Nested sampling applied in Bayesian room-acoustics decay analysis

Validation of Bayesian design for broadband microslit panel absorbers using causal inference

This paper discusses experimental validations of multilayer microslit panels (MSPs) designed via Bayesian inference to obtain both high sound absorption and wide bandwidth simultaneously. Microslit perforation in thin panels is similar to microperforated panels [Xiang, Fackler, Hou, and Schmitt (2022). J. Acoust. Soc. Am. 151(5), 3094-3103]. MSP absorbers in single-layer configurations are functioning in a limited frequency range. By stacking the MSPs in multiple layered structures, absorbing performance may be widened in frequency ranges while retaining high absorption coefficients. Besides design challenges of multiple MSPs in layered structures to fulfill a practical requirement and minimize fabrication complexity, this paper further discusses challenges in experimental validations when experimental results undesirably deviate from the initial Bayesian design. Causation analysis is applied to the validation efforts where a causal model-based inference effectively provides causal reasoning of fabrication inaccuracies. Along with the causal inference, a causal reasoning conducted in this work can guide corrections due to fabrication inaccuracies during the iterative validation process.

Bayesian design of broadband multilayered microperforated panel absorbers

In some noise control and architectural acoustics applications, nonfibrous, hygienic materials are desirable or even strictly required. In meeting such restrictive requirements, microperforated panel (MPP) sound absorbers represent a potential solution. Yet, they typically possess limited absorption bandwidth. Combining multiple MPPs into a multilayer system may broaden the absorption frequency ranges while maintaining high absorption. When increasing the overall absorption bandwidth, each additional MPP layer also increases the complexity of the design process because the design parameters are correspondingly increased by four per each additional layer. This paper applies a Bayesian inferential framework to the design of multilayer MPP absorbers with a parsimonious structural configuration, which penalizes the overlayered configurations. This Bayesian framework demonstrates that the practical design of multilayer MPP absorbers may be accomplished with two levels of model-based inference: model selection and parameter estimation. The design process proceeds inversely from a design target to design parameters, including the required number of MPP layers and their corresponding MPP parameters. This paper discusses the Bayesian design formulation, unified implementation of two levels of Bayesian inference, and experimental validation of a Bayesian design for a multilayered MPP absorber, which is able to meet the design target arising from practice.

Exploration of room acoustics coupling in Hagia Sophia of İstanbul for its different states

İstanbul's Hagia Sophia is a monumental structure with multiple sub-spaces coupled to one another through arches. Its architectural elements have undergone alterations as its function has changed from that of a church to a mosque, a mosque to a museum, and back to a mosque. This study makes use of Hagia Sophia's rich formal and material characteristics to conduct a comprehensive investigation of room acoustics coupling. The methodology involves the application of the diffusion equation model (DEM) for sound energy flow analysis. Energy flow decays and energy flow dips are examined for almost 1000 receiver positions distributed throughout the various sub-spaces of the building. Ray-tracing (Ray-t) simulations are used to support the energy flow decay analysis conducted using DEM. The Ray-t data are subjected to Bayesian analysis to identify the decay parameters and the degree of acoustical coupling. Among the many variables, the source-receiver distance and positioning within different sub-spaces appear to be the underlying determinant of multi-slope sound decay pattern. On the other hand, the cases of multi-slope decays identified within the structure tend to weaken and single-slope cases increase when the overall absorption area increases in the mosque state due to the carpeted floor.

Model-based Bayesian analysis in acoustics-A tutorial

Bayesian analysis has been increasingly applied in many acoustical applications. In these applications, prediction models are often involved to better understand the process under investigation by purposely learning from the experimental observations. When involving the model-based data analysis within a Bayesian framework, issues related to incorporating the experimental data and assigning probabilities into the inferential learning procedure need fundamental consideration. This paper introduces Bayesian probability theory on a tutorial level, including fundamental rules for manipulating the probabilities, and the principle of maximum entropy for assignment of necessary probabilities prior to the data analysis. This paper also employs a number of examples recently published in this journal to explain detailed steps on how to apply the model-based Bayesian inference to solving acoustical problems.

