A novel shape function approach of dynamic load identification for the structures with interval uncertainty

Aiming at uncertain structures, a computational inverse approach is proposed to identify the dynamic load on the basis of the shape function method and interval analysis. The forward model for an uncertain structure is established through the relationship between the uncertain load vector and the assembly matrix of the uncertain responses of the shape function loads in each discrete element in time domain. The uncertainty is characterized by the interval with a closed bounded set of uncertain parameters. On the basis of interval analysis method, the load identification for uncertain structures can be transformed into two kinds of deterministic inverse problems, namely the deterministic dynamic load identification and the first order derivatives of the unknown load to each parameter both at the midpoints of the uncertain parameters. In order to eliminate the ill-posedness of inversion, the regularization method is adopted to solve the deterministic equations. Two numerical examples demonstrates the effectiveness of the proposed method, and example one also gives the identified result using Monte Carlo method to compare with that using the proposed method.