Acoustical Radiosity Research Articles

Theoretical analysis on structure of sound energy field decay of acoustical radiosity model with finite initial excitation.

The acoustical radiosity model (ARM) is a typical algorithm in geometrical acoustics to simulate the sound field in a room of ideally diffusely reflecting boundary. Even in such a room, the sound field decay is a complex process, as the relaxation of the sound field observed in simulations has shown. Based on the Laplace transform of the acoustical radiosity equation, this paper gives a set of properties of the ARM. It shows the system has a series of real or complex conjugate L-eigenvalues and corresponding L-eigenfunctions. Under the relaxation condition, the sound energy decay on the room boundary, generated by finite initial excitation, can be expanded as a summation of decay components, which are composed of real and/or complex conjugate decay modes. Each decay mode is a decaying and oscillating L-eigenfunction corresponding to an L-eigenvalue. The real part of the L-eigenvalue is the exponential decay rate, and the image part is the angular frequency of the oscillation. The reverberant sound field inside the room space has a similar decay structure to the boundary. As an example, the decay structure in a sphere is analyzed. The relaxation of the sound field is explained by the geometrical significance of the sound field decay.

음향라디오시티법을 이용한 잔향수조 음장 해석과 실험검증

The acoustic power is a major acoustical characteristic of an underwater vehicle and could be measured in a reverberant water tank. In order to obtain accurate measurement results, the acoustic field formed by the sound source should be investigated quantitatively in the reverberant water tank. In this research, the acoustic field of a reverberant water tank containing an underwater sound source has been analyzed by using an acoustic radiosity method one of the numerical analysis methods suitable for the acoustic analysis of the highly diffused space. The source level of the underwater sound source and acoustical properties of the water tank input to the numerical analysis have been estimated by applying the reverberant tank plot method through a preliminary experiment result. The comparison of the numerical analysis result with that of the experiment has verified the accuracy of the acoustic radiosity method.

A Hybrid Model for Investigating the Effect of Scattering from Building Façade on Sound Propagation in Street Canyons

Street canyons are basic components of modern cities. Sound propagation in streets has been proven to be significantly affected by reflections from building façades. In this paper, an iterative model combining acoustic radiosity and the image source method (IMCRI) is proposed to investigate the effect of diffuse reflections on sound propagation in urban street canyons. By applying image patches, this model calculates both specular reflected components and diffuse reflected components in every reflection. The accuracy of this model is then validated with full-scale measured data from five actual streets with different scattering conditions. Good agreements of sound pressure level and reverberation time are found between the IMCRI and the measurements. The performance of the IMCRI is found to be superior to those of the existing energy models, especially for the reverberation time simulation.

라디오시티법을 이용한 실내 음향장 해석 연구

Various numerical methods have been adopted for indoor noise assessments of ship plant. Acoustical radiosity method is one of the high frequency approaches for acoustic field analysis, which assumes diffuse reflections by boundaries so that it could be efficiently applied to the acoustically diffused indoor space noise analysis. In this study, an acoustic field analysis program has been developed based on radiosity method, which could apply for acoustically large enclosures such as ship’s indoor space. For this purpose, the procedure of the acoustical radiosity method has been summarized and implemented to an acoustic field analysis program using MATLAB. Numerical example for a rectangular indoor space has investigated validity of the implemented program. Steady state sound pressure levels calculated for a continuous acoustic source signal have shown good agreement with those by other solutions such as an analytic solution and a ray tracing method. Instantaneous sound pressure levels calculated for an impulsive acoustic signal have provided the clues of direct/reflected acoustic field and reverberation time.

Auralizations with loudspeaker arrays from a phased combination of the image source method and acoustical radiosity

In order to create a simulation tool that is well-suited for small rooms with low diffusion and highly absorbing ceilings, a new room acoustic simulation tool has been developed that combines a phased version of the image source with acoustical radiosity and that considers the angle dependence of the surface properties. The new tool is denoted PARISM, and here PARISM is used to create loudspeaker array-based auralizations. Different auralization techniques are compared, such as Ambisonics, vector-based panning, and the method of nearest loudspeaker. The implementations of the auralization techniques with PARISM are described and compared to implementations of auralizations with another geometrical acoustic simulation tool, i.e., ODEON and the LoRA toolbox that applies Ambisonics to ODEON simulations. In opposition to the LoRA toolbox, higher order Ambisonics are also applied to the late part of the PARISM impulse response, because more directional information is available with acoustical radiosity. Small rooms with absorbing surfaces are tested, because this is the room type that PARISM is particularly useful for.

