Equivalent Source Method Research Articles

Mutual Effect Between Swept-and-Leaned Vanes and Acoustic Liners on Fan Interaction-Noise Reduction

The swept-and-leaned vanes and acoustic liners can both be used to reduce the turbofan noise. In this work, an analytical model was proposed under an idealized condition, in which an annular stator cascade and a locally reacting liner exist in an infinite duct at the same time, to study the mutual effect between these two techniques. Based on the transfer element method, the system matrix of multi-elements can be established based on the continuity of disturbance pressure and velocity at the interfaces. The acoustic elements for a stator and a liner were established, respectively, by employing the three-dimensional lifting-surface method and the equivalent surface source method, which are both the so-called methods of singularity. The interface matching pattern between adjacent elements was improved in this paper with more physics included, which can also be combined with the numerical methods easier. Because the technologies for fan-noise reduction, which are the swept-and-leaned vanes and acoustic liners in this paper, are both closely related to the modal acoustic field in the duct, the coupling effect can be strong in some conditions. The results showed that the noise reduction gained by these two techniques cannot be superposed simply. They should not be considered isolatedly. Further discussions on the transmission and reflection between different kinds of acoustic elements should be made to achieve the system optimization in the nacelle.

Analytical Passive Time Reversal Method Combined With Equivalent Source Method for Sound Source Localization in an Enclosure

The analytical passive time reversal method (APTRM) is a powerful technique for sound source localization. In that technique, it generally requires that the frequency response function relating the measurement point to the focusing point should be known in advance. However, inside an enclosure of arbitrary shape, there is no theoretical formulation of this frequency response function, and using the APTRM with the free-field Green's function might lead to inaccurate localization of sound sources. This paper proposes a method combining the APTRM with the equivalent source method (ESM) to locate sound sources in an enclosure of arbitrary shape. In this method, the frequency response function relating the measurement point to the focusing point inside the enclosure is first calculated numerically using the ESM, and then the APTRM with this numerical frequency response function is used to realize the localization of sound sources. Numerical simulations in a rectangular enclosure and an enclosure of arbitrary shape as well as an experiment in a rectangular wooden cabinet are performed to verify the validity of the proposed method. The results demonstrate that the frequency response function in an enclosure can be accurately calculated using the ESM; based on measurements with a spherical array composed of 48 microphones, the proposed method can effectively locate the sound sources in enclosures of different shapes and work stably under the situation of low signal-to-noise ratio.

A Compressed Equivalent Source Method Based on Equivalent Redundant Dictionary for Sound Field Reconstruction

The equivalent source method (ESM) based on compressive sensing (CS) requires that the source has a sparse or approximately sparse representation in a suitable basis or dictionary. However, in practical applications, it is not easy to find the appropriate basis or dictionary due to the indeterminate characteristics of the source. To solve this problem, an equivalent redundant dictionary is constructed, which contains two core parts: one is the equivalent dictionary used in the CS-based ESMs under the sparse assumption, and the other one is the orthogonal basis obtained by the singular value decomposition (SVD). On this foundation, a method named compressed ESM based on the equivalent redundant dictionary (ERDCESM) is proposed to enhance the performances of source field reconstruction for different types of sources. Moreover, inspired by the idea of functional beamforming (FB), ERDCESM with order v (ERDCESM- v ) can possess a high dynamic range when detecting the source location. The numerical simulations are carried out at different frequencies to evaluate the performance of the proposed method, and the results suggest that the proposed method performs well both for sparse and even spatially extended sources. The validity and practicality of the proposed method are also verified by the experimental results.

A time-domain equivalent source method for acoustic scattering based on acoustic velocity

In this paper, a time-domain equivalent source method (ESM) for acoustic scattering prediction is suggested, based on acoustic velocity formulations. Incident and scattered acoustic predictions are realized by acoustic velocity formulation V1A of Ghorbaniasl. Formulation V1A is based on the FW-H equation and allows direct evaluation of the boundary condition, without requiring acoustic pressure gradient computation. The scattering approach is implemented and validated by the analytical case of scattering of a pulsating monopole source by a rigid sphere. The developed methodology is efficient for scattering problems where broadband noise sources are considered.

