Equivalent Source Strength Research Articles

Sparse reconstruction of sound field using pattern-coupled Bayesian compressive sensing.

Conventional near-field acoustic holography based on compressive sensing either does not fully exploit the underlying block-sparse structures of the signal or suffers from a mismatch between the actual and predefined block structure due to the lack of prior information about block partitions, resulting in poor accuracy in sound field reconstruction. In this paper, a pattern-coupled Bayesian compressive sensing method is proposed for sparse reconstruction of sound fields. The proposed method establishes a hierarchical Gaussian-Gamma probability model with a pattern-coupled prior based on the equivalent source method, transforming the sound field reconstruction problem into recovering the sparse coefficient vector of the equivalent source strengths within the compressive sensing framework. A set of hyperparameters is introduced to control the sparsity of each element in the sparse coefficient vector of the equivalent source strengths, where the sparsity of each element is determined by both its own hyperparameters and those of its immediate neighbors. This approach enables the promotion of block sparse solutions and achieves better performance in solving for the sparse coefficient vector of the equivalent source strengths without prior information of block partitions. The effectiveness and superiority of the proposed method in reconstructing sound fields are verified by simulations and experiments.

High-resolution acoustic imaging method based on equivalent source method and reweighted l1 minimization

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.

Sound Field Reconstruction Using Compressed Separable Projection-Based Equivalent Source Method

The compressive-equivalent source method (C-ESM) has been developed for the sound field reconstruction by solving the [Formula: see text] minimization with the predetermined sparsity of the equivalent source strengths. However, the C-ESM would reconstruct the sound field with the error proportional to the measurement noise-related data fidelity constraint that increases with the decrease of the signal-to-noise ratio. Apart from that, the reconstruction stability of the C-ESM would not be guaranteed due to the existence of the measurement noise. To address such problem, the present paper proposes a compressed separable projection-based equivalent source method. In the method, the projections of the measured pressures in the predesigned basis that combines the priors of the sound radiation of the equivalent sources and the measurement noise are obtained by solving the [Formula: see text] minimization. This not only leads to the data fidelity constraint being small and unrelated to the measurement noise, but also separates the measurement noise from the measured sound field. Therefore, the proposed method can theoretically reconstruct the sound field more accurately and stably than the C-ESM. Numerical simulations and experiments are carried out to verify the effectiveness of the proposed method.

Sound field reconstruction using sparse Bayesian learning equivalent source method with hyperparametric-coupled prior

Block sparse Bayesian learning (SBL) equivalent source method (ESM) suffers from the block structure mismatch problem that leads to poor sound field reconstruction accuracy for block sparse sources. To address this issue, this paper proposes to employ a hyperparametric-coupled prior in the SBL-ESM. In the method, a hierarchical SBL model is established based on the ESM, and then the coupling constraint is imposed to the hyper-prior of equivalent source strengths by a projection transformation. The proposed method can produce a coupling effect, such that the sparsity of equivalent source strengths is controlled not only by each corresponding hyper-parameter, but also by their immediate neighbors. Therefore, it enables to promote block sparse solutions and reconstruct the sound fields of block sparse sources well without the prior information of block partition. Numerical simulations of linear-block sources are used to verify the effectiveness and superiority of the proposed method, and the effects of sound power ratio, signal-to-noise ratio and reconstruction distance on the reconstructed results are investigated. Subsequently, the performance of the proposed method is further verified through an experiment of a composite loudspeaker and an experiment of the mixed sources consisting of a small loudspeaker and an impacted steel plate.

Sensor array design for sparse sound field reconstruction

The compressive-equivalent source method can reconstruct the sound field of the sparsely distributed sound sources through promoting the sparsity of the equivalent source strengths. To reduce the mutual coherence of the sensing matrix, the spatially random sampling is performed. However, different samplings would make the reconstruction results instable, and a fixed sampling would not guarantee satisfied reconstruction results when reconstructing the sound field at different frequencies. To handle this issue, the present paper proposes a sensor array design method for sparse sound field reconstruction. After obtaining the matrix by the sum of the frequency-dependentsensing matrices, the optimization problem of the proposed method is formulated based on the mutual coherence minimization principle, and the solutions indicating the selected positions of the sensors are solved by the gradient projection. Numerical simulation and experimental results show that lower reconstruction errors can be obtained with the designed senor array compared to the spatially random sampling.

