Reciprocity Method Research Articles

Sparse angular reciprocity learning for massive MIMO channel estimation

Sparse angular reciprocity refers to the fact that downlink and uplink channels share common sparsity in angular domain. This sophisticated sparsity can be exploited to improve the channel estimation performance for massive multiple-input multiple-output (MIMO) systems. All the existing sparse angular reciprocity methods solve the uplink channel estimation problem independently with an LS estimator in the first stage, and then assist the downlink channel estimation with the sparse angular reciprocity in the second stage. Such a two-stage scheme, as well as the prior LS estimator, will inevitably result in performance loss. To overcome the drawback, we consider the downlink and uplink channel estimation problems as a whole one, and present a new sparse angular reciprocity learning framework to leverage the sparse angular reciprocity. Since the framework provides a joint solution for the downlink and uplink channel estimation in the sense of Bayesian optimality, it is expected to yield higher channel estimation accuracy. Moreover, we devise an efficient variational Bayesian inference (VBI)-based algorithm to automatically decouple the uplink channel. The proposed method can further enhance the channel estimation performance as the prior LS estimator is avoided. Another advantage is that it can be applied to the underdetermined uplink channel estimation problem, where the number of uplink pilot symbols is less than the number of MUs. Simulation results verify the superiority of the proposed method.

WBEM-based analysis of band structures of solid-solid and fluid-fluid phononic crystals with frequency-independent fundamental solutions

A novel method is presented to determine the band structures of two-dimensional solid-solid and fluid-fluid phononic crystals (PCs) with square and triangular lattices using the wavelet-based boundary element method (WBEM). Both sweeping frequency technique and sweeping wave vector technique are used to determine the band structures of PCs. The fundamental solutions for integral equations established in primitive cell are independent of angular frequency, resulting in an avoidance of solving nonlinear eigenvalue problems and much reduction of computing time. The radial integration method and dual reciprocity method are respectively applied to handle the domain integral terms arising from the use of frequency-independent fundamental solutions, and to make the dimension reduction. The physical fields are approximated by B-spline wavelet on the interval and wavelet coefficients in wavelet space. It is proved that the wavelet coefficients still meet the relationship of their corresponding physical quantities, such as Bloch theorem. By means of the vanishing moment characteristic of wavelets, some small entries are produced in the system matrices which are further compressed into sparse ones, and the influence of sparse matrices on the results is discussed. Finally, the high computing speed and accuracy of the proposed method are shown in examples.

Development and evaluation of primary calibration methods in underwater acoustics in a frequency range from 1 Hz to 100 Hz

The project entitled “Metrology for Low Frequency Sound and Vibration” (“INFRA-AUV”), currently active within the European Metrology Programme for Innovation and Research (EMPIR). Measurement of seismic and infrasound activity is very important for monitoring natural extreme events. Low frequency sound and vibration monitoring technologies are well-established, but the sensors are often used for specific and local applications only and lack traceability. This project aims to establish both the first primary measurement standards for low frequency sound (in both air and water) and vibration. The aim of the task “Development and Evaluation of Primary Calibration Methods in Underwater Acoustics in a Frequency Range from 0.5 Hz to 100 Hz” is to develop and evaluate candidate calibration techniques in underwater acoustics for use as primary standards in frequency range of interest. These methods will be evaluated in terms of their limitations, uncertainty contributions and calibration results. The pressure coupler reciprocity method is based on the hydrophone, a transducer and projector which are calibrated inside a relatively small coupling chamber where the acoustic field is homogenous. Through a series of electrical measurements of voltage and current, the acoustic sensitivity of the three devices may be calculated traceable to electrical primary units.