Heli‐borne gravity gradiometry in rugged terrain

ABSTRACTFor airborne gravity gradiometry in rugged terrain, helicopters offer a significant advantage over fixed‐wing aircraft: their ability to maintain much lower ground clearances. Crucially, this provides both better signal‐to‐noise and better spatial resolution than is possible with a fixed‐wing survey in the same terrain. Comparing surveys over gentle terrain at Margaret Lake, Canada, and over rugged terrain at Mount Aso, Japan, demonstrates that there is some loss of spatial resolution in the more rugged terrain. The slightly higher altitudes forced by rugged terrain make the requirements for terrain correction easier than for gentle terrain. Transforming the curvature gradients measured by the Falcon gravity gradiometer into gravity and the complete set of tensor components is done by a Fourier method over gentle terrain and an equivalent source method for rugged terrain. The Fourier method is perfectly stable and uses iterative padding to improve the accuracy of the longer wavelengths. The equivalent source method relies on a smooth model inversion, and the source distribution must be designed to suit the survey design.

2-D Equivalent Source Method for a Finite Periodically Loaded Multiconductor Transmission Line Analysis With an Application to EBG Power Distribution Networks

A novel theoretical model based on an equivalent source method and a modal superposition technique is proposed to derive a dyadic Green's function for two-dimensional (2-D) finite periodically loaded multiconductor transmission lines (MTLs) to efficiently analyze electromagnetic band gap (EBG) structures embedded in power distribution networks (PDNs) for noise suppression. Many of such structures can be easily modeled using an MTL model with periodically loaded series and shunt components. By treating each periodic load as an equivalent local current source at the center of each unit cell, based on equivalent source theory, a finite uniform 2-D MTL excited by a group of equally spaced equivalent current sources is obtained. The amplitude of these local exciting sources may be analytically evaluated for the modes in the structure. Upon identifying these local equivalent current sources, a simple analytical expression for the 2-D dyadic Green's function is derived based on the modal superposition technique. For validation, a mushroom-type EBG structure embedded in a typical PDN is examined using the proposed approach and comparison with full-wave simulations and measurements are presented.

Iteratively Reweighted Spherical Equivalent Source Method for Acoustic Source Identification

Spherical equivalent source method (S-ESM) using rigid spherical microphone arrays can simultaneously identify sound sources in all directions. In this paper, based on the reweighting and sparse representation frameworks, the sparsity-promoting iteratively reweighted least squares (IRLS) and reweighted l 1 -norm minimization (referred as w-l 1 -norm) are exploited to improve the performance of acoustic source identification for S-ESM. The numerical and experimental results indicate accurate acoustic source identification for the two iteratively reweighted algorithms. IRLS can provide good acoustic source identification over the wide frequency and measurement distance ranges, improving the performance of the established S-ESM. In addition, w-l 1 -norm is also an alternative solution strategy for S-ESM, although at the expense of low computational efficiency and given prior information.

Modeling of Acoustic Emission Generated by Filter Capacitors in HVDC Converter Station

The acoustic noise generated by filter capacitors in a high voltage direct current (HVDC) converter station will have a serious negative impact on the residents' lives and the ecological environment. Though accurate enough, traditional modeling methods based on either boundary element method (BEM) or finite element method (FEM) are almost impossible to reconstruct sound field for whole HVDC station filter array because of their extremely high demand for computing resources. To deal with this problem, this paper proposes a novel Tikhonov Regularization Equivalent Source Method (TRESM)-based filter capacitor acoustic model. By constructing multiple point-sound source models, the acoustic characteristics of the actual filter capacitor are simulated and the original sound field is reconstructed. The accuracy of the proposed model is verified by the experimental results and the sound field distribution characteristics of the three-phase filter capacitor array are observed and analyzed using the proposed model.

