Comparison of standard Bayesian methods and PINNs for the reconstruction of acoustic fields in 'in situ' combustion chambers

Acoustic measurements, utilizing sensors such as microphones strategically placed, are commonly employed to monitor acoustic systems and extract quantities of interest, such as acoustic reflection coefficients. Typically, a specialized test rig must be constructed to allow for external harmonic acoustic forcing via loudspeakers. In this study, we propose two different methods: physics-informed neural networks (PINNs) and the extended Kalman filter, to reconstruct the acoustic field of a system and assess the acoustic reflection coefficient at a defined boundary. We demonstrate numerically that a single external broadband forcing signal suffices for these methods. This implies that these methods can be applied to 'in situ' configurations, such as industrial combustion chambers, where the broadband nature of combustion noise serves as the acoustic forcing element. Furthermore, we investigate the performance of the two aforementioned methods in reconstructing the acoustic systems and corresponding acoustic boundaries.