Evaluation of a Loudspeaker-Based Virtual Acoustic Environment for Investigating sound-field auditory steady-state responses

Measuring sound-field auditory steady-state responses (ASSR) is a promising new objective clinical procedure for hearing aid fitting validation, particularly for infants who cannot respond to behavioral tests. In practice, room acoustics of non-anechoic test rooms can heavily influence the auditory stimulus used for eliciting the ASSR. To systematically investigate the effect of the room acoustics conditions on sound-field ASSR, a loudspeaker-based auralization system was implemented using a mixed order Ambisonics approach. The present study investigates the performance of the auralization system in terms of objective room acoustic measurements and sound-field ASSR measurements, both in the actual room and in the simulated and auralized room. The evaluation is conducted for a small room with well-defined acoustic properties. The room is carefully modeled using the novel room acoustic simulation tool PARISM (Phased Acoustical Radiosity and Image Source Method) and validated through measurements. This study discusses the limitations of the system and the potential improvements needed for a more realistic sound-field ASSR simulation.

Development and validation of a combined phased acoustical radiosity and image source model for predicting sound fields in rooms.

A model, combining acoustical radiosity and the image source method, including phase shifts on reflection, has been developed. The model is denoted Phased Acoustical Radiosity and Image Source Method (PARISM), and it has been developed in order to be able to model both specular and diffuse reflections with complex-valued and angle-dependent boundary conditions. This paper mainly describes the combination of the two models and the implementation of the angle-dependent boundary conditions. It furthermore describes how a pressure impulse response is obtained from the energy-based acoustical radiosity by regarding the model as being stochastic. Three methods of implementation are proposed and investigated, and finally, recommendations are made for their use. Validation of the image source method is done by comparison with finite element simulations of a rectangular room with a porous absorber ceiling. Results from the full model are compared with results from other simulation tools and with measurements. The comparisons of the full model are done for real-valued and angle-independent surface properties. The proposed model agrees well with both the measured results and the alternative theories, and furthermore shows a more realistic spatial variation than energy-based methods due to the fact that interference is considered.

Combination of acoustical radiosity and the image source method

A combined model for room acoustic predictions is developed, aiming to treat both diffuse and specular reflections in a unified way. Two established methods are incorporated: acoustical radiosity, accounting for the diffuse part, and the image source method, accounting for the specular part. The model is based on conservation of acoustical energy. Losses are taken into account by the energy absorption coefficient, and the diffuse reflections are controlled via the scattering coefficient, which defines the portion of energy that has been diffusely reflected. The way the model is formulated allows for a dynamic control of the image source production, so that no fixed maximum reflection order is required. The model is optimized for energy impulse response predictions in arbitrary polyhedral rooms. The predictions are validated by comparison with published measured data for a real music studio hall. The proposed model turns out to be promising for acoustic predictions providing a high level of detail and accuracy.

505 音響ラジオシティ法を用いた開口部からの漏れ音の解析

505 音響ラジオシティ法を用いた開口部からの漏れ音の解析

Steady state acoustic radiosity for the prediction of sound pressure levels in enclosures with diffuse surfaces

This paper presents a derivation for and shows practical application of the steady-state diffuse acoustic radiosity method to the prediction of steady state sound levels in rooms. The paper begins with a brief review of the general radiosity literature and a more thorough review of the radiosity method in acoustics and proceeds to derive the general steady state acoustic rendering integral equation applicable to radiative energy exchange enclosures with arbitrary surface reflection properties. The rendering equation is simplified assuming diffuse reflections and the enclosure surface is discretized to convert the integral equations into summations. A closed form matrix solution to the discrete equations and another matrix equation for computing mean square pressure at multiple locations from multiple sources are presented. The computer code used for further analysis is verified by comparison to a closed form solution for a special case. Convergence of the discretized solution is investigated and the method is shown to converge linearly as the patch size decreases. A practical implementation of the method for predicting of sound levels in a classroom is shown. Predictions using radiosity are compared with simple diffuse field theory and measurements of an actual room. The radiosity method is shown to match diffuse ray tracing to within a fraction of a dB and predictions with a discretization with patches as large as 2 m are shown to be within a fraction of a dB of the asymptotic values

Experimental evaluation of radiosity for room sound-field prediction

An acoustical radiosity model was evaluated for how it performs in predicting real room sound fields. This was done by comparing radiosity predictions with experimental results for three existing rooms--a squash court, a classroom, and an office. Radiosity predictions were also compared with those by ray tracing--a "reference" prediction model--for both specular and diffuse surface reflection. Comparisons were made for detailed and discretized echograms, sound-decay curves, sound-propagation curves, and the variations with frequency of four room-acoustical parameters--EDT, RT, D50, and C80. In general, radiosity and diffuse ray tracing gave very similar predictions. Predictions by specular ray tracing were often very different. Radiosity agreed well with experiment in some cases, less well in others. Definitive conclusions regarding the accuracy with which the rooms were modeled, or the accuracy of the radiosity approach, were difficult to draw. The results suggest that radiosity predicts room sound fields with some accuracy, at least as well as diffuse ray tracing and, in general, better than specular ray tracing. The predictions of detailed echograms are less accurate, those of derived room-acoustical parameters more accurate. The results underline the need to develop experimental methods for accurately characterizing the absorptive and reflective characteristics of room surfaces, possible including phase.