Computation of uniform mean flow acoustic scattering by single layer regularized meshless method

The simulation of the acoustic fields propagating in moving flows and the interaction of such fields with the mean flow itself is of importance in aviation acoustic prediction. Volume methods are preferred in this area. Boundary integral method is also concerned because of its own advantages. The transformation space is usually adopted in solving the convective Helmholtz Equation, physical space is also preferred for the convenient boundary condition implementation and combination with other methods. In this paper, the Convective Helmholtz Equation is solved by the Single layer Regularized Meshless Method (SRMM) in the physical space. The SRMM has been proposed by the author for the Laplace equation and Helmholtz Equation. SRMM has similar idea with the Equivalent Source Method (ESM), which represents the fields by the monopoles. But the source points overlap physical points. It overcomes the difficulty of the source points location choice, but the singularity arises. The subtraction and adding-back technique is adopted to get the amplitude of the singularity. The Dual-Surface Method is adopted to avoid irregular frequencies.

Experimental and numerical analysis of the magnetophoresis of magnetic nanoparticles under the influence of cylindrical permanent magnet

Abstract Dye-tracing and concentration-measuring experiments are carried out to investigate the magnetophoresis of magnetic nanoparticles (MNP) in the presence of an external cylindrical permanent magnet. The magnetophoresis of MNP, inducing an obvious forced-convective flowing of the carrier fluid, which can be observed by visualizing flowing of carrier fluid, results in a temporal and spatial variation of particle concentration. Moreover, in order to get insight into the physical mechanisms of magnetophoresis of MNP, a coupled particle-fluid analysis, in which the non-linear drift-diffusion differential equation is incorporated into the Navier-Stokes equation, is adopted to discuss the influence of particle-fluid interaction on the variation of particle concentration and the kinetics of carrier fluid. It is worth noting that the equivalent current source (ECS) method is adopted to obtain a closed-form field analysis, which provides exactly prediction of the Kelvin force and enables magnetophoretic analysis more efficient. In dye-tracing experiments, an obvious vortex can be observed as the methylene blue moves with the convection of carrier fluid. Furthermore, this phenomenon is also predicted by using the coupled particle-fluid model. A comparison between the experimental and numerical results shows that the hydrodynamic interactions between MNP and carrier fluid plays an important role in inducing forced-convective flowing of carrier fluid and enhancing the magnetophoresis of MNP. Furthermore, these results also denote that the coupled particle-fluid model provides a more efficient and accurate method in investigating the magnetophoresis of MNP.

Investigation on the self-assembly of magnetic core-shell nanoparticles under soft-magnet element by using discrete element method

Abstract The self-assembly of magnetic core-shell nanoparticles in the presence of a magnetic template, which consists of an array of soft-magnetic elements embedded in non-magnetic substrate, is analyzed by using discrete element method. An external bias magnetic field is used to magnetize the soft-magnetic elements to saturate state. The high-gradient field produced by elements combined with biased uniform magnetic field provides a flexible way to control the behavior of particles. An equivalent source method is adopted to obtain the closed-form magnetic field analysis, which not only improves the calculation efficiency but also enables accurate prediction of the Kelvin force. In the presence of magnetic field, the behavior of the magnetic nanoparticles is dependent on the magnetic and hydrodynamic forces. Therefore, the assembled structures of magnetic nanoparticles are firstly investigated without considering the magnetic dipole interaction force, in which an unordered nanostructure is formed. As a contrast, the self-assembly of particles is also simulated by taking all forces into account. In this case, the magnetic nanoparticles assemble into an ordered 3D structure, which presents a hexagonal close packed structure. A comparison between the results of the mentioned two cases denotes that the magnetic dipole interaction force plays an important role in controlling the self-assembly of magnetic nanoparticles.

