Energy Decay Functions Research Articles

Neural network for multi-exponential sound energy decay analysis.

An established model for sound energy decay functions (EDFs) is the superposition of multiple exponentials and a noise term. This work proposes a neural-network-based approach for estimating the model parameters from EDFs. The network is trained on synthetic EDFs and evaluated on two large datasets of over 20 000 EDF measurements conducted in various acoustic environments. The evaluation shows that the proposed neural network architecture robustly estimates the model parameters from large datasets of measured EDFs while being lightweight and computationally efficient. An implementation of the proposed neural network is publicly available.

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.

Room acoustical parameters of two electronically connected rooms.

The acoustical properties of two rooms that are one-way connected electroacoustically, e.g., in a telephone/video conference, can be analyzed through the total impulse response from a source in one room to the receiver in the other room. The total impulse response is a convolution of the two involved room impulse responses, and such a model is analyzed in this paper. The room impulse response model used here facilitates convolution analysis as the model is quite simple and composed of two terms only, a direct sound term and an exponentially decaying random Gaussian noise term. Analytical expressions have been derived for the energy decay function, leading to estimates of room acoustical parameters like clarity and the modulation transfer functions for such convolved impulse responses. Background noise expressions are also introduced to allow signal-to-noise ratio studies. Estimates of acoustic parameter values have been compared with measurements to evaluate the model used and verify the results achieved.

Evaluation of the 3-D finite difference implementation of the acoustic diffusion equation model on massively parallel architectures

The diffusion equation model is a popular tool in room acoustics modeling. The 3-D Finite Difference (3D-FD) implementation predicts the energy decay function and the sound pressure level in closed environments. This simulation is computationally expensive, as it depends on the resolution used to model the room. With such high computational requirements, a high-level programming language (e.g., Matlab) cannot deal with real life scenario simulations. Thus, it becomes mandatory to use our computational resources more efficiently. Manycore architectures, such as NVIDIA GPUs or Intel Xeon Phi offer new opportunities to enhance scientific computations, increasing the performance per watt, but shifting to a different programming model. This paper shows the roadmap to use massively parallel architectures in a 3D-FD simulation. We evaluate the latest generation of NVIDIA and Intel architectures. Our experimental results reveal that NVIDIA architectures outperform by a wide margin the Intel Xeon Phi co-processor while dissipating approximately 50W less (25%) for large-scale input problems.

Schroeder integration: Foundation for advanced sound energy decay analysis.

Schroeder’s backward integration method broke the new ground in classical architectural acoustics. Soon after publication of Schroeder’s backward integration method for obtaining sound energy decay functions from room-impulse responses [Schroeder, J. Acoust. Soc. Am. 37, 409–412 (1965)], research activities in this field have been frequently reported in major journal publications. For reverberation time estimation based on a traditional straight-line model, solutions to remedy problems related to the upper limit of backward integration and the background noise in experimentally measured Schroeder decay functions have emerged. Using a parametric model derived from the nature of Schroeder integration, this author proposed a nonlinear regression method [Xiang, J. Acoust. Soc. Am. 98, 2112–2121 (1995)]. The nonlinear regression method yields reverberation time estimates, insensitive to background noise, and the upper limit of integration. Recent interest in acoustically coupled-volume systems has prompted new challenges in analyzing sound energy decay characteristics, which are more complicated than just single-rate decays. This paper will demonstrate a suitable framework for this room-acoustics application using Bayesian inference and the Schroeder backward integration as the foundation of the advanced model-based energy decay analysis. Based on the Schroeder integration, two levels of inference, decay order selection, and decay parameter estimation have been developed for practical applications.

Evaluation of decay times in coupled spaces: Bayesian parameter estimation.

Determination of sound decay times in coupled spaces often demands considerable effort. Based on Schroeder's backward integration of room impulse responses, it is often difficult to distinguish different portions of multirate sound energy decay functions. A model-based parameter estimation method, using Bayesian probabilistic inference, proves to be a powerful tool for evaluating decay times. A decay model due to one of the authors [N. Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] is extended to multirate decay functions. Following a summary of Bayesian model-based parameter estimation, the present paper discusses estimates in terms of both synthesized and measured decay functions. No careful estimation of initial values is required, in contrast to gradient-based approaches. The resulting robust algorithmic estimation of more than one decay time, from experimentally measured decay functions, is clearly superior to the existing nonlinear regression approach.

Direct energy transfer in the diffusion case, numerically treated by the use of Green functions

The energy decay function for an excited donor molecule surrounded by acceptors in diffusional motion is computed for a finite-size donor and arbitrary characteristics of the boundary. We evaluate the donor-acceptor---pair diffusion function via a Green-function approach for the Feynman-Kac equation in Laplace space. Quick and stable numerical solutions for the acceptor-averaged pair diffusion function, and thereby the energy decay functions, can be obtained, thus allowing model parametrization from time-resolved fluorescence measurements.

On the Dynamics of the Ocean Surface Mixed Layer

Abstract This paper describes a theoretical model of the ocean surface mixed layer. A nonstationary one-dimensional system of equations for an Ekman ocean layer and for heat conduction is closed with a system of dynamic turbulence equations. The latter consists of the turbulent energy equation and an equation for the turbulent energy decay function. The eddy viscosity coefficient is then determined from these equations. The values of the surface and lower boundary temperature and of wind velocity as a function of time are taken from Halpern (1974) data. The computational results show that an increase of wind velocity produces deepening of the mixed layer with some time lag. In the region of the jump in density at the bottom of the layer, the increase in the surface wind generates large velocity gradients across an inner boundary layer. Comparison of the solution with experimental data shows that the model realistically simulates the dynamics of mixed layer deepening both qualitatively and quantitatively.