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Pass-by noise generated by high-speed trains is an important influencing factor on the surrounding environment and is getting more and more attention with the increase of speed. In the past, the aerodynamic pass-by noise prediction was usually conducted with the wind tunnel mode, ignoring the Doppler effect. In this paper, an equivalent source method considering the Doppler effect is proposed to study the aerodynamic pass-by noise. A cylinder case is considered first to verify the effectiveness of the method. Then a DSA 380 pantograph of a Chinese high-speed train is considered. The pantograph is divided into three parts, and each part is equivalent to a monopole or dipole sound source. Results show that the upper part of the pantograph is closer to a dipole source, while the middle and lower parts are closer to a monopole source. When the measurement point is directly above the pantogragh, the contribution of the upper part is the largest, while for both sides measurement points of the pantograph, the contribution of the upper part is the smallest.

To solve the problem of sound field reconstruction with fewer measurement points, a sound field reconstruction method based on Bayesian compressive sensing is proposed. In this method, a sound field reconstruction model based on a combination of the equivalent source method and sparse Bayesian compressive sensing is established. The MacKay iteration of the relevant vector machine is used to infer the hyperparameters and estimate the maximum a posteriori probability of both the sound source strength and noise variance. The optimal solution for sparse coefficients with an equivalent sound source is determined to achieve the sparse reconstruction of the sound field. The numerical simulation results demonstrate that the proposed method has higher accuracy over the entire frequency range compared to the equivalent source method, indicating a better reconstruction performance and wider frequency applicability with undersampling. Moreover, in environments with low signal-to-noise ratios, the proposed method exhibits significantly lower reconstruction errors than the equivalent source method, indicating a superior anti-noise performance and greater robustness in sound field reconstruction. The experimental results further verify the superiority and reliability of the proposed method for sound field reconstruction with limited measurement points.

In practical conditions, near-field acoustic holography (NAH) requires the measurement environment to be a free sound field. If vibrating objects are located above the reflective ground, the sound field becomes non-free in the presence of a reflecting surface, and conventional NAH may not identify the sound source. In this work, two types of half-space NAH techniques based on the Helmholtz equation least-squares (HELS) method are developed to reconstruct the sound field above a reflecting plane. The techniques are devised by introducing the concept of equivalent source in HELS-method-based NAH. Two equivalent sources are tested. In one technique, spherical waves are used as the equivalent source, and the sound reflected from the reflecting surface is regarded as a linear superposition of orthogonal spherical wave functions of different orders located below the reflecting surface. In the other technique, some monopoles are considered equivalent sources, and the reflected sound is considered a series of sounds generated by simple sources distributed under the reflecting surface. The sound field is reconstructed by matching the pressure measured on the holographic surface with the orthogonal spherical wave source in the vibrating object and replacing the reflected sound with an equivalent source. Therefore, neither technique is related to the surface impedance of the reflected plane. Compared with the HELS method, both methods show higher reconstruction accuracy for a half-space sound field and are expected to broaden the application range of HELS-method-based NAH techniques.

The equivalent source method (ESM) is a core algorithm in integrated radiation-propagation acoustic field modeling. However, in challenging marine environments, including deep-sea and polar regions, where sound speed profiles exhibit strong vertical gradients, the ESM must increase waveguide stratification to maintain accuracy. This causes computational costs to scale exponentially with the number of layers, compromising efficiency and limiting applicability. To address this, this paper proposes a modal equivalent source (MES) model employing normal modes as basis functions instead of free-field Green’s functions. This model constructs a set of normal mode bases using full-depth hydroacoustic parameters, incorporating water column characteristics into the basis functions to eliminate waveguide stratification. This significantly reduces the computational matrix size of the ESM and computes acoustic fields in range-dependent waveguides using a single set of normal modes, resolving the dual limitations of inadequate precision and low efficiency in such environments. Concurrently, for the construction of basis functions, this paper also proposes a fast computation method for eigenvalues and eigenmodes in waveguide contexts based on phase functions and difference equations. Furthermore, coupling the MES method with the Finite Element Method (FEM) enables integrated computation of underwater target radiation and propagation fields. Multiple simulations demonstrate close agreement between the proposed model and reference results (errors < 4 dB). Under equivalent accuracy requirements, the proposed model reduces computation time to less than 1/25 of traditional ESM, achieving significant efficiency gains. Additionally, sea trial verification confirms model effectiveness, with mean correlation coefficients exceeding 0.9 and mean errors below 5 dB against experimental data.