Extension of sound field separation technique based on the equivalent source method in a sparsity framework

The equivalent source method (ESM)-based sound field separation technique has been successfully introduced into near-field acoustic holography as a preprocessing tool to eliminate the influence of disturbing sources or reflections from the opposite side of the array. In this paper, that technique is further extended in a sparsity framework, which makes it possible to take the advantage of the theory of compressive sensing to achieve reasonable separation accuracy with a limited number of spatial sampling points. In this study, three sparse bases are considered, including two existing bases that are suitable for spatially sparse and spatially extended sources, respectively, and a more flexible, redundant sparse basis that is constructed by combining the two sparse bases above, and the ℓ1-norm minimization is used to promote sparse solutions. Numerical simulation and experimental results demonstrate the validity of the proposed technique and show the superiority of the use of the redundant sparse basis. Besides, the effects of the relative strength of the target source to the disturbing source, the number of spatial sampling points and the signal-to-noise ratio on the separation accuracy are analyzed numerically.

Sound field reconstruction using multipole equivalent source model with un-fixed source locations.

The equivalent source methods (ESM) that have been developed to this point can generally be classified into two categories: one in which a relatively large number of lower order sources are fixed at various locations, and one in which a series of higher order sources are fixed at one location. The present work started with a model in the latter category, but the individual sources were then allowed to move separately to locations which were determined by using a nonlinear optimization procedure based on the measured sound field data. To test this approach, experiments were conducted using a small loudspeaker cabinet; measurements were made using an array of microphones on all sides of the loudspeaker. It was found that by allowing the source components to move, the sound field representation in both the near and far fields was improved, particularly at high frequencies, compared to the model with fixed source locations. By comparison with results obtained from boundary element calculations based on laser vibrometer measurements of the loudspeaker's diaphragm and tweeter velocities, it was found that the proposed ESM can also be used to accurately predict the sound pressure distribution on the source surface.

Improved Equivalent Source Method to Predict Sound Scattered by Solid Surfaces

The equivalent source method is an efficient numerical method to predict sound scattered by solid surfaces. Compared with the conventional boundary element method, the equivalent source method has inherent advantages in avoiding the problems of singularity and nonuniqueness of the solution. However, the equivalent source method can form an ill-conditioned matrix for some specific cases, such as thin scattering surfaces, resulting in serious computational errors in these situations. In this paper, an improved equivalent source method is developed in which an efficient regularization method is proposed to reduce the condition number of the coefficient matrix and the regularization parameter can be easily determined. Numerical test cases validate that the improved method usually can reach a satisfactory computational accuracy for predicting sound scattered by thin structures.

Impact Moderation of Power Transmission Lines on the Environment by the Shielding of Trees

Dense high voltage power transmission lines limit human living space and affect the natural landscape and environment. Concerns about the environment in the corridor of high voltage power transmission lines and the occupied land area need to be addressed. Trees are a dissipative medium that can affect polarization in electric fields, leading to excitation of the induced electric field and shielding the impact of electric fields. A mathematical model for the electric field calculation of trees was established by selecting, mapping, and calculating the larch tree species in an experimental forest field at Northeast Forestry University, Heilongjiang Province, China. This study used the finite element method of equivalent excitation sources and the equivalent tree model to estimate the electric field shielding effectiveness of trees. The shielding effect of trees on the electric field of high voltage transmission lines was obvious. Planting trees reduced the transmission lines corridor width by 50.7%, and the maximum electric field in the ground decreased by 95.9%. Thus, planting trees to reduce the electric field of power transmission lines was more effective than the currently widely used method of erecting wires.

Advanced equivalent source methodologies for near-field acoustic holography

The equivalent source method (ESM) based near-field acoustic holography (NAH) has been used successfully in the reconstruction of the acoustical field over arbitrarily shaped vibrating structures from measurements of the pressure field on a nearby conformal surface. In this work we study the use of the ESM dipole and a combined source representation for NAH reconstructions. Using numerically generated data from an elastic spherical shell acoustic response, the studies are focused on the correct positioning and distribution of the source points in relation to the vibrating surface, accuracy over problematic frequencies and spatial aliasing. Finally, we utilize physical data from a vibrating ship-hull structure to validate the proposed ESM reconstructions.

