Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators.

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 to 0.10 Pa. Notably, our method signifies a paradigm shift as-to our knowledge-no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains.

Just noticeable difference for simulation accuracy between full and reduced order models (L).

Model order reduction techniques significantly reduce the computational time when performing accurate room acoustic simulations with numerical methods that inherently include all the wave phenomena. There is a clear trade-off between physical accuracy and acceleration, but how humans perceive these errors is unknown. This study aims to investigate physical error limit that does not induce perceptual differences. Various two-dimensional rooms and reverberation times are tested with a three-alternative forced-choice listening test. Results reveal that for the presented cases, the threshold stands between a relative root mean square error of 1% and 0.1%, where the reduced order model stimulus results in a statistically significant difference.

Reduced order modelling using parameterized non-uniform boundary conditions in room acoustic simulations.

Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room acoustic scenarios where the surfaces have inhomogeneous acoustic properties, which enables quick evaluations of changing absorption materials for different surfaces in room acoustic simulations. The RBM has shown its benefit to speed up room acoustic simulations by 3 orders of magnitude for uniform boundary conditions. This study investigates the RBM with two main focuses: (1) various source positions in diverse geometries, e.g., square, rectangular, L-shaped, and disproportionate room, (2) two-dimensional and three-dimensional (3D) inhomogeneous surface absorption by parameterizing numerous acoustic parameters of surfaces, e.g., the thickness of a porous material, cavity depth, switching between a frequency independent (e.g., hard surface) and frequency dependent boundary condition. Results of numerical experiments show speedups of more than 2 orders of magnitude compared to a high fidelity numerical solver in a 3D case where reverberation time varies within one just noticeable difference in all the frequency octave bands.

Hidden energies around surfaces, edges, and corners in rooms.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Reduced basis methods for numerical room acoustic simulations with parametrized boundaries.

The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis method (RBM) to achieve a computational cost reduction relative to a traditional full-order model (FOM) for wave-based room acoustic simulations with parametrized boundaries. The FOM solver is based on the spectral-element method; however, other numerical methods could be applied. The RBM reduces the computational burden by solving the problem in a low-dimensional subspace for parametrized frequency-independent and frequency-dependent boundary conditions. The problem is formulated in the Laplace domain, which ensures the stability of the reduced-order model (ROM). We study the potential of the proposed RBM in terms of computational efficiency, accuracy, and storage requirements, and we show that the RBM leads to 100-fold speedups for a two-dimensional case and 1000-fold speedups for a three-dimensional case with an upper frequency of 2 and 1 kHz, respectively. While the FOM simulations needed to construct the ROM are expensive, we demonstrate that the ROM has the potential of being 3 orders of magnitude faster than the FOM when four different boundary conditions are simulated per room surface.

Time-domain room acoustic simulations with extended-reacting porous absorbers using the discontinuous Galerkin method.

This paper presents an equivalent fluid model (EFM) formulation in a three-dimensional time-domain discontinuous Galerkin finite element method framework for room acoustic simulations. Using the EFM allows for the modeling of the extended-reaction (ER) behavior of porous sound absorbers. The EFM is formulated in the numerical framework by using the method of auxiliary differential equations to account for the frequency dependent dissipation of the porous material. The formulation is validated analytically and an excellent agreement with the theory is found. Experimental validation for a single reflection case is also conducted, and it is shown that using the EFM improves the simulation accuracy when modeling a porous material backed by an air cavity as compared to using the local-reaction (LR) approximation. Last, a comparative study of different rooms with different porous absorbers is presented, using different boundary modeling techniques, namely, a LR approximation, a field-incidence (FI) approximation, or modeling the full ER behavior with the EFM. It is shown that using a LR or FI approximation leads to large and perceptually noticeable errors in simulated room acoustic parameters. The average T20 reverberation time error is 4.3 times the just-noticeable-difference (JND) threshold when using LR and 2.9 JND when using FI.

