OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

"Finite Element Model Updating using a Multi-Objective Optimization Framework"

prof. Costas Papadimitriou
University of Thessaly, Greece


Abstract
A multi-objective optimization framework is presented for structural
identification and finite element model updating. Multiple Pareto optimal structural models are obtained that are consistent with the measured data and the norms used for reconciling finite element models with data. The Pareto optimal models are due to uncertainties arising from model and measurement errors. The relation between the multi-objective optimization framework and the conventional single-objective weighted residuals method for model updating is investigated. An optimally weighted residuals method is also proposed to rationally select the most preferred model among the alternative Pareto optimal
models for use in model-based predictions. Theoretical and computational issues involved in estimating the Pareto optimal models are addressed, including issues related to non-uniqueness and unidentifiability.

The relation between the multi-objective identification framework and a
Bayesian identification framework is also established. Bayesian model selection techniques are used to quantify the uncertainty of each Pareto optimal model based on the measured data. This uncertainty is then propagated to uncertainty in the predictions made from the Pareto optimal structural models. The formulation involves integrals under high dimensional parameter space. Asymptotic approximations are proposed to efficiently evaluate these integrals.

Theoretical and computational developments are demonstrated by updating finite element models of small-scale laboratory structures, including a building frame and a vehicle frame, using modal data. It is demonstrated that the Pareto optimal structural models and the corresponding predictions from these models may vary considerably, depending on the fidelity of the finite element model class and the size of measurement errors. The proposed framework is suitable
for uncertainty quantification, identification and propagation in finite element model simulations consistent with measured data.