Characterized source model of the M7.3 2016 Kumamoto earthquake by the 3D reciprocity GFs inversion with special reference to the velocity pulse at KMMH16

The 2016 Kumamoto earthquakes caused severe damage centering on the Mashiki residential area. The velocity waveforms at station KMMH16 in Mashiki, during the M7.3 mainshock, show large pulses. We found that severe damage in Mashiki may be the result of the strong westward velocity pulse. The question raised is how the near-fault ground motions with strong velocity pulse at KMMH16 were generated during the mainshock. We focus on the characterized source model with Strong Motion Generation Areas (SMGA). Empirical Green’s function (EGF) method is widely used for source modeling in this case. However, in case that the target site is located just near the fault in nodal plane of source mechanism (like KMMH16), mechanism of the EGF event should perfectly fit mechanism of the mainshock, which is a rare case. Therefore, instead of using EGFs, we used theoretical 3D Green’s functions. Our approach is a nonlinear source inversion. This method requires calculation of waveforms and comparison with observations for many source models. To accelerate these calculations, we use pre-calculated GFs by the reciprocity method in the JIVSM velocity structure model. By comparison with aftershock records, we validated this structure for periods as short as 1.5 s. Target sites are limited to sites close to the fault: KMM005, KMM006, KMMH14, and KMMH16. First, we look for an initial SMGA source model by the grid search method applied to relatively long-period (> 3 s) waveforms and coarse grid of source parameters. Then, we tune that source model to fit observed short-period waveforms with the simplex search method. Necessary physical constraints for the range of the source parameters are applied here. The important point in our inversion scheme is to describe the Kostrov-like slip velocity functions inside each SMGAs by using two triangles. The resulting source model agrees well with other inversion results. We found that the observed westward pulse at KMMH16 is the result of the constructive interference of two pulses from SMGA1 and SMGA2, located in Hinagu fault and southwestern segment of Futagawa fault.Graphical

A DRM FOR HOMOGENEOUS HELMHOLTZ EQUATIONS IN ANISOTROPIC MATERIALS

We consider the problems involving homogeneous Helmholtz equations in anisotropic materials. The problems considered are solved numerically using a dual reciprocity method (DRM). To test the accuracy of the method, the method is tested using problems with analytic solutions. Numerical solutions obtained by the DRM and the corresponding analytical solutions are compared and discussed.

The Acoustic Center of a Measuring Hydrophone

Various approaches to the formulation of the definition of an acoustic center of a transducer and the problems arising when using them for experimental determination of the acoustic-center position are considered. The reasons for which the formulation and the corresponding method for determining the position of the acoustic center of a microphone are not suitable for a hydrophone are discussed. An experiment is described that demonstrates the proposed method for experimentally determining the position of the acoustic center of a hydrophone during its phase calibration by the reciprocity method.

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively. The LKM is a recently proposed local radial basis function collocation method with the merits of being simple, accurate, and free of mesh and integration. Compared with the traditional domain-type and boundary-type schemes, the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains. Numerical experiments, including two- and three-dimensional heat transfer models, demonstrated the effectiveness and accuracy of the new methodology.

Isogeometric dual reciprocity BEM for solving non-Fourier transient heat transfer problems in FGMs with uncertainty analysis

In this paper, the precise integration multi-patch isogeometric dual reciprocity boundary element method (IG-DRBEM) of the non-Fourier transient heat transfer problem in functionally graded materials (FGMs) is proposed, and the stochastic analysis of multidimensional material uncertainty by hyperbolic truncated adaptive sparse polynomial chaos expansion (PCE) is established based on the determine theory. Up to now, most research results of the isogeometric analysis boundary element method (IGABEM) in transient heat transfer problems are based on Fourier's law. The main reason is the higher-order derivative term with respect to time in the non-Fourier heat transfer control equation leads to additional domain integrals in the boundary-domain integral equation. The dual reciprocity method (DRM) can transform the domain integral to the boundary conveniently and maintain the dimension reduction advantage of the BEM. The introduction of the precise integration method (PIM) can improve the stability and accuracy of the time-domain solution. In the random analysis based on IG-DRBEM, a sparse PCE strategy with hyperbolic truncation is constructed to overcome the dimensional disaster difficulty of traditional PCE. Through the proposed adaptive iterative process, a relatively small number of PCE terms are retained compared with the full PCE on the premise of meeting the error estimation requirements. The presented method is verified to have good accuracy and high efficiency by the complex model similar to actual engineering, which further expands the application extent of IG-DRBEM.

