Development of a high-accuracy impact force identification methodology utilizing truncated impact response

Impact force identification (ImFoId), which involves impact localization and force reconstruction, is recognized as a doubly ill-posed inverse problem in structural dynamics, where even slight measurement noise or modeling inaccuracies can lead to completely erroneous results. To tackle it, a novel hierarchical ImFoId methodology using truncated impact response (TIR) is proposed in this paper, which significantly improves the accuracy and robustness of ImFoId. The proposed method initiates by utilizing variational mode decomposition (VMD) to decompose the complete impact response (CIR), which encompasses the full spectrum of the vibration signal, into several modal impact responses (MIRs). Then, by superimposing these MIRs, the so-called TIR is obtained. The utilization of TIR facilitates the establishment of a high-fidelity forward transfer model, as it excludes frequency components beyond the natural frequencies of structures and eliminates modal truncation errors induced by higher-order modal responses. In the phase of impact localization, an impulse model is employed to approximate the impact force, and the localization is efficiently realized by maximizing the collinearity between the estimated impact response (EIR) and TIR. Following the localization result, the forward transfer matrix between time histories of the impact force and TIR is established, and the unknown impact force is accurately reconstructed by solving the invers problem through truncated singular value decomposition (TSVD) based Tikhonov regularization technique. Numerical simulations conducted on a spring-mass-damper system, along with experimental validations performed on a clamped–clamped beam and a cantilevered metal plate, demonstrate that the proposed method yields both remarked robustness and accurate identification results.