Multi-objective optimization algorithms for finite element model updating

A multi-objective optimization method is presented for estimating the parameters of finite element structural models based on modal residuals. The method results in multiple Pareto optimal structural models that are consistent with the measured modal data and the modal residuals used to measure the discrepancies between the measured modal values and the modal values predicted by the finite element model. The relation between the multi-objective identification method and conventional single-objective weighted modal residuals methods for model updating is explored. Computationally efficient methods for estimating the gradient and Hessians of the objective functions with respect to the model parameters are proposed and shown to significantly reduce the computational effort for solving the single and multi-objective optimization problems. The proposed methods exploit Nelson’s formulation for the sensitivity of the eigenproperties with respect to the parameters. Theoretical and computational developments are illustrated by updating finite element models of a multi-span reinforced concrete bridge using ambient vibration measurements. In particular, multi-objective identification results indicate that there is wide variety of Pareto optimal structural models that trade off the fit in various measured modal quantities.