Evidence-based identification of weighting factors in bayesian model updating using modal data

Abstract eng:
In recent years, model updating of dynamical systems based on experimental data has become increasingly important due to the need for more accurate models that can be used for robust prediction of the structural performance of a target structure. In order to make reliable decisions, model updating should be performed while considering uncertainties so that the entire available information about the structure can be taken into account. The Bayesian statistical framework represents a rigorous approach to addressing this problem. When using Bayesian model updating techniques, parameter identification of structural systems using modal data can be based on the formulation of the likelihood function as a product of two probability density functions, one relating to modal frequencies and one to mode-shape components. The prediction-error variances for the modal frequencies and mode-shape components are weighting factors that control the degree to which the corresponding prediction errors (the differences between the model and experimental modal data) influence the updating process. The selection of the prior distribution of these prediction-error variances has to be performed carefully so that the relative contributions of the two types of modal data are weighted to give balanced results. A methodology is proposed here to select these weights by performing Bayesian updating at the model class level, where the model classes differ by having different ratios of the two prediction-error variances. The most probable model class based on the modal data then gives the best choice for this variance ratio. A numerical example is used to illustrate this approach, pointing out the effect of the different relative contributions of the modal frequencies and mode-shape components to the total amount of information extracted from the modal data.

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