The application of cubic B-spline collocation method in impact force identification

Abstract

The accurate real-time characterization of impact event is vital during the life-time of a mechanical product. However, the identified impact force may seriously diverge from the real one due to the unknown noise contaminating the measured data, as well as the ill-conditioned system matrix. In this paper, a regularized cubic B-spline collocation (CBSC) method is developed for identifying the impact force time history, which overcomes the deficiency of the ill-posed problem. The cubic B-spline function by controlling the mesh size of the collocation point has the profile of a typical impact event. The unknown impact force is approximated by a set of translated cubic B-spline functions and then the original governing equation of force identification is reduced to find the coefficient of the basis function at each collocation point. Moreover, a modified regularization parameter selection criterion derived from the generalized cross validation (GCV) criterion for the truncated singular value decomposition (TSVD) is introduced for the CBSC method to determine the optimum regularization number of cubic B-spline functions. In the numerical simulation of a two degrees-of-freedom (DOF) system, the regularized CBSC method is validated under different noise levels and frequency bands of exciting forces. Finally, an impact experiment is performed on a clamped-free shell structure to confirm the performance of the regularized CBSC method. Experimental results demonstrate that the peak relative errors of impact forces based on the regularized CBSC method are below 8%, while those based on the TSVD method are approximately 30%.