Bayesian Approach for the In Situ Estimation of the Acoustic Boundary Admittance

Abstract

Interior acoustic problems require accurately representing the boundary conditions of all acoustically interacting surfaces to achieve precise acoustic predictions. The complex-valued boundary admittance fully characterizes these properties. Yet, conventional approaches to determine boundary admittances, such as the impedance tube, have limitations which do not accurately represent real-world conditions. This motivates in situ methods, where the acoustic boundary admittance is estimated in the actual mounting condition based on sound pressure measurements at certain observation points within the domain. In contrast to existing deterministic methods, a Bayesian approach is employed in this work, which provides probability distributions for the boundary admittances rather than point estimates. This offers valuable insights into the uncertainty associated with the estimation, proving beneficial for applications where a comprehensive understanding of uncertainty is desired. A finite element model is utilized to generate sound pressure data and serves as the forward model during the inference process. This makes it particularly suited for applications that involve pre-existing geometrical models, such as digital twin applications and model updating. The proposed method is applied to a two-dimensional car cabin model, demonstrating the framework’s efficacy in accurately inferring the acoustic boundary admittance using just ten observation points.