and online operation under dynamic environmental conditions. The review concludes by outlining future research trajectories to advance the accuracy, generalizability, and real-time feasibility of impact force identification methods.