Model updating based on mixed-integer nonlinear programming under model-form uncertainty in finite element model

In this paper, a new finite element model updating (FEMU) method is proposed based on mixed-integer nonlinear programming (MINLP) to deal with model-form uncertainty in FE models. Depending on modelers' preference and experience, various FE models can be constructed for a specific structure in practice. However, no one can guarantee that a specific model representation is always best (Model-form uncertainty). Conventional method should perform model updating for each FE model independently and select a best one among them, so that it becomes computationally intensive with many candidate FE models. To handle model-form uncertainty, this study formulates FEMU as the MINLP problem. The proposed method assigns an integer variable for model choice, while continuous real variables are used for the updating parameters. With this formulation, the optimization algorithm can explore both model and parameter space simultaneously to deal with the model-form uncertainty in FE models. Firstly, three numerical experiments were explored to evaluate the performance of the proposed method by considering possible situations in reality as follows: (1) a true FE model exists in model space with an admissible FE model; (2) only admissible FE model exists in model space; and (3) no true and admissible FE models exist in model space. Then, the proposed method was experimentally validated through a real bridge. The results show that the proposed method can find a best FE model with optimal estimates of the updating parameters with much less computational efforts against the conventional FEMU.