A novel hybrid superposition method for predicting ship seismic wave in shallow sea

A hybrid superposition method (HSM) is developed for predicting seismic wave in elastic seabed excited by low frequency noise from ship submerged in shallow sea. In the scheme of HSM, an array of distributed equivalent sources interior to a radiator are employed to represent this radiator based on wave superposition principle. The equivalent sources that satisfy the boundary conditions of shallow sea are constructed by making inverse Hanker transform to the depth-dependent Green’s function corresponding to displacement potential by aid of wavenumber integration algorithm. The strengths of equivalent sources are determined by matching normal velocities on the boundary surface of radiator and then modified for ship seismic wave computation. The ship seismic wave is conveniently calculated using the superposition of the fields from the equivalent sources. It is the key feature of HSM that truncating and discretizing the field space are not required for the prediction, which reduces original problem by one dimension, while accurate results are achieved. The performance of the present method including accuracy, stability, and convergence is studied numerically. Simulations indicate that this novel method is outstanding and competitive at predicting ship seismic wave in shallow sea.

Separation of nonstationary sound fields based on the time-domain equivalent source method with single layer pressure-velocity measurements.

This paper proposes a sound field separation technique based on the time-domain equivalent source method with single layer pressure-velocity measurements to extract the nonstationary sound field radiated by the target source in a reverberant environment. This technique constructs a formulation that relates the pressures and particle velocities on a measurement surface to the strengths of time-domain equivalent sources arranged for modelling the outgoing and incoming waves. By solving the strengths of time-domain equivalent sources, the sounds coming from different sides of the measurement surface can be separated independently. In the proposed technique, the use of a time-domain equivalent source model allows the measurement surface to be arbitrarily shaped, thus providing the ability to analyze the arbitrarily shaped sources in a reverberant environment. Numerical simulations investigated the performance of the proposed technique when using different types of arrays, including planar, semi-cylindrical, and semi-spherical arrays, and an experiment with three loudspeakers located at two sides of the measurement surface was carried out to test the validity of the proposed technique. Both numerical and experimental results demonstrate that the proposed technique can remove the influence of disturbing sources in both time and space domains and separate out the target sound fields effectively.

Power-based application of frequency-averaged 𝓁1-norm regularisation technique for the synthesis of accelerating indoor tyre pass-by noise

Pass-by noise contribution analysis is an engineering procedure employed to estimate the contributions from various noise sources on a vehicle to the overall sound pressure level. This can be realised by placing a set of microphones close to the various sources to estimate their source strengths and then synthesising the response at a far-field linear array in the presence of the remaining sources. The results described in this paper rely on measured near-field pressure data close to the tyres of an electric vehicle under accelerating conditions. The number and position of the estimated virtual source strengths used is a compromise between complexity and accuracy, which has previously been addressed mostly empirically. A power-based, frequency-averaged 𝓁1-norm regularisation technique is investigated to optimise the equivalent source position and strength for one operating tyre and, subsequently, the far-field pass-by noise pressure estimates. It is shown that for the tyre under investigation, optimising the positions of only two equivalent sources over the frequency range of interest gives a good representation of the measured far-field spectra.

An approach for indoor prediction of the pass-by noise of a vehicle based on the time-domain equivalent source method

An approach based on the time-domain equivalent source method (TESM) is developed for the indoor prediction of the pass-by noise of a vehicle in a small-scale semi-anechoic chamber. In the approach, a vehicle drives on a chassis dynamometer, and a number of microphones are distributed around the vehicle to measure the pressure radiated by the vehicle in the near field. Based on the idea of TESM, the sound sources generated by the vehicle are modeled by a series of time-domain equivalent sources, and the sound radiated from these sources to the microphones is depicted by the half-space Green’s function that takes the reflections from the rigid ground into account. To evaluate the pass-by noise, the strengths of equivalent sources are first solved by using the measured pressures as the input of TESM, and then the pressures on the target points specified by the ISO 362-3 Standard are reconstructed by the superposition of sound fields generated by the equivalent sources. Finally, the sound pressure level (SPL) of the pass-by noise can be calculated from the reconstructed pressures. In particular, the proper arrangement scheme for the equivalent sources is investigated in numerical simulations to ensure the prediction accuracy. Numerical and experimental results demonstrate that the proposed approach can effectively predict the SPL of the pass-by noise of a vehicle for both constant-speed and accelerated test conditions in a small-scale semi-anechoic chamber.

