Evaluation of decay times in coupled spaces: An efficient search algorithm within the Bayesian framework

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Recent application of coupled-room systems in performing arts spaces has prompted active research on sound fields in these complex geometries. This paper applies a diffusion-equation model to the study of acoustics in coupled-rooms. Acoustical measurements are conducted on a scale-model of two coupled-rooms. Using the diffusion model and the experimental results the current work conducts in-depth investigations on sound pressure level distributions, providing further evidence supporting the valid application of the diffusion-equation model. Analysis of the results within the Bayesian framework allows for quantification of the double-slope characteristics of sound-energy decays obtained from the diffusion-equation numerical modeling and the experimental measurements. In particular, Bayesian decay analysis confirms sound-energy flux modeling predictions that time-dependent sound-energy flows in coupled-room systems experience feedback in the form of energy flow-direction change across the aperture connecting the two rooms in cases where the dependent room is more reverberant than the source room.

Section: Quantifying Double-slope Characteristicsmentioning

confidence: 99%

Investigation of acoustically coupled enclosures using a diffusion-equation model

Xiang¹,

Jing²,

Bockman³

2009

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“…The likelihood function Lðw s Þ for the sound energy decay analysis has been well discussed in previous publications, 14,21 it is the probability of the residual error e. The background information I states that the only available information about the error e 2 is that it corresponds to a finite but unknown bounded value which implies a finite variance r 2 .…”

Section: Two Levels Of Bayesian Inferencementioning

confidence: 99%

Nested sampling applied in Bayesian room-acoustics decay analysis

Jasa¹,

Xiang

2012

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Room-acoustic energy decays often exhibit single-rate or multiple-rate characteristics in a wide variety of rooms/halls. Both the energy decay order and decay parameter estimation are of practical significance in architectural acoustics applications, representing two different levels of Bayesian probabilistic inference. This paper discusses a model-based sound energy decay analysis within a Bayesian framework utilizing the nested sampling algorithm. The nested sampling algorithm is specifically developed to evaluate the Bayesian evidence required for determining the energy decay order with decay parameter estimates as a secondary result. Taking the energy decay analysis in architectural acoustics as an example, this paper demonstrates that two different levels of inference, decay model-selection and decay parameter estimation, can be cohesively accomplished by the nested sampling algorithm.

“…This problem is often alleviated using a "burn-in" phase, in which sample X 0 is chosen after a certain amount of initial samples X −m , ... ,X −1 are discarded. The burn-in phase of the algorithm can be avoided using the FS algorithm 12 to choose the initial sample X 0 for both the linear A and decay time T parameters. The ability to choose the initial parameters T and A using the FS algorithm and the ability of the SSMC algorithm to overcome poor choices for w T j and w A j allows for a combined algorithm, which is especially useful in architectural acoustics practice.…”

Section: Initialization and Convergence Of The Ssmc Algorithmmentioning

confidence: 99%

“…Using an analytic example and sample posterior probability density functions ͑PPDFs͒ of acoustically coupled rooms, this paper discusses the difficulty in choosing a good ISMC sampling or MCMC proposal distributions, which often require significant user effort. A deterministic fast search ͑FS͒ algorithm, 12 which is less dependent on user initialization, is only able to estimate decay parameters; however, it cannot quantify uncertainties in the estimates nor can it determine inter-relationships between decay parameters. For data analysis, the uncertainties and inter-relationships of relevant parameters are of as the same importance as the parameters themselves.…”

Section: Introductionmentioning

confidence: 99%

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Efficient estimation of decay parameters in acoustically coupled-spaces using slice sampling

Jasa¹,

Xiang

2009

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Room-acoustic energy decay analysis of acoustically coupled-spaces within the Bayesian framework has proven valuable for architectural acoustics applications. This paper describes an efficient algorithm termed slice sampling Monte Carlo (SSMC) for room-acoustic decay parameter estimation within the Bayesian framework. This work combines the SSMC algorithm and a fast search algorithm in order to efficiently determine decay parameters, their uncertainties, and inter-relationships with a minimum amount of required user tuning and interaction. The large variations in the posterior probability density functions over multidimensional parameter spaces imply that an adaptive exploration algorithm such as SSMC can have advantages over the exiting importance sampling Monte Carlo and Metropolis-Hastings Markov Chain Monte Carlo algorithms. This paper discusses implementation of the SSMC algorithm, its initialization, and convergence using experimental data measured from acoustically coupled-spaces.