Virtual sensing of coupled interior/exterior vibro-acoustic systems
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Virtual sensor technology, as one of the key technologies in digital twins, has been studied for either interior or exterior vibro-acoustic systems to infer quantities that are difficult or impossible to measure with physical sensors, such as full-field pressure and acoustic intensity. However, many engineering applications involve coupled dynamics between an enclosed acoustic domain and the surrounding exterior field, such as automotive cabins and gearboxes, for which existing virtual sensing approaches are not directly applicable. This paper develops a virtual sensing methodology for coupled interior/exterior vibro-acoustic systems, enabling the reconstruction of coupled sound-field responses from a limited set of microphone measurements. The proposed framework integrates a finite-element vibro-acoustic model with sparse microphone data through an extended Kalman filter, where the FE model provides the prediction step and the microphones provide the correction step. To represent the unbounded exterior domain within an FE setting, perfectly matched layers are employed to approximately enforce the Sommerfeld radiation condition and suppress spurious reflections from the computational boundary. In addition, a parametric impedance boundary condition is introduced to capture boundary uncertainties and modeling errors, thereby improving estimation accuracy. To reduce computational cost and to enhance the numerical convergence and robustness of the Kalman filter, Krylov subspace-based parametric model order reduction is applied to the coupled FE model. Additionally, stability-preserving methods are incorporated to ensure the reduced-order model remains stable and suitable for recursive state estimation. The proposed method is successfully validated on the KU Leuven Soundbox experimental platform, demonstrating accurate coupled field reconstruction using only sparse interior/exterior microphone measurements. The resulting virtual sensing approach offers a computational pathway toward digital twins of coupled vibro-acoustic systems and provides access to otherwise unmeasurable responses, including interior pressure fields and exterior radiated pressures.
