Bayesian characterization of multiple-slope sound energy decays in coupled-volume systems

Abstract

Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.

Investigation on the effect of aperture sizes and receiver positions in coupled rooms

“…They cannot characterize multiple-sloped decay processes with the accuracy necessary to provide deep insight into energy decay characteristics in coupled-volume systems. 12,13 Therefore the previous studies have not yet been able to articulate the physical changes of sound energy decay when changing the aperture size.…”

“…Xiang et al 8 and Jing and Xiang 15 also applied the diffusion equation model to investigate coupled-volume systems to reveal the sound energy flows across the coupling aperture. More recently, Xiang et al 13 have discussed a rigorous approach to the characterization of multiple-sloped energy decays using a parametric decay model based on the nature of Schroeder integration 19 and statistical room-acoustics. 20 The primary focus of this recent work is to introduce the approach, which exploits two levels of Bayesian inference, rather on systematic investigations on aperture sizes and energy decay characteristics over large audience (receiver) areas.…”

Nested sampling applied in Bayesian room-acoustics decay analysis

“…Xiang and Goggans 1 utilized marginalization of the acoustic model along with an assumption on the form of the posterior distribution which works well for many single-slope and double-slope decays; however, once the decay model is of third or higher order, or the second-slope decay is significantly low in level, these assumption can cease to be valid. 1,4 Battle et al 3 accomplished model selection for geo-acoustics inversion problems using an importance sampling algorithm, the success of which depends critically on proper choice of the importance sampling distribution. In recent work by Xiang et al 4 and Dettmer and Dosso, 5 Bayesian model selection applied to room-acoustic decay order estimation, room acoustics energy decay analysis, and geo-acoustic inversion problems was solved using the Bayesian information criterion (BIC).…”

“…1,4 Battle et al 3 accomplished model selection for geo-acoustics inversion problems using an importance sampling algorithm, the success of which depends critically on proper choice of the importance sampling distribution. In recent work by Xiang et al 4 and Dettmer and Dosso, 5 Bayesian model selection applied to room-acoustic decay order estimation, room acoustics energy decay analysis, and geo-acoustic inversion problems was solved using the Bayesian information criterion (BIC). The BIC is based on the assumption that the posterior probability distribution is well approximated by a multivariate Gaussian probability distribution.…”

“…Bayesian methods have been utilized in a wide range of acoustics applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] with increasing attention being given to the task of performing Bayesian model selection. A few of the most recent applications of Bayesian model selection can be found in such acoustics applications as roomacoustics energy decay analysis 1 and geo-acoustics inversion, 2,3 where the model selection problems are tackled separately from that of parameter estimation.…”