Alexandre Garcia

Boundary element method for the acoustic characterization of a machine in bounded noisy environment

In this article, a boundary element method is used to recover free field conditions from noisy bounded space situations. The proposed approach is based on the Helmholtz integral formulation. The method requires the knowledge of double layer pressure fields on two parallel closed surfaces surrounding the source. First, the outgoing and ingoing pressure field are separated using Helmholtz integral. Then, the incident field scattered by the tested source is subtracted from the outgoing field to recover the pressure field which would have been radiated in free space. To simplify the process, rigid body approximation for the source is used. The method is numerically tested in the following conditions: the chosen sound source is the upper spherical cap of a rigid sphere, the source is located at the center of a rigid spherical cavity, and a monopole secondary source is added to blur the primary pressure field. Simulations give good results for ka up to 5 when the discretization of the surfaces is sufficient.

Measurement of confined acoustic sources using near-field acoustic holography

Due to excessive reverberation or to the presence of secondary noise sources, characterization of sound sources in enclosed space is rather difficult to perform. In this paper a process layer is used to recover the pressure field that the studied source would have radiated in free space. This technique requires the knowledge of both acoustic pressure and velocity fields on a closed surface surrounding the source. The calculation makes use of boundary element method and is performed in two steps. First, the outgoing pressure field is extracted from the measured data using a separation technique. Second, the incoming field then scattered by the tested source body is subtracted from the outgoing field to recover free field conditions. The studied source is a rectangular parallelepiped with seven mid-range loudspeakers mounted on it. It stands at 40 cm from the rigid ground of a semi-anechoic chamber which strongly modifies the radiated pressure field, especially on the underside. After the measured data have been processed, the loudspeaker positions are recovered with a fairly good accuracy. The acoustic inverse problem is also solved to calculate the velocity field on the source surface.

Evaluation of a separation method for source identification in small spaces

This paper investigates the efficiency of a field separation method for the identification of sound sources in small and non-anechoic spaces. When performing measurements in such environments, the acquired data contain information from the direct field radiated by the source of interest and reflections from walls. To get rid of the unwanted contributions and assess the field radiated by the source of interest, a field separation method is used. Acoustic data (pressure or velocity) are then measured on a hemispheric array whose base is laying on the surface of interest. Then, by using spherical harmonic expansions, contributions from outgoing and incoming waves can be separated if the impedance of the tested surface is high enough. Depending on the probe type, different implementations of the separation method are numerically compared. In addition, the influence of the walls reflection coefficient is studied. Finally, measurements are performed using an array made-up of 36 p-p probes. Results obtained in a car trunk mock-up with controlled sources are first presented before reporting results measured in a real car running on a roller bench.

Evaluation of a method for the measurement of subwoofers in usual rooms

This paper evaluates the potential of the field separation method (FSM) for performing subwoofer measurements in a small test room with poor absorbing properties, as is commonly available. The FSM requires the knowledge of both acoustic pressure and velocity fields on a closed surface surrounding the tested source. Pressures and velocities, measured using a p-p probe on a half-sphere mesh, are collected under various conditions: in a room with variable reverberation time (6.4-0.6 s) and with four measurement half-sphere radii. The measured data are expanded on spherical harmonics, separating outward and inward propagation. The pressure field reflected by walls of the surrounding room is then subtracted from the measured field to estimate the pressure field that would have been radiated under free-field conditions. Theoretical frequency response of the subwoofer is computed using an analytical formulation derived from an extended Thiele and Small model of the membrane motion, coupled to a boundary element model for computing the radiated pressure while taking into account the actual subwoofer geometry. Measurement and simulation results show a good agreement. The effects of the measurement distance, the measurement point number, and the room reverberation time on the separation process are then discussed.

Data completion method for the characterization of sound sources

This paper presents a different approach to solve the inverse acoustic problem. This problem is an ill-posed problem since the solution is very sensitive to measurement precision. A classical way to solve this problem consists in inversing a propagation operator which relates structure quantities (acoustic pressures or gradients) to near-field quantities (acoustic pressures or gradients). This can be achieved by using near-field acoustical holography (NAH) in separable coordinate systems. In order to overcome this limitation, the inverse boundary element method (IBEM) can be implemented to recover all acoustic quantities in a three-dimensional space and on an arbitrary three-dimensional source surface. In this paper, the data completion method (DCM) is developed: the acoustic gradients and pressures are known on a surface surrounding the source, but are unknown on its structure. The solution is given by the resolution of the Helmholtz formulation applied on the empty domain between the two boundaries made by the measurements quantities and the structure of the source. The conventional method applies directly the integral formulation for the empty domain. Another way of solving this Helmholtz formulation can be achieved by splitting it in two well-posed subproblems in a Steklov-Poincarés formulation. The data completion method allows one to solve the problem with acoustic perturbations due to sources on the exterior domain, or due to a confined domain, without altering the results.