Surface Deformation and Induced Seismicity Due to Fluid Injection and Oil and Gas Extraction in Western Texas

AbstractTexas is experiencing increasing seismicity, likely related to the oil and gas production process. We used satellite InSAR (Interferometric Synthetic Aperture Radar) to monitor surface deformation at three study sites in western Texas with similar geologic characteristics. The deformation data were compared to earthquake distribution, groundwater changes, volumes of produced and injected fluid, and calculated pore pressure change and Coulomb failure stress change to assess causes of deformation and seismicity. Site 1 experienced surface uplift due to fluid injection but no increase in seismicity. The average media properties were estimated based on the deformation using a poroelastic model. Site 2 experienced subtle surface subsidence and elevated seismicity. Subsidence here might reflect groundwater withdrawal. Simulated pore pressure changes using MODFLOW suggest the earthquakes are likely induced by fluid injection. Site 3 experienced significant surface subsidence and seismicity. InSAR time series, water level data, and oil/gas extraction history suggest that subsidence in the northern part of this site reflects oil/gas extraction, while subsidence in the southern part is mainly due to groundwater withdrawal. An Okada tensile model was used to derive the equivalent source strength causing the subsidence, then Coulomb failure stress changes associated with this source were calculated. We found that pore pressure change (simulated using MODFLOW) due to fluid injection is likely the main contributor to elevated seismicity at this site. Variations in oil/gas production activity, seismicity, and surface deformation between our three sites suggest the importance of local rock structure and media properties in determining susceptibility to induced seismicity.

An accurate and efficient computational method for time-domain aeroacoustic scattering

This paper presents a convective time-domain equivalent-source method for determining the scattered acoustic pressure field in a uniform moving medium. The proposed method is based on the solution of the time-domain convective Ffowcs Williams–Hawkings (FW–H) equation while the strengths of equivalent sources are determined by the required pressure gradient boundary condition on the scattering surface. The scattered acoustic pressure can be calculated once the strengths of equivalent sources have been determined. The current paper adopts the recently published analytical time-domain formulation for the acoustic pressure gradient in a moving medium to evaluate the incident pressure gradient on the scattering surface. This makes the proposed method considerably more efficient and accurate than a direct method. The total acoustic pressure consists of the scattered and the incident components. The latter can be obtained by the time-domain acoustic pressure formulation of the convective FW–H equation. Causes of possible instability in the proposed method are analyzed and an effective stabilizing method is proposed. Three test cases are considered to demonstrate the validity of the proposed method: a point monopole source field scattered by: (1) a rigid sphere in a stationary medium, (2) an infinite flat plate in uniform flow parallel to its surface, and (3) a cylinder of infinite length in axial uniform flow. To demonstrate the usefulness of the proposed method in practical engineering applications, the scattering of a point monopole source field by a slender wing in uniform flow is considered.

Application of ℓp norm regularisation techniques in the synthesis of indoor tyre pass-by noise with the inverse method

Pass-by noise measurements can nowadays be realised in a laboratory environment with a microphone array and a stationary vehicle on a rolling road, according to ISO – 362–1:2016. Within this indoor testing procedure, the contributions from the various noise sources in a car can be estimated, with a set of microphones close to the various sources, and the pass-by noise then synthesised. The methods described in this paper use measured near field pressure data close to a rolling tyre at 50 km/h to estimate virtual source strength, using the inverse method, and the synthesised far field tyre noise is then compared with the one measured directly at a far field microphone array. A combination of ℓ1 norm and ℓ2 norm regularisation methods are investigated to optimise the equivalent source position and strength and, subsequently, the far field pass-by noise pressure estimates through the frequency range of interest. It is shown that by optimising the positions of 4 equivalent sources, acceptable representations of the measured far field spectra can be synthesised.

