Parameter estimation with correlated outputs using fidelity maps

This paper introduces a new approach for parameter estimation and model update based on the notion of fidelity maps. Fidelity maps refer to the regions of the parameter space within which the discrepancy between computational and experimental data is below a user-defined threshold. It is shown that fidelity maps provide an efficient and rigorous approach to approximate likelihoods in the context of Bayesian update or maximum likelihood estimation. Fidelity maps are constructed explicitly in terms of the parameters and aleatory uncertainties using a Support Vector Machine (SVM) classifier. The approach has the advantage of handling numerous correlated responses, possibly discontinuous, without any assumption on the correlation structure. The construction of accurate fidelity map boundaries 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 fidelity map is based on several natural frequencies and mode shapes to be matched simultaneously. Various statistical estimators are derived from the map.