Equivalent Source Model Research Articles

Setting boundary conditions on the Khokhlov–Zabolotskaya equation for modeling ultrasound fields generated by strongly focused transducers

An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov–Zabolotskaya equation.

Estimating aircraft noise levels and spectra from aircraft flyover and ground operations

The noise from military aircraft operations can adversely affect people within the civilian community near an airbase and within the military community living and operating within the confines of the airbase. The aircraft noise levels and spectra should be estimated to determine the building noise attenuation treatments to achieve the desired interior noise levels. This presentation describes a method to estimate the noise levels and spectra from both ground operations and flyover operations of high performance military jet aircraft for the community near the airbase and the airbase proper. Sound levels are predicted over a typical airbase region using an equivalent source model for a fighter jet aircraft and atmospheric propagation modeling. Overall level contours are generated over the entire area, and spectral levels are predicted at desired points corresponding to noise sensitive building locations. [Work supported by USAFRL through ORISE.]

Inclusion of a ground-reflecting plane in wavepacket modeling of military jet noise

Equivalent source models for high-speed jet noise are intended to represent the acoustic properties of the turbulent mixing noise. A wavepacket ansatz previously applied to obtain equivalent sources from anechoic laboratory measurements is modified to include both a direct and image complex pressure representation of the source to model the presence of a ground-reflecting plane. This is important for modeling the sound field at maintainer and flight deck personnel positions because the interference effects caused by ground-reflected propagation paths significantly influence the sound levels and vary with frequency and location. The ability of the direct-plus-image wavepacket model to yield the interference patterns observed across large planes of data (2 m tall by 23 m long) measured near a high-performance military aircraft is evaluated. In particular, the variation in the nulls of the sound pressure level across the planes as a function of frequency predicted by this wavepacket model are compared to the measurements between 4 and 25 m from the engine nozzle exit. Comparisons with previous work based on a Rayleigh-distributed source amplitudes are also provided. [Work supported by the Office of Naval Research.]

A rapid noninvasive characterization of CT x-ray sources.

The aim of this study is to generate spatially varying half value layers (HVLs) that can be used to construct virtual equivalent source models of computed tomography (CT) x-ray sources for use in Monte Carlo CT dose computations. To measure the spatially varying HVLs, the authors combined a cylindrical HVL measurement technique with the characterization of bowtie filter relative attenuation (COBRA) geometry. An apparatus given the name "HVL Jig" was fabricated to accurately position a real-time dosimeter off-isocenter while surrounded by concentric cylindrical aluminum filters (CAFs). In this geometry, each projection of the rotating x-ray tube is filtered by an identical amount of high-purity (type 1100 H-14) aluminum while the stationary radiation dose probe records an air kerma rate versus time waveform. The CAFs were progressively nested to acquire exposure data at increasing filtrations to calculate the HVL. Using this dose waveform and known setup geometry, each timestamp was related to its corresponding fan angle. Data were acquired using axial CT protocols (i.e., rotating tube and stationary patient table) at energies of 80, 100, and 120 kVp on a single CT scanner. These measurements were validated against the more laborious conventional step-and-shoot approach (stationary x-ray tube). At each energy, HVL data points from the COBRA-cylinder technique were fit to a trendline and compared with the conventional approach. The average relative difference in HVL between the two techniques was 1.3%. There was a systematic overestimation in HVL due to scatter contamination. The described method is a novel, rapid, accurate, and noninvasive approach that allows one to acquire the spatially varying fluence and HVL data using a single experimental setup in a minimum of three scans. These measurements can be used to characterize the CT beam in terms of the angle-dependent fluence and energy spectra along the bowtie filter direction, which can serve as input for accurate CT dose computations.

An equivalent source model for simulating high intensity focused ultrasound fields using a nonlinear parabolic equation

The nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation is commonly used for simulation of nonlinear focused fields generated by medical ultrasound transducers. Axially symmetric codes can be easily implemented on personal computers with simulation times on the order of tens of minutes even for the most extensive simulations of shock formation conditions. However, model accuracy can be limited for high intensity focused ultrasound sources with large convergence angles. In previous studies, it was shown that nonlinear parabolic modeling can provide good matching with measurements and full diffraction modeling in the focal region for both single element piston sources and multi-element arrays. Boundary conditions for the modeling were adjusted by varying the aperture of an equivalent planar source with a uniform pressure magnitude and a phase distribution for parabolic focusing. With this approach, there were slight discrepancies in the lateral pressure distributions in the focal plane. Here, it is proposed that an additional variation in the position of the equivalent source enables matching both axial and lateral distributions of the real HIFU sources with higher accuracy. Several examples are presented to compare modeling and measurements of the fields generated by laboratory and clinical HIFU transducers. [Work supported by RSF 14-12-00974 and NIH EB007643.]

