Robustness Analysis for A Computationally efficient Virtual Sensing Framework in time-domain for Exterior Vibroacoustics problems

Reconstruction of acoustic radiation from vibrating structures is central in vibroacoustic, as full-field sound information is essential for identifying radiation mechanisms and improving structural-acoustic performance. Conventional microphone-based measurements are limited by spatial sampling constraints and high experimental cost, while purely numerical approaches such as Finite Element Method (FEM) simulations, particularly in the frequency domain, offer flexibility but are strongly affected by parameter uncertainties, discretization errors, and imperfect boundary conditions. To overcome these drawbacks, this work develops a hybrid time-domain framework that couples vibration measurements with FEM-based acoustic models. The FEM model is reduced using Krylov subspace projection, yielding a compact state-space representation that captures the dominant vibroacoustic modes while remaining computationally efficient for sequential data assimilation. The acoustic radiation domain is truncated with perfectly matched layers (PML) to eliminate non-physical reflections, which are formulated for arbitrary convex boundaries to achieve efficient model size. Fusion of measurement and simulation is achieved via a discrete-time Kalman filter, which operates as a state observer for the reduced vibroacoustic system. The FEM model provides time-domain predictions of the radiated field, while the Kalman update step incorporates acceleration data from accelerometer measurements to correct model drift, compensate for parameter uncertainties, and attenuate experimental noise. In this work, the robustness of the proposed framework is systematically investigated. Particular attention is given to the the influence of model-measurement mismatch on estimation accuracy and stability, sensitivity to sensor configurations, and conditioning of covariance matrices. A series of numerical tests are conducted to evaluate the reliability and convergence behavior of the Kalman-based virtual sensing approach under controllable model uncertainties and dummy sensor employment, for stable and accurate reconstruction of acoustic fields from structural measurements in practical vibroacoustic systems.