Acoustic source reconstruction and visualization based on acoustic radiation modes

Fourier-based Nearfield Acoustical Holography (NAH), Statistically Optimized Nearfield Acoustical Holography (SONAH) and the Equivalent Source Method (ESM) are widely used in noise source identification and as important tools to guide design modification for noise control purposes. Fourier transform-based NAH requires the sound field to fall to negligible levels outside the measurement aperture, which is a requirement that is rarely met in practice. To overcome this difficulty, SONAH and ESM have been developed. In addition, the Inverse Boundary Element Method (IBEM) can also be used, given sufficient computational resources. Unfortunately, none of these methods can directly guide the design modifications required to unequivocally reduce noise radiation from sources. Previously, radiation mode analysis has been primarily associated with the forward prediction of sound power radiated from noise sources. Since radiation modes contribute independently to the sound power radiation, it is only necessary to modify the surface vibration so that it is not strongly coupled with those modes having high radiation efficiencies in order to ensure sound power reduction. In the current work, an inverse method based on radiation modes was investigated, in which the radiation modes were used as the basis functions to describe surface motion of a source. Thus, this procedure allows the surface vibration that results in the majority of the radiated sound power to be identified unequivocally, and so will, in turn, guide the design changes needed to reduce radiated sound power.

Self-calibration of dual, closed surface microphone arrays

With the recent availability of very inexpensive, miniature digital MEMS microphones, the construction of large count microphone arrays is financially within the reach of the basic researcher. Using various mathematical techniques such as the Helmholtz-Kirchhoff integral and the equivalent source method (ESM), dual surface microphone arrays provide the ability to separate incident and scattered fields instantaneously in time. When these arrays form a closed surface, this separation is extremely accurate. However, one of the concerns with any microphone array is the calibration of the individual elements, especially near the resonance frequency of the diaphragm. In this paper, a self-calibration technique is proposed, based on ESM, that uses external loudspeakers in a simple laboratory facility not required to be anechoic. The approach is tested numerically on a dual surface, 256 element pair spherical microphone array, and uses an algorithm for the minimization of a cost function based on the extinction of the scattered field when the unknown individual calibration coefficients of the array elements are varied. Use of a Burton-Miller approach to model the ESM sources of the scattered field improves dramatically the accuracy at specific frequencies. The problematic interior Dirichlet eigenfrequencies are addressed. [Work supported by the Office of Naval Research.]

Quantifying the error level in computed magnetic amplitude data for 3D magnetization inversion

Three-dimensional inversion plays an important role in the quantitative interpretation of magnetic data in exploration problems, and magnetic amplitude data can be an effective tool in cases in which remanently magnetized materials are present. Because amplitude data are typically calculated from total-field anomaly data, the error levels must be characterized for inversions. Lack of knowledge of the error in amplitude data hinders the ability to properly estimate the data misfit associated with an inverse model and, therefore, the selection of the appropriate regularization parameter for a final model. To overcome these challenges, we have investigated the propagation of errors from total-field anomaly to amplitude data. Using parametric bootstrapping, we find that the standard deviation of the noise in amplitude data is approximately equal to that of the noise in total-field anomaly data when the amplitude data are derived from the conversion of total-field data to three orthogonal components. We then illustrate how the equivalent source method can be used to estimate the error in total-field anomaly data when needed. The obtained noise estimate can be applied to amplitude inversion to recover an optimal inverse model by applying the discrepancy principle. We test this method on synthetic and field data and determine its effectiveness.

Sound field separation with cross measurement surfaces.

With conventional near-field acoustical holography, it is impossible to identify sound pressure when the coherent sound sources are located on the same side of the array. This paper proposes a solution, using cross measurement surfaces to separate the sources based on the equivalent source method. Each equivalent source surface is built in the center of the corresponding original source with a spherical surface. According to the different transfer matrices between equivalent sources and points on holographic surfaces, the weighting of each equivalent source from coherent sources can be obtained. Numerical and experimental studies have been performed to test the method. For the sound pressure including noise after separation in the experiment, the calculation accuracy can be improved by reconstructing the pressure with Tikhonov regularization and the L-curve method. On the whole, a single source can be effectively separated from coherent sources using cross measurement.