Bayesian decay time estimation in a reverberation chamber for absorption measurements.

This work investigates the use of the initial decay time to obtain the Sabine absorption coefficient from measurements conducted in a reverberation chamber. Due to non-uniform distribution of sound absorption in the test chamber, measured energy decay functions exhibit multiple slopes, which cannot be evaluated unambiguously using linear regression as prescribed in the current standard (ISO 354, International Organization for Standardization, Geneva, Switzerland, 2003). As an alternative, this study proposes a Bayesian framework that allows estimating multiple decay parameters, hence capturing more accurately the energy decay features. Measurements are carried out in a reverberation chamber with and without diffusing elements to investigate the influence of diffusers on the absorption coefficient and on the decay process. Measured absorption coefficients of a porous sample are compared to theoretical values estimated with a transfer matrix model. The results show that the Sabine absorption coefficient calculated using the shortest decay time agrees well with the size-corrected theoretical absorption coefficient.

Characterization of sound scattering using near-field pressure and particle velocity measurements.

The acoustic properties of surfaces are commonly evaluated using samples of finite size, which generate edge diffraction effects that are often disregarded. This study makes use of sound scattering theory to characterize such finite samples. In a given sound field, the samples can be described by a unique complex directivity function called the far-field pattern. Numerical results show that the far-field pattern contains extensive information on the tested samples, including sound absorption and surface scattering, as well as scattering due to finiteness. In this paper, a method is introduced to estimate the far-field pattern of a finite sample. The method relies on measurements of the sound pressure and acoustic particle velocity in the near-field of the sample, and it makes use of the Helmholtz integral equation. The proposed technique is examined in an anechoic room where the sound field near the test sample is scanned with a three-dimensional sound intensity probe. The estimated far-field pattern is compared with numerical predictions up to 1 kHz.

Time domain room acoustic simulations using the spectral element method.

This paper presents a wave-based numerical scheme based on a spectral element method, coupled with an implicit-explicit Runge-Kutta time stepping method, for simulating room acoustics in the time domain. The scheme has certain features which make it highly attractive for room acoustic simulations, namely (a) its low dispersion and dissipation properties due to a high-order spatio-temporal discretization; (b) a high degree of geometric flexibility, where adaptive, unstructured meshes with curvilinear mesh elements are supported; and (c) its suitability for parallel implementation on modern many-core computer hardware. A method for modelling locally reacting, frequency dependent impedance boundary conditions within the scheme is developed, in which the boundary impedance is mapped to a multipole rational function and formulated in differential form. Various numerical experiments are presented, which reveal the accuracy and cost-efficiency of the proposed numerical scheme.

Prediction of sound absorption based on specific airflow resistance and air permeability of textiles.

Both specific airflow resistance and air permeability can be used as a parameter to estimate the sound absorption of textiles. The measurement of specific airflow resistance is specified in ISO 9053 (Int. Standards Org., 1991), but it is known to be inaccurate for low specific airflow resistance. This paper compares the measured specific airflow resistance according to ISO 9053 and those calculated from air permeability according to ISO 9237 (Int. Standards Org., 1995). The sound absorption coefficients predicted by Pieren's model [R. Pieren, Textile Res. J. 82(9), 864-874 (2012)] are compared with measurements by the impedance tube method, which concludes that those predicted from the air permeability are more accurate than those from the measured specific airflow resistance for textiles.

A wavenumber approach to quantifying the isotropy of the sound field in reverberant spaces.

This study proposes an experimental method for evaluating isotropy in enclosures, based on an analysis of the wavenumber spectrum in the spherical harmonics domain. The wavenumber spectrum, which results from expanding an arbitrary sound field into a plane-wave basis, is used to characterize the spatial properties of the observed sound field. Subsequently, the obtained wavenumber spectrum is expanded into a series of spherical harmonics, and the moments from this spherical expansion are used to characterize the isotropy of the wave field. The analytical framework is presented. The method is examined numerically and experimentally, based on array measurements in four chambers: two anechoic chambers (one with a single source and another with an array of 52 sources), a reverberation chamber, and the same reverberation chamber with a sample of absorbing material on the floor. The results indicate that the proposed methodology is suitable for assessing the isotropy of a sound field.