A laser pistonphone designed for absolute calibration of infrasound sensors from 10 mHz up to 20 Hz

There has been an increased demand for traceable calibrations at infrasonic frequencies in support of geophysical monitoring applications, an example being the Comprehensive Nuclear-Test-Ban Treaty Organization, which provides global international coverage for a nuclear testing ban, and requires the International Monitoring System. In this paper, a new laser pistonphone design is presented with the objective of establishing primary standards for sound pressure at very low frequencies down to 10 mHz. The piston is a modified accessorized loudspeaker driver whose diameter is equal to the diameter of the front pistonphone cavity. The volume velocity of the piston is measured through a laser interferometer and the current version was designed to have an upper frequency limit of 20 Hz, to overlap with the closed coupler reciprocity method of calibration. Particular attention has been given to the sealing to avoid pressure leakage loss. The dimensions of the front cavity were designed to allow the calibration of a large variety of sensors, including microphones, barometers, manometers and microbarometers. Examples of calibrations for several sensors are presented and also an uncertainty budget for the Brüel & Kjær type 4160 laboratory standard microphones, commonly used for primary calibrations. Finally, the metrological performance of the laser pistonphone is demonstrated by comparing the calibration results with those obtained with alternative methods.

Development of calibration technique for underwater transducers in free field conditions below 1000 Hz with results on an acoustical recorder.

A calibration technique with potential for low frequencies and sizeable systems of underwater transducers is being developed at the Swedish Defence Research Agency. The technique is based on the three-transducer spherical wave reciprocity method for use in an ice-covered lake with a depth of 220 m in the Swedish arctic zone. The calibration is performed at a depth of approximately 100 m with inter-transducer separations of 50 m, 86.6 m, and 100 m, allowing for frequencies down to 59 Hz using time-gated tone burst signals. In this paper, the calibration location, system, and technique are introduced, and the calibration results of an acoustical recorder in the range of 59 Hz-1 kHz are presented. The sensitivity is varying with frequency around -148 dB re 1 V/μPa, and the uncertainty budget is discussed.

A non‐overlapping domain decomposition dual reciprocity method for solving the forward–backward heat equation in two‐dimension

AbstractWe apply a boundary element dual reciprocity method (DRBEM) to the numerical solution of the forward–backward heat equation in a two‐dimensional case. The method is employed for the spatial variable via the fundamental solution of the Laplace equation and the Crank–Nicolson finite difference scheme is utilized to treat the time variable. The physical domain is divided into two non‐overlapping subdomains resulting in two standard forward and backward parabolic equations. The subproblems are then treated by the underlying method assuming a virtual boundary in the interface and starting with an initial approximate solution on this boundary followed by updating the solution by an iterative procedure. In addition, we show that the time discrete scheme is unconditionally stable and convergent using the energy method. Furthermore, some computational aspects will be suggested to efficiently deal with the formulation of the proposed method. Finally, two forward–backward problems, for which the exact solution is available, will be numerically solved for two different domains to demonstrate the efficiency of the proposed approach.

A novel spatial-temporal radial Trefftz collocation method for the backward heat conduction analysis with time-dependent source term

In this paper, a novel spatial-temporal radial Trefftz collocation method (STRTCM) is proposed to solve 2D and 3D backward heat conduction equations with time-dependent source term. Unlike the traditional time-domain discretization strategies (Laplace/Fourier transformation and time-stepping methods), the proposed spatial-temporal meshless collocation method employs the derived semi-analytical spatial-temporal radial Trefftz basis function as basis function, which naturally satisfies the governing equation with zero source term in advance. Due to this property, only the final conditions and boundary conditions need to be discretized. For non-zero source term, the extended multiple reciprocity method (E-MRM) is introduced to transform the original governing equation with several specific source terms to the high-order governing equation without the source term. By deriving the high-order semi-analytical spatial-temporal radial Trefftz basis function, the STRTCM can also avoid the node discretization of governing equation. For solving the backward heat conduction equations, the present numerical scheme uses the final temperature distribution and the related boundary conditions to obtain the unknown initial temperature field. Finally, the accuracy and efficiency of the proposed method is numerically verified by four benchmark examples about backward heat conduction equations with time-dependent source term.

