Assessment of the Influence of Boundary Conditions on the Accuracy of Impact Force Identification

Abstract

This article focuses on the identification of impact forces acting on elastic struc-tures, a key area of structural health monitoring (SHM). The objective is to ana-lyze the effect of boundary conditions on the accuracy of force reconstruction. Structural health monitoring is an inverse problem that is both complex and gen-erally considered ill-posed. In particular, the deconvolution of measured signals is inherently unstable, requiring the application of Tikhonov regularization to obtain a reliable solution. The formulation of the forward problem is presented under the assumption of elastic supports. Using the Euler-Bernoulli model, the study leads to the development of the transfer matrix equation based on the deformation response. Simulations performed on a beam show that support stiffness plays a central role in the accuracy of force reconstruction. When the supports are too flexible, the reconstruction error is significant, especially in the presence of noise. However, beyond a certain stiffness threshold, the error stabilizes, indicating the existence of an optimal rigidity level.