An alternating iterative algorithm for sound source identification based on equivalent source method

Near-field acoustical holography (NAH) based on equivalent source method (ESM) is an efficient technique for sound source identification. Conventional ESM with Tikhonov regularization (TRESM), ESM based on CVX MATLAB toolbox (CVX) and wideband acoustic holography (WBH) are commonly used methods for calculating equivalent source strengths. However, all of them have their respective limitations. To address some of these, an alternating iterative algorithm for sound source identification based on equivalent source method (AIESM) is proposed in this article, which is a combination of alternating direction method and a non-monotone line search technique. The method makes use of sparse regularization under the principle of compressive sensing (CS) to calculate equivalent source strengths. Moreover, inspired by the idea of functional beamforming (FB), AIESM with order n can yield an improved dynamic range when detecting the source location. Numerical simulations are carried out at different frequencies, and the results suggest that the computational efficiency of the proposed method is close to that of TRESM. In addition, AIESM has a better reconstruction accuracy than TRESM and WBH in a relatively wide frequency range. Compared with ESM based on CVX, AIESM is slightly better in reconstruction accuracy and has a higher computational efficiency. Meanwhile, AIESM with order n can provide more accurate source position and better resolution. The validity and practicality of the proposed method are further supported by experimental results.

A Novel Transfer Matrix-Based Approach for Pilot Protection of Hybrid Transmission Lines Considering HIF Location

Distance protection encounters some problems such as time coordination, protection of short lines, capacitive charging current and high impedance faults. Its shortcomings are extended in the case of protection of hybrid transmission lines, including overhead line and underground cable. To cope with the mentioned problems, in this paper, a novel approach is proposed for pilot protection of hybrid transmission lines. The proposed approach utilizes three phase voltage and current signals of both ends and transfer matrix of the hybrid line. Indeed, voltage and current angles of specific points on the line are calculated from both ends and the absolute values of the differences between the results obtained from the sending and receiving ends are computed for each point to detect the fault and identify its exact location and phase. The achieved results confirm the security, dependability, and efficiency of the algorithm in critical conditions of power system, i.e., high impedance fault occurrence, power swing, different strengths of equivalent sources at both ends, loss of time synchronization of remote end data, and different fault locations with various inception angles. Although the proposed method is very simple, its performance is surprisingly satisfactory and it is suitable for practical implementation in real-life applications.

Application of lp-norm regularisation techniques in the synthesis of indoor tyre pass-by noise with the inverse method

The indoor pass-by noise measurement can nowadays be realised in a laboratory environment with a far field microphone array and a stationary vehicle on a rolling road, according to ISO-362-1:2016. Within this indoor testing procedure, there exists the ability to quantify the contributions from the various noise sources in a car to gain further insight into the total noise disturbance. The tyre noise contribution can be estimated by using an additional set of microphones close to the tyre and performing an inverse method. This work assumes measured near field pressure data close to a rolling tyre at different car speeds. The inverse method is utilised to find the corresponding source strength estimates which are then used to synthesise the far field tyre noise contribution and compare it with the one measured directly at the far field microphone array. A combination of novel l1 regularisation and conventional l2 regularisation methods is finally investigated to further optimise the equivalent source strength estimates and, subsequently, the far field pass-by noise pressure estimates through the frequency range of interest.

Robust reconstruction of equivalent source method based near-field acoustic holography using an alternative regularization parameter determination approach.

The core of equivalent source method based near-field acoustic holography is to solve the equivalent source strength with the measured pressure and the transfer matrix, which is a typical ill-posed inverse problem. In this work, an explicit formula is proposed in which the regularization parameter is proportional to the product of the hologram distance and the maximum singular value of the transfer matrix. Utilizing the proposed approach, robust acoustic field reconstruction can be achieved even when the hologram distance is 5 times larger than the average microphone spacing.

Reconstruction of instantaneous surface normal velocity of a vibrating structure using interpolated time-domain equivalent source method

Abstract Interpolated time-domain equivalent source method is extended to reconstruct the instantaneous surface normal velocity of a vibrating structure by using the time-evolving particle velocity as the input, which provides a non-contact way to overall understand the instantaneous vibration behavior of the structure. In this method, the time-evolving particle velocity in the near field is first modeled by a set of equivalent sources positioned inside the vibrating structure, and then the integrals of equivalent source strengths are solved by an iterative solving process and are further used to calculate the instantaneous surface normal velocity. An experiment of a semi-cylindrical steel plate impacted by a steel ball is investigated to examine the ability of the extended method, where the time-evolving normal particle velocity and pressure on the hologram surface measured by a Microflown pressure-velocity probe are used as the inputs of the extended method and the method based on pressure measurements, respectively, and the instantaneous surface normal velocity of the plate measured by a laser Doppler vibrometry is used as the reference for comparison. The experimental results demonstrate that the extended method is a powerful tool to visualize the instantaneous surface normal velocity of a vibrating structure in both time and space domains and can obtain more accurate results than that of the method based on pressure measurements.

