Identification of distributed impact force using the finite element model based on regularization method

Abstract

The aim of this paper is to invent a technique based on the finite element method which makes it possible to identify the impact load occurring on the elastic bodies.Identifying the periodical signal like a distributed pressure caused by an impact that occurs on the elastic plate can contribute to structural health monitoring.The inverse formulation of the objective function based on the finite element method has been established.The first part of this work will be devoted to modal analysis, the objective of which is to formulate the transfer function between the impact zone and the sensors implemented at known positions in the frequency domain.To switch from the frequency domain to the time domain, the inverse fast Fourier Transformation is used.Here, the identification of the impact force acting on linear elastic structures such as plates was considered.In the first place, it is convenient to look for the parameters that define the impact area using a minimization technique based on the Maxwell-Betti theorem.Once, the localization is determined, the reconstruction of the impact force-signal characteristics is done by the regularization methods.The regularization based on the truncation of the generalized singular values decomposition (TGSVD) has been adapted in this work.The TGSVD shows a relative error equal to 2.10%.This value is lower than that of literature value where Tikhonov regularization with the L-curve criterion was used & results in a relative error of about 40%".Further, the current work for a more complicated case that generates a nonpunctual impact for the same type of force shows the efficiency of the TGSVD method to reconstruct the impact signal.The influence of sensor locations, modal truncation, noise level, and discrete transfer functions on the reconstructed impact characteristics are discussed.