Prediction Of Sound Field Research Articles

Far-field sound field estimation using robotized measurements and the boundary elements method

Sound Field Estimation (SFE) is a numerical technique widely used to identify and reconstruct the acoustic fields radiated by unknown structures. In particular, SFE proves to be useful when data is only available close to the source, but information in the whole space is required. However, the practical implementation of this method is still hindered by two major drawbacks: the lack of efficient implementation of existing numerical methodologies, and the time-consuming and tedious roll-out of acoustic measurements. This paper aims to provide a solution to both issues. First, the measurements step is fully automated by using a robotic arm, able to accurately gather geometric and acoustic data without any human assistance. In this matter, a particular attention has been paid to the impact of the robot on the acoustic pressure measurements. The sound field prediction is then tackled using the Boundary Element Method (BEM), and implemented using the FreeFEM++ BEM library. Numerically simulated measurements have allowed us to assess the method accuracy, and the overall solution has been successfully tested using actual robotized measurements of an unknown loudspeaker.

Influence of viscous shear boundary layers on the sound performance of acoustic metasurfaces

Acoustic metasurfaces are mostly designed in a static medium, ignoring the influence of flow characteristics. However, in actual aeroacoustic noise reduction, e.g., aircraft engine liner design, the background flow can have effects on the sound performance of acoustic metasurfaces, especially for a viscous shear flow. The effect of a viscous shear flow is often neglected in previous studies on the design and sound field prediction of acoustic metasurfaces. For considering the viscous and thermal dissipation effects, an analytical model is developed to predict the sound field of a periodic metasurface in a viscous shear boundary layer. In this model, the effective impedance based on the high-frequency limits is utilized to consider both the actual impedance of the acoustic metasurface and the effect of a finite-thickness viscous shear boundary layer. An acoustic metasurface designed in the static medium or even redesigned with only the effect of an inviscid shear flow is not suitable for wave manipulation when the Reynolds number (Re) changes significantly, since the viscosity is an important and non-negligible factor affecting the sound performance. For the cases in this work, the sound performance gradually deteriorates with the decrease in Re when Re≥5×106. When Re≤1×106, especially at Re=1×105, the existence of viscous shear flows could result in the destruction of expected anomalous reflection and significant intensity change of the reflected waves. This research provides a method for the design of acoustic metasurfaces under viscous shear flow conditions, which is significant for future aeroacoustic applications.

Research on reconstruction of the global sound speed profile combining partial underwater prior information

The sound speed profile (SSP) is an important factor affecting the acoustic propagation characteristics of the ocean, making the accurate acquisition of SSP a crucial step in the interdisciplinary research of oceanography and underwater acoustics. Limited by the cost of in-situ measurement and the performance of the instrument itself, direct measurement of SSP inevitably leads to insufficient depth or even missing information. In this paper, we propose using partial underwater prior information (UWPI) only including underwater sound speed to obtain preliminary reconstruction results of global SSP for the first time. The empirical orthogonal function (EOF) reconstruction algorithm is optimized by employing assimilated SSP as the background SSP to further reduce reconstruction errors. The maximum global average reconstruction error and root mean square error (RMSE) after optimization decrease by >51% and 71%, respectively, which indicates that the performance of the optimized algorithm combined with partial UWPI is further improved. Finally, the performance of the optimized algorithm is discussed from the perspective of acoustic propagation. This research provides a reliable technical approach for SSP reconstruction under incomplete depth conditions, which can be applied in underwater sound field prediction and acoustic detection in the future.

Predicting ocean pressure field with a physics-informed neural network.

Ocean sound pressure field prediction, based on partially measured pressure magnitudes at different range-depths, is presented. Our proposed machine learning strategy employs a trained neural network with range-depth as input and outputs complex acoustic pressure at the location. We utilize a physics-informed neural network (PINN), fitting sampled data while considering the additional information provided by the partial differential equation (PDE) governing the ocean sound pressure field. In vast ocean environments with kilometer-scale ranges, pressure fields exhibit rapidly fluctuating phases, even at frequencies below 100 Hz, posing a challenge for neural networks to converge to accurate solutions. To address this, we utilize the envelope function from the parabolic-equation technique, fundamental in ocean sound propagation modeling. The envelope function shows slower variations across ranges, enabling PINNs to predict sound pressure in an ocean waveguide more effectively. Additional PDE information allows PINNs to capture PDE solutions even with a limited amount of training data, distinguishing them from purely data-driven machine learning approaches that require extensive datasets. Our approach is validated through simulations and using data from the SWellEx-96 experiment.

