A multi-objective optimization approach for FE model updating based on a selection criterion of the preferred Pareto-optimal solution

Multi-objectives optimization problems are often solved constructing the Pareto front and applying a decision-making strategy to select the preferred solution among the Pareto-optimal solutions. With the aim to reduce the computational effort in multi-objective optimization problems, this paper presents a procedure for the direct evaluation of the preferred updated model, without the need to evaluate the whole Pareto front. For this purpose, the objective function to minimize is defined as the distance between a candidate point and the equilibrium point in the objective function space. The choice of the criterion of the minimum distance from the equilibrium point comes from a preliminary study carried out to assess the performances of different selection criteria. The robustness and the efficiency of the proposed procedure are assessed through the comparison with the results obtained from the estimation of the Pareto-optimal solutions and the subsequent selection of the preferred one for two numerical case studies. The proposed procedure is finally applied to the calibration of a complex FE model with respect to experimental modal data. Results show that the proposed procedure is effective and considerably reduces the computational effort. Moreover, the procedure is able to directly estimate the optimal weighting factor that allows to know the relative importance between the selected objectives and can be used to solve the multi-objective optimization with the weighed sum method.