Bayesian calibration using fidelity maps

This paper introduces a new approach for model calibration based on 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, which are built explicilty in terms of the calibration parameters and aleatory variables, provide a rigourous approximation of the likelihood for maximum likelihood estimation or Bayesian update. Because the maps are constructed using a support vector machine classifier (SVM), the approach has the advantage of handling numerous correlated responses, possibly discontinuous, at a moderate computational cost. This is made possible by the use of a dedicated adaptive sampling scheme to refine the SVM classifier. A simply supported plate with uncertainties in the boundary conditions is used to demonstrate the methodology. In this example, the construction of the map and the Bayesian calibration is based on several natural frequencies and mode shapes to be matched simultaneously.