Vector intensity reconstruction using the data completion method

This paper presents an application of the data completion method (DCM) for vector intensity reconstructions. A mobile array of 36 pressure-pressure probes (72 microphones) is used to perform measurements near a planar surface. Nevertheless, since the proposed method is based on integral formulations, DCM can be applied with any kind of geometry. This method requires the knowledge of Cauchy data (pressure and velocity) on a part of the boundary of an empty domain in order to evaluate pressure and velocity on the remaining part of the boundary. Intensity vectors are calculated in the interior domain surrounded by the measurement array. This inverse acoustic problem requires the use of a regularization method to obtain a realistic solution. An experiment in a closed wooden car trunk mock-up excited by a shaker and two loudspeakers is presented. In this case, where the volume of the mock-up is small (0.61 m(3)), standing-waves and fluid structure interactions appear and show that DCM is a powerful tool to identify sources in a confined space.

Solving the hypersingular boundary integral equation for the Burton and Miller formulation

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version αu2009=u2009ik/(k(2u2009)+u2009λ) of the classical BM coupling factor αu2009=u2009i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Cancellation of room reflections over an extended area using Ambisonics

This paper investigates the compensation of room reflections based on Ambisonics. A multichannel room equalization method for Ambisonic playback systems is proposed. The compensation filters are designed to operate in the spherical harmonics domain, prior to the decoding step. Their design requires the inversion of a matrix which can be ill-conditioned at low frequencies and for higher Ambisonic orders. A crossover and cross-order method is proposed to circumvent this problem and to reduce the amount of necessary regularization. Simulation results are presented in frequency, space, and temporal domains over a wide-range of frequencies. It is shown that the proposed method is efficient and can reduce the reproduction error to -14u2009dB in the reconstruction area defined in free field. Practical considerations such as Ambisonic room response estimation and robustness of the method are investigated. Experimental results are provided and show good agreement with the theory. Finally, a glimpse into the extension of the proposed method to create three-dimensional measurement-based Ambisonic reverberation is discussed.

Sound localization models as evaluation tools for tactical communication and protective systems

Tactical Communication and Protective Systems (TCAPS) are hearing protection devices that sufficiently protect the listeners ears from hazardous sounds and preserve speech intelligibility. However, previous studies demonstrated that TCAPS still deteriorate the listeners situational awareness, in particular, the ability to locate sound sources. On the horizontal plane, this is mainly explained by the degradation of the acoustical cues normally preventing the listener from making front-back confusions. As part of TCAPS development and assessment, a method predicting the TCAPS-induced degradation of the sound localization capability based on electroacoustic measurements would be more suitable than time-consuming behavioral experiments. In this context, the present paper investigates two methods based on Head-Related Transfer Functions (HRTFs): a template-matching model and a three-layer neural network. They are optimized to fit human sound source identification performance in open ear condition. The methods are applied to HRTFs measured with six TCAPS, providing identification probabilities. They are compared with the results of a behavioral experiment, conducted with the same protectors, and which ranks the TCAPS by type. The neural network predicts realistic performances with earplugs, but overestimates errors with earmuffs. The template-matching model predicts human performance well, except for two particular TCAPS.

Measurement of low‐frequency sources in non‐anechoic room using near‐field acoustic holography

to perform because free field conditions can not be easily achieved properly. Moreover, some industrial sources have to be measured in situ. In such a case, a Field Separation Method (FSM) can be used to subtract the pressure field reflected by walls of the testing room from the measured data. This approach required the knowledge of both acoustic pressure and velocity on a closed surface surrounding the source. In this paper, a spherical harmonic expansion of measured data is used to solve the problem. The proposed method is applied to the measurement of the frequency response of a closed box subwoofer tested under various conditions: in a room with variable reverberation time (6.4 s to 0.6 s). Theoretical frequency response of the subwoofer is also calculated using the Thiele and Small model. Results show a good agreement between separated data and simulations. The influences of the measurement distance and of the measurement point number required on the separation process are discussed.