This paper examines five regularization algorithms for sound source identification, particularly in near-field acoustic holography applications that employ the equivalent source method (ESM) based on ℓ 1 norm and ℓ 2 norm. Both simulations and experimental tests were conducted to evaluate the performance of Tikhonov regularization, ℓ 1 -CVX, Bregman iteration (BI), fast iterative shrinkage-thresholding algorithm for ESM (FISTESM), and iterative reweighted least squares (IRLS). These algorithms were assessed based on their accuracy in localizing both single and coherent sound sources across a range of frequencies. Findings reveal that ℓ 1 -CVX and BI achieve high levels of resolution and stability, especially for coherent sources, while FISTESM proves to be highly efficient at higher frequencies. In contrast, Tikhonov regularization exhibits limitations when applied to sparse sound sources, and IRLS demonstrates particular effectiveness at lower frequencies. This comparative study provides critical guidance for selecting the most suitable algorithm according to specific frequency and source characteristics.

A low immission due to structure-borne sound sources is a major component of the acoustic quality inside buildings. After many years of research, methods have been standardised to characterise such sources (EN 15657) and to predict their impact in buildings (EN 12354-5). This contribution is dedicated to the question what the uncertainty of the source descriptors and the predicted installed sound power is. To answer this question, an interlaboratory test with an artificial source was performed. Altogether seven laboratories participated, and estimates for the uncertainties of the source quantities could be deduced from the measurement results. Additionally, measurements were performed with a standardised structure-borne sound source, the ISO tapping machine, by all participating laboratories. The measured source quantity for this source turned out to be in good agreement with the theoretically predicted values thereby validating this theoretical prediction.

Sparse regularization has been successfully applied to equivalent source method (ESM) in order to improve the acoustic imaging resolution. However, the application is not always feasible, especially at low frequencies. To overcome the problem, this paper proposes a high-resolution acoustic imaging method. In this method, reweighted l1 minimization is introduced to ESM to deal with the ill-posed inverse problems. Then the obtained equivalent source strengths are used to locate the sound sources. Compared to the sparse regularization-based ESM, the proposed method can provide a low side lobe and higher spatial resolution of acoustic imaging. Meanwhile, by arranging equivalent sources in three-dimensional space, the proposed method can also realize the acoustic imaging in three-dimensional sound field with high resolution. The results of the simulation and experiment demonstrate the validations.

Marine propulsors represent one of the most important contributors among anthropogenic sounds radiated into water. Blade based propulsors, e.g., propellers, generate tones at the blade passing frequency and its harmonics, especially in cavitating conditions. In addition to hydrodynamic noise, pressure fluctuations cause vibrations in ship hull leading to mechanical noise. For noise prediction purposes, it is highly beneficial to characterize the noise sources as simplified, complex valued arrays having information on source positions, source strengths and phases. In this paper, procedure to characterize marine propulsors as acoustic sources with inverse method is introduced. First, the numerical model with complete hydro-acoustic sources is investigated. Second, a source model composed of sensible number and distribution of elementary (“equivalent”) compact sources is specified. Then selected responses are used as input in source characterization with inverse method. Finally, the model with equivalent sources is solved and the results are validated by comparison against the results from the complete simulation model. The introduced acoustic source characterization procedure of marine propulsors is applicable also for the responses determined experimentally, e.g., in a cavitation tunnel when the pressure transducer array is determined appropriately.

Acoustic sensing systems play a critical role in identifying and determining weak sound sources in various fields. In many fault warning and environmental monitoring processes, sound-based sensing techniques are highly valued for their information-rich and non-contact advantages. However, noise signals from the environment reduce the signal-to-noise ratio (SNR) of conventional acoustic sensing systems. Therefore, we proposed novel nonlinear gradient-coiling metamaterials (NGCMs) to sense weak effective signals from complex environments using the strong wave compression effect coupled with the equivalent medium mechanism. Theoretical derivations and finite element simulations of NGCMs were executed to verify the properties of the designed metamaterials. Compared with nonlinear gradient acoustic metamaterials (Nonlinear-GAMs) without coiling structures, NGCMs exhibit far superior performance in terms of acoustic enhancement, and the structures capture lower frequencies and possess a wider angle acoustic response. Additionally, experiments were constructed and conducted using set Gaussian pulse and harmonic acoustic signals as emission sources to simulate real application scenarios. It is unanimously shown that NGCMs have unique advantages and broad application prospects in the application of weak acoustic signal sensing, enhancement and localization.

The equivalent source method is widely applied to study structural acoustic radiation in an underwater environment. However, there is still uncertainty in arranging the equivalent source, and the current mainstream configuration method needs a large number of equivalent sources, limiting its practical applicability. In this paper, an equivalent source configuration method that is simple, effective, and easy to implement, and which based on a tradeoff between the ill condition of the transfer matrix and the adequacy of the simulated structure’s radiated sound field, is proposed. The optimization method can derive the appropriate positions and quantity of monopole equivalent sources simultaneously. The method does not yield an optimal solution in a strict mathematical sense but provides satisfactory results compared with those obtained by uniformly distributed equivalent sources. Numerical simulation results showed that the optimization method derives accurate sound field calculation results with a relatively small number of equivalent sources, significantly reducing the number of subsequent calculations needed. Finally, the experiments conducted with a cylindrical shell structure verified the validity and practicality of the proposed method.