Pareto optimal structural models and predictions consistent with data and modal residuals

A multi-objective identification method for model updating based on modal residuals is proposed. The method results in multiple Pareto optimal structural models that are consistent with the measured modal data, the class of models used to represent the structure and the modal residuals used to judge the closeness between the measured and model predicted modal data. The conventional single-objective weighted modal residuals method for model updating is also used to obtain Pareto optimal structural models by varying the values of the weights. Theoretical and computational issues related to the solution of the multi-objective and single optimization problems are addressed. The model updating methods are compared and their effectiveness is demonstrated using experimental results obtained from a three-story laboratory structure tested at a reference and a mass modified configuration. The variability of the Pareto optimal models and their associated response prediction variability are explored using two structural model classes, a simple 3-DOF model class and a higher fidelity 546-DOF finite element model class. It is shown that the Pareto optimal structural models and the corresponding response predictions may vary considerably. The variability of Pareto optimal structural model is affected by the size of modelling and measurement errors. This variability reduces as the fidelity of the selected model classes increases.