Virtual measurements for exterior vibro-acoustic problems using experimental modal models

This paper presents a virtual sensor scheme for vibroacoustic radiation applications based on experimental modal state-space models and sparse measurements. A Kalman filter is used for the estimation combining data from the acoustical and the structural domain together with the numerical modal process model. It is proposed to use Gramians, as an energy-related measure of a system's observability which enables assessing the observability of the coupled vibroacoustic system in the modal state-space domain and the physical state domain counterpart. This Gramian-based observability metric reveals modes or states of high observability, which ensure good estimation results in the subsequent estimation. The proposed method is validated using an industrial test setup for which, due to its high complexity, modelling with first-principle techniques is not feasible. The estimation results demonstrate improved performance compared to a pure forward use of the identified model, indicating the effectiveness of the virtual sensor approach. Additionally, the newly proposed Gramian-based observability criterion outperforms state-of-the-art metrics for sensor placement in terms of estimation accuracy for particular states of interest, as demonstrated in a sensor placement task. Overall, this paper provides a promising approach for virtual sensing for vibroacoustic applications, enabling accurate and efficient system monitoring and control.