Non-iterative reconstruction of time-domain sound pressure and rapid prediction of large-scale sound field based on IG-DRBEM and POD-RBF

In this paper, a novel non-iterative reconstruction method of time-domain sound pressure and rapid prediction scheme of large-scale sound field are proposed respectively based on the isogeometric dual reciprocity boundary element method (IG-DRBEM) and proper orthogonal decomposition - radial basis functions (POD-RBF). By establishing the non-iterative inversion theory in the meaning of least squares, infinite domain acoustic holography is achieved with a small number of measured sound pressure information. Furthermore, the POD-RBF network is adopted to predict large-scale sound pressure. The presented work further expands the scope of application of IG-DRBEM, and gives full play to its advantage of not having to calculate the coefficient matrix repeatedly when analyzing the sound field at different moments. Moreover, in order to satisfy the integral regularization conditions, a suitable convergence condition about variation coefficients is investigated. Numerical results show that the proposed method has high accuracy and good stability even when the sound pressure of complex airship model is predicted with large-scale freedom.

Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling

The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity.

An Improved Acoustic Diffusion Equation Model for Long-Channel Underground Spaces.

The acoustic diffusion equation model has been widely applied in various scenarios, but a larger prediction error exists when applied to underground spaces, showing a significantly lower characteristic of the sound pressure level in the later stage compared to field tests since underground spaces have a more closed acoustic environment. Therefore, we analyze the characteristics of underground spaces differentiating from aboveground spaces when applying the model and propose an improved model from the perspective of energy balance. The energy neglected in the calculation of the acoustic diffusion equation model is compensated in long channel underground spaces named "acoustic escape compensation". A simulation and two field experiments are conducted to verify the effectiveness of the proposed compensation strategy in long-channel underground spaces. The mean square error is used to evaluate the differences between the classical model and the improved model, which shows a numerical improvement of 1.3 in the underground field test. The results show that the improved model is more suitable for describing underground spaces. The proposed strategy provides an effective extension of the acoustic diffusion equation model to solve the problem of sound field prediction and management in underground spaces.

A modal expansion method for simulating reverberant sound fields generated by a directional source in a rectangular enclosure

The prediction of reverberant sound fields generated by a directional source is of great interest because practical sound sources are not omnidirectional, especially at high frequencies. For an arbitrary directional source described by cylindrical and spherical harmonics, this paper developed a modal expansion method for calculating the reverberant sound field generated by such a source in both two-dimensional and three-dimensional rectangular enclosures with finite impedance walls. The key is to express the modal source density using the cylindrical or spherical harmonic expansion coefficients of the directional source. A method based on the fast Fourier transform is proposed to enable the fast computation of the summation of enclosure modes when walls are lightly damped or rigid. This makes it possible to obtain accurate reverberant sound fields even in a large room and/or at high frequencies with a relatively low computational load. Numerical results with several typical directional sources are presented. The efficiency and the accuracy of the proposed method are validated by the comparison to the results obtained using the finite element method.

Performance of single empirical orthogonal function regression method in global sound speed profile inversion and sound field prediction

The sound speed profile (SSP) reflects the change in sound speed from the surface to the bottom of the seawater, which will have an important influence on underwater acoustic detection and communication. Depending on the inversion of sea surface data sets measured by satellite to obtain near-real-time and high-precision SSPs has become a research hotspot. In this paper, based on the Argo data and the sea surface data sets, we use the single empirical orthogonal function regression (sEOF-r) method to inverse the global SSPs and evaluate the performance of this method. There are also differences in the performance of inversed results at different sites and in different months at the global scale of the ocean. The eddy kinetic energy (EKE) affects the accuracy of inversion, we propose to add the EKE into the inversion formula at the same time to further optimize the inversed results and improve the accuracy, the global average inversion error after optimization reduces by 20%. Finally, we verify the effectiveness of the optimized method from the perspective of sound field prediction. In most cases, the correlation coefficient of the transmission loss (TL) calculated through the inversion SSP and Argo-SSP exceeds 0.7 and the error is controlled below 6 dB, which will have important implications for the actual sound field prediction and hydroacoustic communication.