Prediction of Near-Field Jet Cross Spectra

A prediction method is developed based on the acoustic analogy for the cross-power spectral density in the convecting near field of compressible fluid turbulence. Equivalent source near-field, midfield, and far-field terms within the model integrand create corresponding near-field, midfield, and far-field radiating waves. These equivalent sources are modeled with a single equation for the two-point cross correlation of the Lighthill stress tensor that is dependent on the jet operating conditions. An alternative equivalent source model based on steady Reynolds-averaged Navier–Stokes solutions is proposed. The cross-power spectral density model automatically reduces to a traditional autopower spectral density model when observers are at the same location. Predictions of radiation intensity and coherence compare favorably with measurements in the near field, midfield, and far field for a wide range of jet Mach numbers and temperature ratios.

Size optimization of conical piezoelectric energy harvesters

The optimal design of piezoelectric patches on a piezoelectric conical energy harvester is presented in this study. Based on the equivalent voltage source model, the power of the resistance load is derived firstly. The origin location of the piezoelectric patch is set at the peak points of the modal voltage. The piezoelectric patch is in the region formed by the zero lines where the modal voltage is zero. The location of the peak points and the zero lines are determined by the spatial distribution of the modal voltage and the open-circuit voltage. Three parameters are chosen to locate the piezoelectric patch, i.e. the circumferential width, the length from the origin to the minor end and the length from the origin to the major end. Solving the extremum of the power equation with respect to the three parameters yields the optimal size of the piezoelectric patch. Case studies are given to evaluate the power of the optimal piezoelectric energy harvester. The results indicate that with the origin located at the optimal location, the power of resistance load firstly increases with the width and the lengths until the maximum and then decreases. The optimal width of the piezoelectric patch is 75% of the half-wave length for all of the evaluated modes.

Numerical simulation of guided waves using equivalent source model of magnetostrictive patch transducers

While magnetostrictive patch transducers have become more widely used for damage inspection of waveguides such as plates or pipes, the numerical simulation of guided waves excited by the transducers is very limited. Recently, one-way, coupled time-harmonic, finite element analysis based on the linearized magnetostrictive coupling equation has been conducted, but transient analysis must be carried out to extract more information including the reflected waves from cracks. Naturally, fully coupled or one-way coupled multiphysics transient finite element analysis would require substantial computational resources and cost. In order to utilize an efficient structural finite element method or code, we newly propose equivalent distributed force models that can describe the actuation mechanism of the magnetostrictive patch transducer without explicitly solving coupled multiphysics equations. Once equivalent force models are established, transient wave simulations in inspected waveguides can be accomplished efficiently through any structural finite element code. The essence of this approach is to establish the equivalent actuating force models useful for various types of magnetostrictive patch transducers currently available. The validity of the developed models is checked by investigating the wave radiation patterns of the Rayleigh–Lamb and shear–horizontal waves in test waveguides, and the simulated results obtained with the proposed models are compared against the available experimental results.

An equivalent source model for the sound intensity in the vicinity of a high-performance military aircraft

The sound field of the F-22A Raptor has been measured extensively using arrays of microphones including an intensity probe to the sideline and rear of the aircraft. Recently, an equivalent source model (ESM) has been proposed that incorporates two arrays of monopole sources placed along the jet axis and their image sources to account for the hard ground. The monopole amplitudes in each case are described by a Rayleigh distribution, and one array includes a phase angle between the monopoles to produce correlated noise steered in a specific direction. The model closely replicates the measured SPL at the majority of measurement locations. However, agreement with energy-based quantities such as the vector acoustic intensity may not follow from agreement with the pressure measurements alone. Hence, in this work, the ESM’s ability to produce intensity estimates that match the measured F-22A intensity is evaluated. A new method of estimating acoustic intensity, known as the phase and amplitude gradient estimation (PAGE) method, is applied to the measured F-22A data. The PAGE method accurately estimates intensity in a larger bandwidth than the traditional finite difference method, expanding this discussion of the ESM's accuracy. In addition, sensitivity of ESM parameter selection, e.g., correlated source phase angle and peak amplitude location, on changes in the predicted intensity is examined. [Work sponsored by ONR.]