Estimation of surface impedance at oblique incidence based on sparse array processing.

A method is proposed to estimate the surface impedance of a large absorptive panel from free-field measurements with a spherical microphone array. The method relies on the reconstruction of the pressure and the particle velocity on the studied surface using an equivalent source method based on spherical array measurements. The sound field measured by the array is mainly composed of an incident and a reflected wave, so it can be represented as a spatially sparse problem. This makes it possible to use compressive sensing in order to enhance the resolution and the quality of the estimation. The results indicate an accurate reconstruction for angles of incidence between 0° and 60°, and between approximately 200 and 4000 Hz. Additionally, experimental challenges are discussed, such as the sample's finiteness at low frequencies and the estimation of the background noise.

Bayesian inference of the flow resistivity of a sound absorber and the room's influence on the Sabine absorption coefficients.

A Bayesian analysis is applied to determine the flow resistivity of a porous sample and the influence of the test chamber based on measured Sabine absorption coefficient data. The Sabine absorption coefficient measured in a reverberation chamber according to ISO 354 is influenced by the test chamber significantly, whereas the flow resistivity is a rather reproducible material property, from which the absorptive characteristics can be calculated through reliable models. Using Sabine absorption coefficients measured in 13 European reverberation chambers, the maximum a posteriori and the uncertainty of the flow resistivity and the test chamber's influence are estimated. Inclusion of more than one chamber's absorption data helps the flow resistivity converge towards a reliable value with a standard deviation below 17%.

On-site and laboratory evaluations of soundscape quality in recreational urban spaces.

CONTEXT: Regulations for quiet urban areas are typically based on sound level limits alone. However, the nonacoustic context may be crucial for subjective soundscape quality. AIMS: This study aimed at comparing the role of sound level and nonacoustic context for subjective urban soundscape assessment in the presence of the full on-site context, the visual context only, and without context. MATERIALS AND METHODS: Soundscape quality was evaluated for three recreational urban spaces by using four subjective attributes: loudness, acceptance, stressfulness, and comfort. The sound level was measured at each site and simultaneous sound recordings were obtained. Participants answered questionnaires either on site or during laboratory listening tests, in which the sound recordings were presented with or without each site's visual context consisting of two pictures. They rated the four subjective attributes along with their preference toward eight sound sources. RESULTS: The sound level was found to be a good predictor of all subjective parameters in the laboratory, but not on site. Although all attributes were significantly correlated in the laboratory setting, they did not necessarily covary on site. Moreover, the availability of the visual context in the listening experiment had no significant effect on the ratings. The participants were overall more positive toward natural sound sources on site. CONCLUSION: The full immersion in the on-site nonacoustic context may be important when evaluating overall soundscape quality in urban recreational areas. Laboratory evaluations may not fully reflect how subjective loudness, acceptance, stressfulness, and comfort are affected by sound level.

Kurtosis of room impulse responses as a diffuseness measure for reverberation chambers.

This study presents a kurtosis analysis of room impulse responses as a potential room diffuseness measure. The early part of an impulse response contains a direct sound and strong reflections. As these reflections are sparse and strong, the sound field is unlikely to be diffuse. Such deterministic reflections are extreme events, which prevent the pressure samples from being distributed Gaussianly, leading to a high kurtosis. This indicates that the kurtosis can be used as a diffuseness measure. Two rooms are analyzed. A non-uniform surface absorption distribution tends to increase the kurtosis significantly in a small room. A full scale reverberation chamber is tested with different diffuser settings, which shows that the kurtosis calculated from broadband impulse responses from 125 Hz to 4 kHz has a good correlation with the Sabine absorption coefficient according to ISO 354 (International Organization for Standardization, Geneva, Switzerland, 2003).