Scattering characteristics analysis of conformal array based on sound field prediction method

In order to study the problem that the array manifold of conformal arrays deviates from the ideal value due to the sound scattering caused by the rigid baffles of arrays, in this paper, the influence of the scattering phenomenon caused by the rigid baffle on the receiving response of array is analyzed by using sound field prediction method based on a conformal array-semi-cylindrical volume array. The sound field distribution of conformal array at different angles is calculated by using the sound field modeling and simulation. Based on the above distribution, an actual array manifold is constructed under consideration of rigid barrier, and its variation under the influence of scattered sound is analyzed. The variation is described by two physical quantities defined in this paper: the first-order response composed of amplitude and phase and the second-order response composed of cross-correlation. Simulation shows that compared with the ideal model, the scattered signals generated by rigid baffles on conformal array varies with the azimuth and signal-to-noise ratio(SNR), which further leads to the deviation of each hydrophone of conformal array. The experimental data verifies that the simulation results are basically consistent with the actual situation. The effect of the scattering on the conformal array should be considered when designing and performing in practice.

The Effects of Bubble Scattering on Sound Propagation in Shallow Water

As sea waves break, a bubble layer forms beneath the sea surface. The bubble scattering affects sound propagation, thus influencing the accuracy of sound field prediction. This paper aims to investigate the effects of bubble scattering on the statistical characteristics of the sound field, the distribution of transmission loss (TL), and the average scattering attenuation in shallow water. A bubble layer model based on the bubble spectrum and a parallel Parabolic Equation (PE) model are combined to calculate and analyse the sound field in the marine environment with bubbles. The effects of the bubble layer are then compared with those of the fluctuant sea surface. The results show that the bubble scattering causes additional energy loss and random fluctuations of the sound field. The TL distribution properties and the average scattering attenuation are related to the wind speed, range, frequency, and source position relative to the negative gradient sound speed layer in shallow water. The comparison demonstrates that the random variation caused by the fluctuation of the sea surface is more significant than that caused by bubbles, and the energy loss caused by bubble scattering is more significant than the fluctuant sea surface under strong wind conditions.

Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries.

Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating acoustics makes handling dynamic scenes with moving sources challenging, requiring intractable memory storage. A physics-informed neural network (PINN) method in one dimension is presented, which learns a compact and efficient surrogate model with parameterized moving Gaussian sources and impedance boundaries and satisfies a system of coupled equations. The model shows relative mean errors below 2%/0.2 dB and proposes a first step in developing PINNs for realistic three-dimensional scenes.

A Finite-Difference Wavenumber-Time Domain Method for Sound Field Prediction in a Uniformly Moving Medium

Sound field prediction has practical significance in the control of noise generated by sources in a flow, for example, the noise in aero-engines and ventilation systems. Aiming at accurate and flexible prediction of time-dependent sound field, a finite-difference wavenumber-time domain method for sound field prediction in a uniformly moving medium is proposed. The method is based on the second-order convective wave equation, and the wavenumber-time domain representation of the sound pressure field on one plane is forward propagated via a derived recursive expression. In this paper, the recursive expression is first deduced, and then numerical stability and dispersion of the proposed method are analyzed, based on which the stability condition is given and the correction of dispersion related to the transition frequency is made. Numerical simulations are conducted to test the performance of the proposed method, and the results show that the method is valid and robust at different Mach numbers.

Direct discrete complex image method for sound field evaluation above a non-locally reacting layer.

