A Physics-Informed Neural Network Approach for Nearfield Acoustic Holography

In this manuscript, we describe a novel methodology for nearfield acoustic holography (NAH). The proposed technique is based on convolutional neural networks, with autoencoder architecture, to reconstruct the pressure and velocity fields on the surface of the vibrating structure using the sampled pressure soundfield on the holographic plane as input. The loss function used for training the network is based on a combination of two components. The first component is the error in the reconstructed velocity. The second component is the error between the sound pressure on the holographic plane and its estimate obtained from forward propagating the pressure and velocity fields on the structure through the Kirchhoff–Helmholtz integral; thus, bringing some knowledge about the physics of the process under study into the estimation algorithm. Due to the explicit presence of the Kirchhoff–Helmholtz integral in the loss function, we name the proposed technique the Kirchhoff–Helmholtz-based convolutional neural network, KHCNN. KHCNN has been tested on two large datasets of rectangular plates and violin shells. Results show that it attains very good accuracy, with a gain in the NMSE of the estimated velocity field that can top 10 dB, with respect to state-of-the-art techniques. The same trend is observed if the normalized cross correlation is used as a metric.

A FEM/Kirchhoff-Helmholtz integral model for noise diffractors on low height noise barriers

So-called noise diffractors are a novel way to reduce traffic noise. As opposed to blocking or absorbing noise, diffractors bend noise in an upward direction, creating a shadow zone of reduced noise levels behind the diffractor. The diffraction is most effectively induced by quarter-wavelength resonators. The resonators can be placed in the ground but can also be mounted on top of a (low height) noise barrier, which provides additional reduction. In this paper, we describe a finite element/Helmholtz integral model for a diffractor mounted on a low height noise barrier. The finite element model is used to calculate the scattered acoustic field in the proximity of the diffractor for a noise source sufficiently far away from the diffractor. The acoustic pressure and particle velocity on the outer boundary of the finite element domain are subsequently used in the Kirchhoff-Helmholtz integral formulation to evaluate the acoustic field in the far field. The major benefit of this approach is a large reduction of the model size and reduced calculation times. This allows us to assess the reduction values at different barrier heights, larger distance from source to diffractor and larger distances from diffractor to evaluation points, with an example shown for highway traffic noise.

Boundary Element Modeling of Sound Attenuation in Acoustically Lined Curved Pipes

The results of a modeling study for the numerical solution of the interior surface Helmholtz integral for acoustically lined curved pipes with rectangular cross-section are presented. The solution of the Helmholtz integral equation is calculated by using the boundary element method (BEM). The sound attenuation spectra of different possible models with regard to the lining on the boundaries are compared with the analytical solution. The acoustic behavior of different models is discussed and the features of the model that gives more accurate results are presented.

2D isotropic elastic Gaussian-beam migration for common-shot multicomponent records

Gaussian-beam migration (GBM) is flexible and adaptable for imaging geologically complicated areas. It avoids some limitations, such as amplitude singularity in caustic zones and an inability to image multiple arrivals, of traditional ray-based migration approaches. Previous studies on GBM mainly focused on acoustic media. We have developed a 2D isotropic elastic GBM scheme for common-shot multicomponent records. Our method extrapolates P- and S-mode wavefields simultaneously using the Kirchhoff-Helmholtz integral solution of the isotropic elastodynamic equation. We separate the extrapolated wavefields into compressional and shear modes using the Helmholtz decomposition, and we then implement a modified dot-product imaging condition. This approach enables us to produce clear PP-images and avoid polarity reversal issues for PS-images. In addition, based on the theory of wavefield approximation in the effective vicinity of central rays, we derive a formula to compute the propagation angles of paraxial rays, which can be used to extract angle-domain common-image gathers.

Low-frequency sound transmission through rough bubbly air–water interface at the sea surface

Transmission of a sound generated by a localized point source in the air through a realistic sea surface is studied by the use of the Kirchhoff-Helmholtz integral. An earlier approach had been based on the Kirchhoff-Helmholtz integral which only considered the effects of rough surface. In the current study, not only the effect of the rough surface is taken into account but also the effects of subsurface bubbles are included in modeling the real phenomenon more accurately. In order to include the effects of subsurface bubble population, the classic relations of the Kirchhoff-Helmholtz integral are reformulated. Accordingly, a three-phase region of air, water, and bubbly water at the sea surface is analyzed, and the rough interface of bubbly water–air is discretized. Through considering an element area Ai, the transmission coefficient [Formula: see text], incident angle [Formula: see text], transmitted angle [Formula: see text], and local surface acoustical roughness Ri are investigated for each individual element. Also, the effects of subsurface bubbles, transmission change as a function of frequency f, wind speed W, incident angle [Formula: see text], source/receiver position ratio (D/H), surface acoustical roughness, and subsurface bubble population are examined. Results of the modified Kirchhoff-Helmholtz integral method display good agreement against available experimental data.

The Burton and Miller Method: Unlocking Another Mystery of Its Coupling Parameter

The phenomenon of irregular frequencies or spurious modes when solving the Kirchhoff–Helmholtz integral equation has been extensively studied over the last six or seven decades. A class of common methods to overcome this phenomenon uses the linear combination of the Kirchhoff–Helmholtz integral equation and its normal derivative. When solving the Neumann problem, this method is usually referred to as the Burton and Miller method. This method uses a coupling parameter which, theoretically, should be complex with nonvanishing imaginary part. In practice, it is usually chosen proportional or even equal to [Formula: see text]. A literature review of papers about the Burton and Miller method and its implementations revealed that, in some cases, it is better to use [Formula: see text] as coupling parameter. The better choice depends on the specific formulation, in particular, on the harmonic time dependence and on the fundamental solution or Green’s function, respectively. Surprisingly, an unexpectedly large number of studies is based on the wrong choice of the sign in the coupling parameter. Herein, it is described which sign of the coupling parameter should be used for different configurations. Furthermore, it will be shown that the wrong sign does not just make the solution process inefficient but can lead to completely wrong results in some cases.