Algebraic reconstruction combined with the signal space separation method for the inverse magnetoencephalography problem with a dipole-quadrupole source

This paper presents an algebraic reconstruction method for dipole-quadrupole sources using magnetoencephalography data. Compared to the conventional methods with the equivalent current dipoles source model, our method can more accurately reconstruct two close, oppositely directed sources. Numerical simulations show that two sources on both sides of the longitudinal fissure of cerebrum are stably estimated. The method is verified using a quadrupolar source phantom, which is composed of two isosceles-triangle-coils with parallel bases.

Radiation Characteristics of Heat Sink in Propulsive Wheel of Mobile Robots

Electromagnetic interference easily appears in the propulsive wheel - a key component of the mobile robots, because internal space of propulsive wheel is very small, there are numerous electronic devices, and signal communication is complex. So electromagnetic shielding is very important for the propulsive wheel. In this paper, a wheel model and an equivalent source model of electromagnetic interference of the wheel were developed based on considerations of the internal electromagnetic properties. At the same time, a secondary source of electromagnetic interference is formed by heat sink. Hence, shielding effectiveness is taken as one of the evaluation criteria for the Electro-Magnetic Compatibility (EMC) problem, and the Genetic Algorithm (GA) in the software Ansoft HFSS platform was used to optimize the first resonance frequency of heat sink.

동축 프로브 급전구조에 대한 FDTD 전원 모델들의 상호 관계에 관한 비교 연구

RF 및 마이크로파 대역에서 동축 프로브 급전구조에 대한 효율적인 유한 차분 시간 영역(FDTD: Finite-Difference Time-Domain) 해석을 위한 등가 전원 모델링 기법들의 상호 관계를 연구하였다. 기존에는 델타 갭(delta-gap) 또는 자기 프릴(magnetic-frill) 개념을 FDTD에 도입한 등가 전원 모델들이 여러 연구진에 의해서 개발되었다. 이러한 등가 전원 모델들의 FDTD 구현 방법과 모의 계산의 정확성은 서로 조금 다르다는 정도로만 잘 알려져 있었다. 본 논문에서는 준정적 근사(quasi-static approximation)하에서 동축-프로브 급전 구조에 대한 FDTD 등가 전원 모델들의 상호 관계를 제시하였다. FDTD 등가 전원 모델들의 적용방법에 따라 동축 급전된 원추형 모노폴 안테나의 시간영역과 주파수영역 응답을 수치계산하였다. 또한, FDTD 모의계산의 정확성과 효율성에 대한 비교 결과를 제시하였다. For an efficient finite-difference time-domain(FDTD) analysis of coaxial-probe feeding structures in radio frequency(RF) and microwave bands, an interrelation between equivalent source modeling techniques is investigated. In existing literature, equivalent source models with delta-gap or magnetic-frill concepts have been developed by many researchers. It is well known that FDTD implementation and computational accuracy of these source models are slightly different. In this paper, the interrelation between FDTD equivalent source models for coaxial feeding structures under the quasi-static approximation(QSA) is presented. As a function of FDTD equivalent source models, time-domain and frequency-domain responses of a coaxial-probe fed conical monopole antenna are calculated numerically. And comparison results of computational accuracy and efficiency are provided.

Farfield and Nearfield Source Identification for Machine Tools Using Microphone Array Imaging Systems

Farfield and nearfield microphone arrays are proposed for noise source identification (NSI) and sound field visualization (SFV). Farfield acoustic imaging algorithms including the delay and sum (DAS) algorithm, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are employed to estimate direction of arrival (DOA). Results demonstrate that the MUSIC algorithm can attain the highest resolution of localizing sound sources positions. In the nearfield array signal processing, one formulation termed the indirect equivalent source model (ESM)-based nearfield acoustical holography (NAH) is derived from discretizing the simple layer potential. As indicated by the experimental results, the proposed technique proved effective in identifying the noise sources from various machine tools such as milling machine, turning lathe and shearing machine.