Thin layers of porous media are widely adopted in sound absorption and noise control applications due to their compact arrangement. Particularly, porous media with low flow resistivity exhibit complex, non-local reaction behavior. Therefore, sound field prediction above these media is computationally challenging. This is due to singularities and branch points in the expression for the reflection coefficient. This paper introduces a framework based on the direct discrete complex image method to analyze the sound field above a rigid-backed, non-locally reacting porous sample. In contrast to traditional complex image applications, the proposed framework avoids the extraction of the quasi-static term and the poles from the reflection coefficient. Instead, the reflection coefficient-including its singularities-is directly approximated in terms of a series of complex exponentials, whose coefficients are determined with the matrix pencil method. This study analyzes the sound field above two test samples made of melamine and rockwool. The sound field computation is efficient and accurate in the near- and in the far-field. Moreover, predicted specific impedances agree well with experimental in situ impedance measurements. The proposed framework serves for more applications including object detection in multilayered porous grounds or sound propagation prediction in layered atmosphere.

Prediction and analysis of sound field in long enclosures with a modal-based method

In this paper, the efficacy of porous ceiling treatment to reduce noise levels inside a typical tunnel is examined with a validated modal-based prediction method. It is found that, for a point source, the effect of increasing porous ceiling thickness on sound pressure level (SPL) attenuation along the tunnel is limited. A porous ceiling with thickness of 0.3 m is comparable with an infinite porous ceiling in middle and high frequency ranges. For a line source, the effect of ceiling thickness on SPL reduc- tion in this typical tunnel is limited. Sound pressure level reduction of 4 dBA is real- ized with 0.3 m porous ceiling, which is the same as infinite ceiling and only 1 dBA smaller than the theoretically optimized value. These results suggest that, in the event only ceiling treatment is considered, 0.3 m porous material is sufficient for noise re- duction in this typical tunnel.

Design and application of sound barrier for substation noise control

After measuring the noise of transformers, substation boundary and noise-sensitive area of a 110 kV substation, it’s known that the noise at substation boundary contains transformer noise component via analyzing the 1/3-octave band spectrums. The octave band sound pressure level on the roof of the east residential building derived from the transformer is obtained by sound field prediction of SoundPLAN. Moreover, the NR-40 curve is used to evaluate the octave band sound pressure level to calculate the theoretical noise reduction of the east residential building. Considering the direct propagation and another propagation path undergoing reflection, a sound barrier that composed of sound insulation board with a significant sound insulation effect is designed for the frequency band below 1000 Hz. After completely installing the sound barrier, the noise level at measuring point 16 at night is reduced from 55.9 dB(A) to 46.7 dB(A), with noise reduction of 9.2 dB(A); while it is reduced from 56.3 dB(A) to 44.5 dB(A) at measuring point 21, with noise reduction of 11.8 dB(A).

A combined sound field prediction method in small classrooms

In this paper, a new combination method for sound field prediction is proposed. An optimization approach based on the genetic algorithm is employed for optimizing the transition frequency of the combined sound field prediction method in classrooms. The selected optimization approach can identify the optimal transition frequency so that the combined sound field prediction can obtain more efficient and accurate prediction results. The proposed combined sound field prediction method consists of a wave-based method and geometric acoustic methods that are separated by the transition frequency. In low frequency domain (below the transition frequency), the sound field is calculated by the finite element method (FEM), while a hybrid geometric acoustic method is employed in the high frequency domain (above the transition frequency). The proposed combined prediction models are validated by comparing them with previous results and experimental measurements. The optimization approach is illustrated by several examples and compared with traditional combination results. Compared to existed sound field prediction simulations in classrooms, the proposed combination methods take the sound field in low frequencies into account. The results demonstrate the effectiveness of the proposed model. Practical applications: This study proposes a combined sound field prediction method separated by transition frequency. A genetic algorithm optimization method is employed for searching the optimal transition frequency. The outcomes of this paper are essential for acoustical designs and acoustical environmental assessments.

Sound field reconstruction of structural source based on element radiation superposition method

In order to improve the sound field reconstruction accuracy of distributed structural source, a new near-field acoustic holography is established based on the element radiation superposition method (ERSM). In the proposed method, the surface of structural source is divided into several regular pistons. The sound field of structural source is considered as the superposition of sound field of pistons. Firstly, we compare the sound field calculated by ERSM with that by Rayleigh's integral. It is proved that ERSM is quite accurate in sound field prediction. Based on ERSM, a vibration acoustic transfer (VAT) function is derived. The VAT function has computable analytical expression and embodies the transfer relationship between the structural source surface and the radiated sound field. The VAT function can precisely characterize the acoustic propagation of continuous distributed coherent sources. Subsequently, we employ the VAT function to replace the Green's function, and apply the VAT function to sound field reconstruction. Different with the equivalent source method (ESM) which is widely used in sound field reconstruction, ERSM directly divides the piston-sources on the surface of structural source rather than constructing the equivalent point-sources on a plane behind the structural source. Furthermore, we introduce a weight matrix into ERSM and iteratively calculate the vibration velocity for a more accurate result, and we call the proposed method as iterative weighted ERSM (IWERSM). In this paper, the simulations and experiment of sound field reconstruction of a rectangular plate are performed. In the proposed method, the rectangular plate is divided into several rectangular pistons. The reconstruction results of ERSM and IWERSM are compared with that of ESM and iterative weighted ESM (IWESM) respectively. The reconstruction accuracies at different distances between the plate and array (test distances) are analyzed. The simulation results show the accuracy of ERSM and IWERSM are better than that of ESM and IWESM respectively. With the increase of test distance, the phenomenon is more obvious, and IWERSM even shows a good reconstruction accuracy while the test distance is more than half a wavelength. The experiment results also validate that ERSM and IWERSM have better reconstruction accuracy than ESM and IWESM respectively at the same test distance. In a word, the simulations and experiments demonstrate that the proposed method can improve the sound field reconstruction accuracy of regular structural source and expand the valid test distance of near-field acoustic holography.

A Prediction Method for Acoustic Intensity Vector Field of Elastic Structure in Shallow Water Waveguide

Compared with scalar sound field, vector sound field explained the spatial structure of sound field better since it not only presents the sound energy distribution but also describes the sound energy flow characteristics. Particularly, with more complicated interaction among different wavefronts, the vector sound field characteristics of an elastic structure in a shallow water waveguide are worthy of studying. However, there is no reliable prediction method for the vector sound field of an elastic structure with a high efficiency in a shallow water waveguide. To solve the problem, transfer functions in the waveguide have been modified with some approximations to apply for the vector sound field prediction of elastic structures in shallow water waveguides. The method is based on the combined wave superposition method (CWSM), which has been proved to be efficient for predicting scalar sound field. The rationality of the approximations is validated with simulations. Characteristics of the complex acoustic intensity, especially the vertical components are observed. The results show that, with constructive and destructive interferences in the depth direction, there could be quantities of crests and vortices in the spatial structure of time-dependent complex intensity, which manifest a unique dynamic characteristic of sound energy. With more complicated interactions among the wavefronts, a structure source could not be equivalent to a point source in most instances. The vector sound field characteristics of the two sources could be entirely different, even though the scalar sound field characteristics are similar. Meanwhile, source types, source parameters, ocean environment parameters, and geo parameters may have influence on the vector sound field characteristics, which could be explained with the normal mode theory.

Prediction of sound fields after propagation through sound barriers by CNN and DCNN algorithms

Sound fields are affected by the size of the space and the surrounding environments. The ray tracing method analyze the sound propagation through geometric constraints. For prediction of sound fields in a real-time to investigate the influence of surrounding environments, an effective calculation method is required. During the prediction, it is necessary to calculate the sound field distribution according to the layout of equipment or sound reflecting devices to minimize noise in working spaces. This procedure is required for an optimal arrangement of barriers according to noise sources. To improve this repetitive work, it is devised to develop a machine learning model that predicts the change in the sound field according to the position of sound barrier through CNN and DCNN algorithms. Training data were generated by using a commercial tool. The proposed approach recognizes the characteristics of sound fields at spaces after acoustic barriers.