Model order reduction of time-domain vibro-acoustic finite element simulations with admittance boundary conditions for virtual sensing applications

Virtual sensing employs an estimator that combines a numerical model and a limited set of measurements to estimate the full field pressure of a vibro-acoustic system in the time domain. A key aspect of virtual sensing is to create a reduced-order model of the vibro-acoustic system, such that the numerical model can be effectively employed in the virtual sensing scheme. This paper aims to create a reduced-order vibro-acoustic finite element model with frequency dependent admittance boundary conditions for virtual sensing applications using a Kalman filter. The frequency-dependent components in admittance boundary conditions always result in a frequency-dependent damping matrix which hinders the modeling in the time domain. This paper first treats the vibro-acoustic system as a negative feedback interconnection of two subsystems: a state-space model of admittance transfer functions and a vibro-acoustic system with rigid boundary conditions. Stacking the states of these two subsystems gives the final descriptor system. Then, due to the passivity of the admittance transfer function and the definiteness of the system matrices, the second-order form of the descriptor model is modified to give a full-order model which is proven to be stability-preserving under one-sided projection methods. A coupled vibro-acoustic system is experimentally presented which demonstrates that the proposed methodology can provide a stable reduced order model and allows the full field estimation of the pressure in the presence of frequency-dependent boundary conditions.