Sensitivity analysis of an equivalent source model for a military jet aircraft

The noise from a tied-down F-22A Raptor is modeled with an equivalent source consisting of two line arrays of monopole sources and their image sources, to represent the interference from the ground. These arrays, one correlated and one uncorrelated, with Rayleigh-distributed amplitudes, mimic properties of fine and large-scale turbulent mixing noise. [Morgan et al., Noise Control Eng. J. 60, 435-449 (2012)]. The equivalent source modeling parameters (the distributions’ peak locations, amplitudes, widths, and the relative phase angle between correlated sources) are selected using Bayesian optimization implemented with simulated annealing and fast Gibbs sampler algorithms. The resulting equivalent source model reasonably predicts the radiated midfield up to 1250 Hz [Hart et al., POMA 19, 055094 (2013)]. In this study, the relationship between the correlated array’s peak location and its phase angle has been further analyzed. Although sensitivity analysis of the results reveals non-uniqueness of the model, it also yields additional physical insight in the form of bounds for the dominant aeroacoustic source region as a function of frequency. The far field sound radiation predicted by the equivalent source model for a wide range of frequencies will be compared to measured far-field directivities. [Sponsored by the Office of Naval Research.]

Reconstruction of arbitrary sound fields with a rigid-sphere microphone array

Over the last few years, several studies have examined the potential of using rigid-sphere microphone arrays for reconstructing sound fields with near-field acoustic holography (NAH). The existing methods provide a reconstruction of the sound field based on a spherical harmonic expansion. However, because of the basis functions used, the reconstruction can only be performed in spherical surfaces concentric to the array and inside the source-free region, which imposes a severe limitation on the applicability of the technique due to geometrical constrains. In this paper, a method based on an equivalent source model is proposed, where a combination of point sources is used to describe the incident sound field on the array. This method makes it possible to reconstruct the entire sound field at any point of the source-free domain without being restricted to a spherical surface. Additionally, this approach adds versatility (the reconstruction can be based on the microphones that are closer to the source, for a better conditioning of the problem, or also use non-uniform sampling). The method is presented, examined numerically and experimentally, and compared to the existing methods based on a spherical harmonic expansion.

Development and validation of a measurement‐based source model for kilovoltage cone‐beam CT Monte Carlo dosimetry simulations

The purpose of this study is to adapt an equivalent source model originally developed for conventional CT Monte Carlo dose quantification to the radiation oncology context and validate its application for evaluating concomitant dose incurred by a kilovoltage (kV) cone-beam CT (CBCT) system integrated into a linear accelerator. In order to properly characterize beams from the integrated kV CBCT system, the authors have adapted a previously developed equivalent source model consisting of an equivalent spectrum module that takes into account intrinsic filtration and an equivalent filter module characterizing the added bowtie filtration. An equivalent spectrum was generated for an 80, 100, and 125 kVp beam with beam energy characterized by half-value layer measurements. An equivalent filter description was generated from bowtie profile measurements for both the full- and half-bowtie. Equivalent source models for each combination of equivalent spectrum and filter were incorporated into the Monte Carlo software package MCNPX. Monte Carlo simulations were then validated against in-phantom measurements for both the radiographic and CBCT mode of operation of the kV CBCT system. Radiographic and CBCT imaging dose was measured for a variety of protocols at various locations within a body (32 cm in diameter) and head (16 cm in diameter) CTDI phantom. The in-phantom radiographic and CBCT dose was simulated at all measurement locations and converted to absolute dose using normalization factors calculated from air scan measurements and corresponding simulations. The simulated results were compared with the physical measurements and their discrepancies were assessed quantitatively. Strong agreement was observed between in-phantom simulations and measurements. For the radiographic protocols, simulations uniformly underestimated measurements by 0.54%-5.14% (mean difference = -3.07%, SD = 1.60%). For the CBCT protocols, simulations uniformly underestimated measurements by 1.35%-5.31% (mean difference = -3.42%, SD = 1.09%). This work demonstrates the feasibility of using a measurement-based kV CBCT source model to facilitate dose calculations with Monte Carlo methods for both the radiographic and CBCT mode of operation. While this initial work validates simulations against measurements for simple geometries, future work will involve utilizing the source model to investigate kV CBCT dosimetry with more complex anthropomorphic phantoms and patient specific models.