Model-based Bayesian direction of arrival analysis for sound sources using a spherical microphone array

In many room acoustics and noise control applications, it is often challenging to determine the directions of arrival (DoAs) of incoming sound sources. This work seeks to solve this problem reliably by beamforming, or spatially filtering, incoming sound data with a spherical microphone array via a probabilistic method. When estimating the DoA, the signal under consideration may contain one or multiple concurrent sound sources originating from different directions. This leads to a two-tiered challenge of first identifying the correct number of sources, followed by determining the directional information of each source. To this end, a probabilistic method of model-based Bayesian analysis is leveraged. This entails generating analytic models of the experimental data, individually defined by a specific number of sound sources and their locations in physical space, and evaluating each model to fit the measured data. Through this process, the number of sources is first estimated, and then the DoA information of those sources is extracted from the model that is the most concise to fit the experimental data. This paper will present the analytic models, the Bayesian formulation, and preliminary results to demonstrate the potential usefulness of this model-based Bayesian analysis for complex noise environments with potentially multiple concurrent sources.

Bayesian Inference for Acoustic Direction of Arrival Analysis Using Spherical Harmonics

This work applies two levels of inference within a Bayesian framework to accomplish estimation of the directions of arrivals (DoAs) of sound sources. The sensing modality is a spherical microphone array based on spherical harmonics beamforming. When estimating the DoA, the acoustic signals may potentially contain one or multiple simultaneous sources. Using two levels of Bayesian inference, this work begins by estimating the correct number of sources via the higher level of inference, Bayesian model selection. It is followed by estimating the directional information of each source via the lower level of inference, Bayesian parameter estimation. This work formulates signal models using spherical harmonic beamforming that encodes the prior information on the sensor arrays in the form of analytical models with an unknown number of sound sources, and their locations. Available information on differences between the model and the sound signals as well as prior information on directions of arrivals are incorporated based on the principle of the maximum entropy. Two and three simultaneous sound sources have been experimentally tested without prior information on the number of sources. Bayesian inference provides unambiguous estimation on correct numbers of sources followed by the DoA estimations for each individual sound sources. This paper presents the Bayesian formulation, and analysis results to demonstrate the potential usefulness of the model-based Bayesian inference for complex acoustic environments with potentially multiple simultaneous sources.

A model-based Bayesian framework for sound source enumeration and direction of arrival estimation using a coprime microphone array

Coprime microphone arrays use sparse sensing to achieve greater degrees of freedom, while the coprimality of the microphone subarrays help resolve grating lobe ambiguities. The result is a narrow beam at frequencies higher than the spatial Nyquist limit allows, with residual side lobes arising from aliasing. These side lobes can be mitigated when observing broadband sources, as shown by Bush and Xiang [J. Acoust. Soc. Am. 138, 447-456 (2015)]. Peak positions may indicate directions of arrival in this case; however, one must first ask how many sources are present. In answering this question, this work employs a model describing scenes with potentially multiple concurrent sound sources. Bayesian inference is used to first select which model the data prefer from competing models before estimating model parameters, including the particular source locations. The model is a linear combination of Laplace distribution functions (one per sound source). The likelihood function is explored by a Markov Chain Monte Carlo method called nested sampling in order to evaluate Bayesian evidence for each model. These values increase monotonically with model complexity; however, diminished returns are penalized via an implementation of Occam's razor.

A comparison of three geoacoustic models using Bayesian inversion and selection techniques applied to wave speed and attenuation measurements

Many geoacoustic models have been developed to study sandy sediments. In this work, Bayesian inference techniques are used to compare three such models: the VGS(λ) model, the most recent of Buckingham's viscous grain-shearing models, the Biot-Stoll poroelastic model, and an extension to the Biot-Stoll model proposed by Chotiros called the corrected and reparametrized extended Biot (CREB) model. First, Bayesian inversion is applied to wave speed and attenuation measurements previously made in the laboratory to determine the degree to which each of the model input parameters can be resolved by wave speed and attenuation data. Then, Bayesian model selection techniques are utilized to assess the degree to which the predictions of these models match the measured data and to ascertain the Bayesian evidence in favor of each. Through these studies it is determined that the VGS(λ) and CREB models outperform the Biot-Stoll model, both in terms of parameter resolution and in their ability to produce predictions in agreement with measurements. The VGS(λ) model is seen to have the highest degree of Bayesian evidence in its favor.

