Sound field reconstruction for outdoor sound field control applications

This Ph.D. study investigates sound field reconstruction techniques for the characterization of the acoustic transfer functions between the loudspeakers and the control areas in outdoor sound field control applications. The focus of the thesis is placed on low frequency sound from open air concerts.

The performance of a sound field control system is directly dependent on the accuracy of the estimation of the acoustic transfer functions between the loudspeakers in the system and the controlled area. In indoor applications, the transfer functions are commonly estimated with acoustic measurements between each loudspeaker and a dense grid of locations.

Outdoors, the application of sound field control systems is a challenging problem. The estimation of the transfer functions over large areas requires hundreds of measurements at locations that might be impractical to reach. Besides, the atmospheric conditions continuously change, which requires the re-estimation of the transfer functions in order to keep the adequate performance of the system.

The primary purpose of the study is to develop a model that efficiently reconstructs, from a small set of spatially sparse measurements, the sound field created over extended areas outdoors by a set of coherent loudspeakers. The study addresses four main topics, namely the characterization of the direct sound field from the loudspeakers to the control area, the characterization of the indirect sound field in the controlled area that results from the interaction of the direct sound field with surfaces and obstacles, the efficient modeling of low frequency sound propagation in variable atmospheric conditions, and the uncertainty quantification of the reconstructed sound fields.

Regarding the reconstruction of the direct sound, as pherical harmonics model is proposed to characterize in situ the sound radiation of loudspeakers in sound field control systems. Results show that the proposed model can substantially improve the performance of sound field control systems where the measurement data is scarce.

The use of Gaussian processes (GPs) is investigated and proposed for the reconstruction of the sound field due to reflections and scattering. GPs allow to reconstruct fields based on spatial correlation functions or kernels. A hierarchical kernel that adapts to variable degrees of sparsity in the field is introduced.

Regarding the propagation of low frequency sound outdoors, a heuristic propagation model based on frequency dependent speed of sound is proposed. Finally, this work contributes to the uncertainty quantification in sound field reconstruction problems via Bayesian inference, as GPs keep uncertainty information in a closed form.

In the case that the Bayesian inference problem presents no closed form solution, the study proposes Hamiltonian Monte Carlo as an efficient sampling method for hierarchical models. It is the purpose of this dissertation to examine and discuss the relevant findings and review the contributions of the Ph.D. study in relation to the existing body of knowledge.