A Novel Method for Force Identification Based on the Discrete Cosine Transform

Abstract

Force identification is a classical inverse problem, in which the measured data and the mathematical models of mechanical structures are used to determine the applied force. However, the identified force may seriously diverge from the true solution due to the unknown noise contaminating the measured data and the inverse of the illposed transfer matrix characterizing the mechanical structure. In this paper, a novel method based on the discrete cosine transform (DCT) in the time domain is proposed for force identification, which overcomes the deficiency of the illposedness of the transfer matrix. The unknown force is expanded by a set of cosine basis functions and then the original governing equation is reformulated to find the coefficient of each cosine basis function. Furthermore, a modified generalized crossvalidation (GCV) criterion for determining the regularization parameter is developed for the truncated singular value decomposition (TSVD), Chebyshev polynomial, and DCT solutions. Numerical simulation reveals that compared with the Lcurve criterion, the modified GCV criterion is quite robust in the presence of noise. Finally, a clampedfree shell structure that is excited by an impact hammer is selected as an example to validate the performance of the proposed method. Experimental results demonstrate that compared with the TSVDbased and Chebyshevbased methods, the DCTbased method combined with the modified GCV criterion can reconstruct the force time history and identify the peak of impact force with high accuracy. Additionally, the identification of force location using the DCTbased method is also discussed.