Fidelity Maps for Model Update under Uncertainty with Correlated Outputs

This paper introduces a new approach for model update based on the notion of delity maps. Fidelity maps refer to the regions of the parameter space within which the discrepancy between computational and experimental data is below a user-dened threshold. It is shown that delity maps provide an ecient and rigorous approach to approximate likelihoods in the context of Bayesian update or maximum likelihood estimation. The delity maps are constructed explicitly in terms of the calibration parameters and aleatory uncertainties using a Support Vector Machine (SVM) classier. The approach has the advantage of handling numerous correlated responses, possibly discontinuous, without any assumption on the correlation structure. The construction of accurate boundaries of delity maps at a moderate computational cost is made possible through a dedicated adaptive sampling scheme. A simply supported plate with uncertainties in the boundary conditions is used to demonstrate the methodology. In this example, the construction of the delity map is based on several natural frequencies and mode shapes to be matched simultaneously. Various statistical estimators are derived from the map.