Structural model updating based on l 2 and l ∞ norm regularizations

For structural damage detection (SDD), an accurate finite element (FE) model plays a vital role to evaluate structural states. Due to the ill-posedness of structural model updating problems, regularization methods have been introduced to obtain stable solutions. However, the l_q (0 < q ≤ 1) norm regularization methods have strong constraint effects so they are not suitable for structural model updating. In this paper, based on properties of regularization methods, the l _∞ norm regularization is adopted for model updating. Both l ₂ and l _∞ norm penalties are respectively chosen to define objective functions for comparative studies. Some numerical simulations in spring-mass model and simply supported beam are conducted to verify their effectiveness. The results show that the l _∞ norm regularization has good performances in model updating problems when design variables in many elements have same order in magnitude, while the l ₂ norm regularization is suitable to update stiffness changes in magnitudes for contiguous elements.