Model based virtual intensity measurements for exterior vibro-acoustic radiation

•A model based virtual sensor is derived to estimate the acoustic intensity.•The virtual sensor works by combining acoustic measurements with a numerical model.•The numerical model uses infinite elements to model the radiation to infinity.•Model order reduction is used to reduce the finite element model in size.•The effectiveness of the virtual sensor is verified with several experiments. In this work a method for the virtual sensing of the acoustic intensity is derived for exterior vibro-acoustic radiation of a complex deepdrawn structure. The proposed method estimates the acoustic intensity and acoustic pressure resulting from structural excitation in the full acoustic domain, by utilizing a model-based state estimator in the form of a Kalman filter. The used model is a high fidelity, fully coupled vibro-acoustic finite element model with infinite elements to model the acoustic radiation to infinity. The model is reduced to about 0.1% of the original size by a Krylov based model order reduction technique that preserves the stability of the full model. This allows for the usage of the model in a Kalman filter. The effectiveness of the Kalman filter is demonstrated with several numerical experiments, in which both the measured pressure and the measured sound intensity are compared with the estimations from the filter at several locations. Furthermore, the robustness of the filter to changing acoustic environments is assessed.