Sound radiation of cylinder in shallow water investigated by combined wave superposition method

It can be a difficult problem to precisely predict the sound field radiated from a finite elastic structure in shallow water channel because of its strong coupling with up-down boundaries and the fluid medium, whose sound field cannot be calculated directly by current methods, such as Ray theory, normal mode theory and other different methods, which are adaptable to sound fields from idealized point sources in waveguide. So far, there is no reliable prediction method to solve this kind of problem. A combined wave superposition method is proposed for such a problem, which combines the traditional wave superposition method with the transfer function in shallow water channel and the multi-physics field coupling numerical model. This method mainly consists of three sections:1) obtaining the normal velocity on the elastic structure surface in shallow water channel by the finite element method (FEM), whose FEM model includes the up-down boundaries and the completely absorbent sound boundaries in the horizontal direction; 2) getting the equivalent point source strength by traditional wave superposition method; 3) calculating the total sound field by adding up each point source field which is obtained by normal mode method. This method is verified by numerical simulation and theoretical analysis by using an imaginary and elastic spherical sound source respectively, and the results demonstrate that the method is valid and has high precision and calculating efficiency. The acoustic radiation characteristics from elastic cylindrical shells is investigated for different acoustic radiation sources, ocean environments and measurements. The cylindrical shell material is steel, whose radius and length are 3 m and 30 m respectively. The shallow water channel is an ideal waveguide with 50 m in depth, at the upper boundary, i.e., the free surface, the lower boundary is the Neumann boundary, i.e., the normal derivative of the acoustic pressure should be zero. The analysis frequency range is from 30 Hz to 200 Hz. The results show that due to a significant coupling effect of up-down direction boundaries on the sound field, the elastic structure can be equivalent to the point source only in low frequency and far field. The spatial field directivity distribution is more obvious at high frequency. The acoustic power measured by vertical line arrayis greatly influenced by ocean boundary and the depth of target.

Equivalent Source Method-Based Nearfield Acoustic Holography in a Moving Medium

To identify sound sources situated in a fluid flow, an equivalent source method (ESM)-based nearfield acoustic holography (NAH) in a moving medium is proposed, and two types of acoustic inputs, pressure and particle velocity, are considered. In particular, an analytical relationship between the particle velocity perpendicular to the flow direction and the equivalent source strength is deduced, which makes it possible to realize the reconstruction with particle velocity input. Compared to the planar NAH in a moving medium, the proposed method is applicable to sound sources with more complicated geometries. Numerical simulations with sound sources distributed over two types of geometries including planar geometry and nonplanar one are conducted to test the performances of the proposed method. The results indicate that the proposed method provides satisfactory reconstructed results whatever with pressure input or with particle velocity input, and it is valid and robust over a wide range of flow velocities and frequencies and under different levels of background noise.

Suppressing the onset of instabilities in the time-domain equivalent source method using a multistep approach.

Numerical instability is an important issue that should be addressed in the time-domain equivalent source method (TESM). This study proposes a multistep method to stabilize TESM when using the measured acoustic pressure data to optimize equivalent source strengths. Unlike the conventional single-step method that solves each time step in the time-marching process of TESM, the proposed method performs a one-time solution for several time steps. The multistep solution can potentially reduce the accumulation rate of error, and improves filtering effects by changing the structure of the matrix that needs to be inverted when the truncated singular value decomposition or Tikhonov regularization is used in the time-marching process. Numerical simulations with three examples demonstrate the effectiveness of the multistep method in improving the stability of solutions compared with the single-step method. Effects of the number of merged time steps on the solutions are also discussed to guide the selection process. Finally, the sensitivity of the multistep method to numerical parameters is investigated to demonstrate its consistency under different configurations of numerical parameters.