Room acoustic modal analysis using Bayesian inference

Strong modal behavior can produce undesirable acoustical effects, particularly in recording studios and other small rooms. Although closed-form solutions exist to predict modes in rectangular rooms with parallel walls, such solutions are typically not available for rooms with even modest geometrical complexity. This work explores a method to identify multiple decaying modes in experimentally measured impulse responses from existing spaces. The method adopts a Bayesian approach working in the time domain to identify numerous decaying modes in an impulse response. Bayesian analysis provides a unified framework for two levels of inference: model selection and parameter estimation. In this context model selection determines the number of modes present in an impulse response, while parameter estimation determines the relevant parameters (e.g., decay time and frequency) of each mode. The Bayesian analysis in this work is implemented using an approximate numerical technique called nested sampling. Experimental measurements are performed in a test chamber in two different configurations. Experimentally measured results are compared with simulated values from the Bayesian analyses along with other, more classical calculations. Discussion of the results and the applicability of the method is provided.

Prediction of break-out sound from a rectangular cavity via an elastically mounted panel

The break-out sound from a cavity via an elastically mounted panel is predicted in this paper. The vibroacoustic system model is derived based on the so-called spectro-geometric method in which the solution over each sub-domain is invariably expressed as a modified Fourier series expansion. Unlike the traditional modal superposition methods, the continuity of the normal velocities is faithfully enforced on the interfaces between the flexible panel and the (interior and exterior) acoustic media. A fully coupled vibro-acoustic system is obtained by taking into account the strong coupling between the vibration of the elastic panel and the sound fields on the both sides. The typical time-consuming calculations of quadruple integrals encountered in determining the sound power radiation from a panel has been effectively avoided by reducing them, via discrete cosine transform, into a number of single integrals which are subsequently calculated analytically in a closed form. Several numerical examples are presented to validate the system model, understand the effects on the sound transmissions of panel mounting conditions, and demonstrate the dependence on the size of source room of the "measured" transmission loss.

Reverberation decay functions for narrow bands obtained from filtered time-windowed room impulse responses (L)

This study introduces a method to obtain the reverberation decay functions for narrow bands from the filtered time-windowed broadband room impulse responses. The method corresponds to the free decay process of the band-pass sound energy. The filtering process is independent of the band-pass filter phase responses and it reduces the filtering influence on the decay rates. It places no limit on the permissible product BT of the bandwidth B and the reverberation time T when evaluating the decay rates of the obtained decay functions.

Tipping point analysis of atmospheric oxygen concentration

We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the observed data using Bayesian and wavelet techniques.

A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion

This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.].

A Bayesian direction-of-arrival model for an undetermined number of sources using a two-microphone array

Sound source localization using a two-microphone array is an active area of research, with considerable potential for use with video conferencing, mobile devices, and robotics. Based on the observed time-differences of arrival between sound signals, a probability distribution of the location of the sources is considered to estimate the actual source positions. However, these algorithms assume a given number of sound sources. This paper describes an updated research account on the solution presented in Escolano et al. [J. Acoust. Am. Soc. 132(3), 1257-1260 (2012)], where nested sampling is used to explore a probability distribution of the source position using a Laplacian mixture model, which allows both the number and position of speech sources to be inferred. This paper presents different experimental setups and scenarios to demonstrate the viability of the proposed method, which is compared with some of the most popular sampling methods, demonstrating that nested sampling is an accurate tool for speech localization.

Nested sampling for Bayesian model comparison in the context of Salmonella disease dynamics

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.

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

Some recent concert hall designs have incorporated coupled reverberation chambers to the main hall that have stimulated a range of research activities in architectural acoustics. The coupling apertures between two or more coupled-volume systems are of central importance for sound propagation and sound energy decays throughout the coupled-volume systems. In addition, positions of sound sources and receivers relative to the aperture also have a profound influence on the sound energy distributions and decays. This work investigates the effect of aperture size on the behavior of coupled-volume systems using both acoustic scale-models and diffusion equation models. In these physical and numerical models, the sound source and receiver positions relative to the aperture are also investigated. Through systematic comparisons between results achieved from both physical scale models and numerical models, this work reveals valid ranges and limitations of the diffusion equation model for room-acoustic modeling.

Bayesian approach of nearfield acoustic reconstruction with particle filters

This paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the Bayesian approach of parameter estimation. In particular, the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method (ESM). A state-space model is formulated in light of the ESM. The parameters to estimate are amplitudes and locations of the equivalent sources. The parameters constitute the state vector which follows a first-order Markov process with the transition matrix being the identity for every frequency-domain data frame. Filtered estimates of the state vector obtained are assigned weights adaptively. The implementation of recursive Bayesian filters involves a sequential Monte Carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function (PMF) which evolves with iteration. The weight update equation governs the evolution of this PMF and depends primarily on the likelihood function and the prior distribution. It is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation.