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We consider the problem of identifying the acoustic impedance of a wall surface from noisy pressure measurements in a closed room using a Bayesian approach. The room acoustics is modeled by the interior Helmholtz equation with impedance boundary conditions. The aim is to compute moments of the acoustic impedance to estimate a suitable density function of the impedance coefficient. For the computation of moments we use ratio estimators and Monte-Carlo sampling. We consider two different experimental scenarios. In the first scenario, the noisy measurements correspond to a wall modeled by impedance boundary conditions. In this case, the Bayesian algorithm uses a model that is (up to the noise) consistent with the measurements and our algorithm is able to identify acoustic impedance with high accuracy. In the second scenario, the noisy measurements come from a coupled acoustic-structural problem, modeling a wall made of glass, whereas the Bayesian algorithm still uses a model with impedance boundary conditions. In this case, the parameter identification model is inconsistent with the measurements and therefore is not capable to represent them well. Nonetheless, for particular frequency bands the Bayesian algorithm identifies estimates with high likelihood. Outside these frequency bands the algorithm fails. We discuss the results of both examples and possible reasons for the failure of the latter case for particular frequency values., Comment: 22 pages, 16 figures

In many applications, knowledge of the sound pressure transfer to the eardrum is important. The transfer is highly influenced by the shape of the ear canal and its acoustic properties, such as the acoustic impedance at the eardrum. Invasive procedures to measure the sound pressure at the eardrum are usually elaborate or costly. In this work, we propose a numerical method to estimate the transfer impedance at the eardrum given only input impedance measurements at the ear canal entrance by using one-dimensional first-order finite elements and Nelder-Mead optimization algorithm. Estimations on the area function of the ear canal and the acoustic impedance at the eardrum are achieved. Results are validated through numerical simulations on ten different ear canal geometries and three different acoustic impedances at the eardrum using synthetically generated data from three-dimensional finite element simulations., Comment: 16 pages, 15 figures

In this paper we consider an in-ear headphone equipped with an inner microphone and multiple loudspeakers and we propose an optimization procedure with a convex objective function to derive a fixed multi-loudspeaker ANC controller aiming at minimizing the sound pressure at the ear drum. Based on the virtual microphone arrangement (VMA) technique and measured acoustic paths between the loudspeakers and the ear drum, the FIR filters of the ANC controller are jointly optimized to minimize the power spectral density at the ear drum, subject to design and stability constraints. For an in-ear headphone with two loudspeakers, the proposed multi-loudspeaker VMA controller is compared to two single-loudspeaker VMA controllers. Simulation results with diffuse noise show that the multi-loudspeaker VMA controller effectively improves the attenuation by up to about 10 dB for frequencies below 300 Hz when compared to both single-loudspeaker VMA controllers., Comment: 5 pages, 4 pages, Submitted to IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022)

In this paper we consider an in-ear headphone equipped with an external microphone and aim to minimize the sound pressure at the ear drum by means of a fixed feedforward ANC controller. Based on measured acoustic paths to predict the sound pressure generated by external sources and the headphone at the ear drum, the FIR filter coefficients of the ANC controller are optimized for different sound fields. Due to the acoustic feedback path between the loudspeaker and the microphone, a stability constraint based on the Nyquist stability criterion is introduced. Performance degradations due to reinsertions of the headphone and intra-subject variations are addressed by simultaneously optimizing the controller for several measurement repetitions of the acoustic paths. Simulations show that the controller optimized for an ipsilateral excitation produces an attenuation of at least -10 dB that extends approximately to +45{\deg} and -65{\deg} from the ipsilateral DoA. The controller optimized for a diffuse-field excitation achieves an attenuation of at least -10 dB over a wider range of DoAs on the ipsilateral side, namely +90{\deg} to -90{\deg}. Optimizing the controller for several measurement repetitions is shown to be effective against performance degradations due to reinsertions and intra-subject variations., Comment: 8 pages, 5 figures, to be published in proceedings of the 27th International Congress on Sound and Vibration