Quantification and propagation of uncertainties in electroacoustic absorbers due to temperature effects using Bayesian inference

Among technologies available for active noise control, electroacoustic absorbers (EAs) are devices whose acoustic impedance can be controlled to match a desired target value. This control depends on the electromechanical properties of the loudspeaker used in constructing the EA, known as Thiele-Small parameters. As these properties can be affected by environmental factors, such as temperature and humidity, uncertainties in the parameters of loudspeaker model can introduce uncertainty into the control law itself. This work proposes the quantification of the uncertainties in the Thiele-Small parameters of EAs due to temperature variations using a Bayesian inference framework, along with the propagation of these uncertainties to key operational metrics, namely the frequency response function (FRF) and the normal absorption coefficient. The acoustic impedance of multiple EAs is measured using an impedance tube over a broad temperature range, from −10 °C to +50 °C, and a pole-residue model is used to identify the variation of the Thiele-Small parameters with temperature. Both the Metropolis–Hastings and the affine invariant ensemble sampling (AIES) algorithms are then employed to sample the posterior distribution of the Thiele-Small parameters, and their performances are compared. Metropolis–Hastings exhibited bias, underdispersion and convergence failure when estimating correlated parameters, whereas the ensemble sampler efficiently captured the full posterior at higher computational cost. Uncertainty propagation using the AIES-derived posteriors produced predictive intervals for the FRF and absorption coefficient that fully encompassed the experimental data.