TU‐G‐103‐04: The Accuracy of Monte Carlo Based Dose Estimates Compared to In‐Vivo Dose Measurements

Purpose: The purpose of this study was to extend the validation of Monte Carlo (MC) simulation based dose estimates by comparing simulated values with in‐vivo measurements from clinical patient scans. Methods: The Institutional Review Board approved the acquisition of in‐vivo rectal dose measurements in a pilot study of 9 patients undergoing CT Colonography on an MDCT (LightSpeed VCT, GE Healthcare). Per patient, two scans, prone and supine, were acquired both using a fixed mAs technique. In‐vivo dose measurements were obtained using TLD capsules that were affixed to the inner lumen of rectal catheters. Dose from the TLDs were determined taking into account their energy response. Simulations were performed using voxelized models of the patients and the TLDs based on CT image data. A previously developed MC based model was used to simulate the scanner and each patient scan. Dose to the TLD was estimated for each patient scan. The measured and simulated in‐vivo TLD dose values were compared for all 9 patients and the Root Mean Square (RMS) error was calculated as well as the correlation. Additionally the simulated results were compared with calculated Size Specific Dose Estimates (SSDEs) for each patient. Results: The RMS error between TLD measurements and MC simulations was 12.2% with a maximum of 20.3% and minimum of ‐ 19.7%. Comparison of simulations and SSDE resulted in an RMS of 17.0% with a minimum of ‐ 22.9% and maximum of 22.8%. Conclusion: The results of this study demonstrated that MC simulations using voxelized patient and equivalent source model Result in reasonably accurate doses compared to actual measured doses. Several possible improvements to the performance of the MC model were identified (including reconstructing images at the biggest field of view for full coverage of the anatomy, etc.) Dr. Michael McNitt‐Gray; Institutional research agreement, Siemens AG; Recipient research support Siemens AG; Consultant, Flaherty Sensabaugh Bonasso PLLC; Consultant, Fulbright and Jaworski, LLC; Maryam Khatonabadi and Kyle McMillan ripient research support Siemens AG

A Bayesian based equivalent sound source model for a military jet aircraft

The two-source model for jet noise holds that turbulent mixing noise in jets is generated by uncorrelated, fine-scale (FSS) and partially correlated, large-scale (LSS) turbulent structures [Tam et al., J. Fluid Mech. 615, 253-292, (2008)]. The noise from an F-22A Raptor is modeled with an equivalent source consisting of two line arrays of monopole sources. These arrays, one correlated and one uncorrelated, with Rayleigh distributed amplitudes, account for both FSS and LSS sound propagation [J. Morgan, J. Acoust. Soc. Am. 129, 2442 (2011)]. The equivalent source parameters are selected based on Bayesian methods implemented with simulated annealing and fast Gibbs sampler algorithms. This method yields the best fit parameters, and the sensitivity of the solution is indicated by the generated posterior probability distributions. Analysis of the resulting equivalent sources shows that the directional, correlated line array has greater effect on the near field sound, and the sensitivity of the array's parameters increases as the frequency increases. This equivalent source model can generate results up to 2500 Hz and accurately predict both near field and far field measurements. The analysis suggests that the shape of the source distribution changes as the frequency increases. [Work sponsored by the Office of Naval Research.]

3-D FE Wire Modeling and Analysis of Electromagnetic Signatures From Electric Power Drive Components and Systems

A 3-D finite-element (FE) optimized equivalent source numerical model for the analysis of low frequency electromagnetic field signatures in electric drives is proposed. An example electric drive system including a synchronous generator, an induction motor and power cables connecting a load is used to implement the model. The arrangement of the system setup is developed using a fully detailed 3DFE model to verify and compare with the results of the proposed equivalent source model. The proposed technique provides the exact field solution without large computational even with the presence of superposition. The equivalent source model (wire model) is created based on numerical techniques and physical theory of wave propagation. The superposition of the various components in this study is considered. The results of the proposed wire models match the results of the original models. For further verification, experimental results of the setup are compared with the numerical results. The importance of the proposed equivalent source is that it can be used for the evaluation of electromagnetic signatures and radiation patterns at the design stage. This enables performing various designs iterations to achieve compliant designs to electromagnetic compatibility standards. The proposed model can also be used for dynamic monitoring and diagnosing failures in the system.

Near Field Characterization of an Imaging System Based on a Frequency Scanning Antenna Array

This contribution describes the concept of frequency scanning for imaging applications. The designed frequency scanning antenna array, which works in Ku frequency band, is used for the sectoral illumination of the scene under investigation, enabling the recovery of information restricted to the selected area. While the proposed idea simplifies beam scanning techniques with respect to mechanical or electrically-controlled scanning systems, the price-to-pay is the limitation on the amount of scattered field information. The near field radiation of the frequency scanning antenna array is characterized through an equivalent source model to assess accurately the incident field used in the imaging algorithm. This analysis also enables the evaluation of the frequency steering performance of the antenna in the near field, validating its use for the proposed application.