Fidelity maps for model update under uncertainty: Application to a piano soundboard

This paper presents a new approach for model updating based on fidelity maps. Fidelity maps are used to explicitly define regions of the random variable space within which the discrepancy between computational and experimental data is below a threshold value. It is shown that fidelity maps, built as a function of epistemic and aleatory uncertainties, can be used to calculate the likelihood for maximum likelihood estimates or Bayesian update. The fidelity map approach has the advantage of handling numerous correlated responses at a moderate computational cost. This is made possible by the use of an adaptive sampling scheme to build accurate boundaries of the fidelity maps. Although the proposed technique is general, it is specialized to the case of model update for modal properties (natural frequencies and mode shapes). A simple plate and a piano soundboard finite element model with uncertainties on the boundary conditions are used to demonstrate the methodology.