Predicting the Sabine absorption coefficients of fibrous absorbers for various air backing conditions with a frequency-dependent diffuseness correction.

Fibrous absorbers can be installed with various air backing conditions to fulfil a given low frequency acoustic requirement. Since absorber manufacturers cannot provide the absorption coefficients for all possible mounting conditions, acousticians have difficulties knowing the absorption characteristics of their own configurations. This study aims to predict the absorption coefficient for various mounting conditions from a single measurement of an arbitrary mounting condition by extracting the air flow resistivity of the test specimen and the frequency-dependent effect of the chamber on the measured absorption coefficients. With two homogeneous fibrous absorbers, the predicted absorption coefficients agree well with the measurements.

Effect of modulation depth, frequency, and intermittence on wind turbine noise annoyance.

Amplitude modulation (AM) may be an important factor for the perceived annoyance of wind turbine noise (WTN). Two AM types, typically referred to as "normal AM" (NAM) and "other AM" (OAM), characterize WTN AM, OAM corresponding to having intermittent periods with larger AM depth in lower frequency regions than NAM. The extent to which AM depth, frequency, and type affect WTN annoyance remains uncertain. Moreover, the temporal variations of WTN AM have often not been considered. Here, realistic stimuli accounting for such temporal variations were synthesized such that AM depth, frequency, and type, while determined from real on-site recordings, could be varied systematically. Listening tests with both original and synthesized stimuli showed that a reduction in mean AM depth across the spectrum led to a significant decrease in annoyance. When the spectrotemporal characteristics of the original far-field stimuli and the temporal AM variations were taken into account, the effect of AM frequency remained limited and the presence of intermittent OAM periods did not affect annoyance. These findings suggest that, at a given overall level, the AM depth of NAM periods is the most crucial AM parameter for WTN annoyance.

In situ measurements of the oblique incidence sound absorption coefficient for finite sized absorbers.

Absorption coefficients are mostly measured in reverberation rooms or with impedance tubes. Since these methods are only suitable for measuring the random incidence and the normal incidence absorption coefficient, there exists an increasing need for absorption coefficient measurement of finite absorbers at oblique incidence in situ. Due to the edge diffraction effect, oblique incidence methods considering an infinite sample fail to measure the absorption coefficient at large incidence angles of finite samples. This paper aims for the development of a measurement method that accounts for the finiteness of the absorber. A sound field model, which accounts for scattering from the finite absorber edges, assuming plane wave incidence is derived. A significant influence of the finiteness on the radiation impedance and the corresponding absorption coefficient is found. A finite surface method, which combines microphone array measurements over a finite sample with the sound field model in an inverse manner, is proposed. Besides, a temporal subtraction method, a microphone array method, impedance tube measurements, and an equivalent fluid model are used for validation. The finite surface method gives promising agreement with theory, especially at near grazing incidence. Thus, the finite surface method is proposed for further measurements at large incidence angles.

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.

Acoustic behavior of porous ceiling absorbers based on local and extended reaction.

The acoustic behavior of ceiling absorbers can be predicted under different surface reaction assumptions: Local and extended reaction. This study aims to experimentally validate acoustic transfer functions near a ceiling absorber in an anechoic chamber based on the two surface reaction models. First, a ceiling absorber with two mounting conditions is modeled by equivalent fluid models, such as Delany-Bazley's, Miki's, and Komatsu's model, in various ways: (1) Local vs extended reaction and (2) plane-wave vs spherical-wave incidence. For a single absorber under anechoic conditions, the acoustic transfer functions for four source-receiver pairs are simulated using a pressure-based image source model, and then compared with measurements. For a rigid backing condition, both the local and extended reaction models agree well with the measurement. For an absorber backed by an air cavity, the extended reaction model agrees better at larger incidence angles at lower frequencies than the local reaction model.