Relaxation of sound fields in rooms of diffusely reflecting boundaries and its application in acoustical radiosity simulation

The acoustical radiosity method is a computationally expensive acoustical simulation algorithm that assumes an enclosure with ideal diffuse reflecting boundaries. Miles observed that for such an enclosure, the sound energy decay of every point on the boundaries will gradually converge to exponential manner with a uniform decay rate. Therefore, the ratio of radiosity between every pair of points on the boundaries will converge to a constant, and the radiosity across the boundaries will approach a fixed distribution during the sound decay process, where radiosity is defined as the acoustic power per unit area leaving (or being received by) a point on a boundary. We call this phenomenon the "relaxation" of the sound field. In this paper, we study the relaxation in rooms of different shapes with different boundary absorptions. Criteria based on the relaxation of the sound field are proposed to terminate the costly and unnecessary radiosity computation in the later phase, which can then be replaced by a fast regression step to speed up the acoustical radiosity simulation.

Application of acoustic radiosity methods to noise propagation within buildings

The prediction of sound pressure levels in rooms from transmitted sound is a difficult problem. The sound energy in the source room incident on the common wall must be accurately predicted. In the receiving room, the propagation of sound from the planar wall source must also be accurately predicted. The radiosity method naturally computes the spatial distribution of sound energy incident on a wall and also naturally predicts the propagation of sound from a planar area source. In this paper, the application of the radiosity method to sound transmission problems is introduced and explained.

A comparison of partially specular radiosity and ray tracing for room acoustics modeling

Partially specular (PS) radiosity is an extended form of the general radiosity method. Acoustic radiosity is a form of bulk transfer of radiant acoustic energy. This bulk transfer is accomplished through a system of energy balance equations that relate the bulk energy transfer of each surface in the system to all other surfaces in the system. Until now acoustic radiosity has been limited to modeling only diffuse surface reflection. The new PS acoustic radiosity method can model all real surface types, diffuse, specular and everything in between. PS acoustic radiosity also models all real source types and distributions, not just point sources. The results of the PS acoustic radiosity method are compared to those of well known ray tracing programs. [Work supported by NSF.]

Investigation of the validity of radiosity for sound-field prediction in cubic rooms

This paper explores acoustical (or time-dependent) radiosity using predictions made in four cubic enclosures. The methods and algorithms used are those presented in a previous paper by the same authors [Nosal, Hodgson, and Ashdown, J. Acoust. Soc. Am. 116(2), 970-980 (2004)]. First, the algorithm, methods, and conditions for convergence are investigated by comparison of numerous predictions for the four cubic enclosures. Here, variables and parameters used in the predictions are varied to explore the effect of absorption distribution, the necessary conditions for convergence of the numerical solution to the analytical solution, form-factor prediction methods, and the computational requirements. The predictions are also used to investigate the effect of absorption distribution on sound fields in cubic enclosures with diffusely reflecting boundaries. Acoustical radiosity is then compared to predictions made in the four enclosures by a ray-tracing model that can account for diffuse reflection. Comparisons are made of echograms, room-acoustical parameters, and discretized echograms.

A comparison of computational models for predicting speech intelligibility and speech privacy

Speech intelligibility (SI) and speech privacy (SP) are very important considerations in the design of classrooms, auditoria, conference rooms, and offices. Predictions of SI and SP are usually done with simple analytic models using Sabine/Eyring theory or CAD programs such as CATT, EASE or ODEON. In this paper we will compare the predictions of speech intelligibility index (SII), speech transmission index (STI), and privacy index (PI) using analytic theories of Sabine/Eyring and a simplified acoustic radiosity theory, a simple computational model using acoustic radiosity and CAD prediction using CATT acoustics. Predictions will be compared with the results of a similar study by Bistafa and Bradley [J. Acoust. Soc. Am. 109(4), 1474–1482 (2001)].

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms.

This paper explores acoustical (or time-dependent) radiosity--a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

Acoustic radiosity for computation of sound fields in diffuse environments

The use of image and ray tracing methods (and variations thereof) for the computation of sound fields in rooms is relatively well developed. In their regime of validity, both methods work well for prediction in rooms with small amounts of diffraction and mostly specular reflection at the walls. While extensions to the method to include diffuse reflections and diffraction have been made, they are limited at best. In the fields of illumination and computer graphics the ray tracing and image methods are joined by another method called luminous radiative transfer or radiosity. In radiosity, an energy balance between surfaces is computed assuming diffuse reflection at the reflective surfaces. Because the interaction between surfaces is constant, much of the computation required for sound field prediction with multiple or moving source and receiver positions can be reduced. In acoustics the radiosity method has had little attention because of the problems of diffraction and specular reflection. The utility of radiosity in acoustics and an approach to a useful development of the method for acoustics will be presented. The method looks especially useful for sound level prediction in industrial and office environments. [Work supported by NSF.]