A reciprocity method for validating acoustic ear-probe source calibrations.

Measurements of wideband acoustic immittance (WAI) rely on the calibration of an ear probe to obtain its acoustic source parameters. The clinical use of WAI and instruments offering the functionality are steadily growing, however, no international standard exists to ensure a certain reliability of the hardware and methods underlying such measurements. This paper describes a reciprocity method that can evaluate the accuracy of and identify errors in ear-probe source calibrations. By placing the ear probes of two calibrated WAI instruments face-to-face at opposite ends of a short waveguide, the source parameters of each ear probe can be measured using the opposite calibrated ear probe. The calibrated and measured source parameters of each ear probe can then be compared directly, and the influence of possible calibration errors on WAI measurements may be approximated. In various exemplary ear-probe calibrations presented here, the reciprocity method accurately identifies errors that would otherwise remain undetected and result in measurement errors in real ears. The method is likely unsuitable for routine calibration of WAI instruments but may be considered for conformance testing as part of a potential future WAI standard.

Indirect boundary element formulation with dual reciprocity in elastodynamics

In this paper, a new indirect boundary element formulation for two-dimensional elastodynamic problems is presented. The formulation makes use of a static fundamental solution. For accurate solution, the location of the fictitious boundary is chosen to be the same as problem boundary. The relevant fundamental solution is integrated over lines. The method is combined with the Dual Reciprocity Method (DRM), for handling the domain integral concerning to the domain inertia terms. A suitable approximation (traditional function C-R is used) for the inertia terms (or, domain accelerations), is used to transform the domain integral to the boundary. The discretization is performed on the boundary, or a boundary-like geometry. The method is easy to code and efficient as presented by the numerical examples.

A Monopole-Based Wideband Absorber for Ultralarge Angles

This article develops a broadband absorber by fully using the radiation features of monopole antennas for ultrawide-angle absorption application. A unit cell (UC) based on monopole antennas is proposed, and its working polarization is analyzed with the antenna reciprocity method and image theory. A wide-angle impedance matching layer is also introduced to further enhance the absorption at large angles. The optimized monopole-based UC reveals 90% absorptivity from 5.5–14.76 GHz at the incident angle of 80°. To the best of our knowledge, this is the first time to report an absorber that can work perfectly under such ultrawide angles in a broadband manner. An 11 × 36 array is configured and simulated to verify the effectiveness of the monopole-based UC. The monostatic and bistatic scattering are both reduced significantly as well as other diffuse scattering directions from the simulated results. A prototype of 110 mm × 360 mm is fabricated and measured. Time gating methods are adopted to diminish the direct coupling effect. The measurements are in good agreement with the full-wave simulation results.

THE NUMERICAL MESHLESS APPROACH FOR SOLVING THE 2D TIME NONLINEAR MULTI-TERM FRACTIONAL CABLE EQUATION IN COMPLEX GEOMETRIES

The cable equation plays a prominent role in biological neuron models, for instance, in spiking neuron models and electrophysiology. Thus, the current investigation scrutinizes the 2D time nonlinear multi-term fractional cable equation. By adopting a valid meshfree technique, the nonlinear multi-term time-fractional cable equations (NM-TTFCEs) that consist of government equations and their boundary conditions are transformed into the boundary value problems. For this purpose, the finite difference method is derived for temporal discretization such that the considered NM-TTFCEs can be transformed into a sequence of boundary value problems in inhomogeneous Helmholtz-type equations. The dual reciprocity method (DRM) is implemented to obtain a particular solution and the improved singular boundary method (ISBM) is employed to evaluate the homogeneous solution. Moreover, we apply the meshless method for solving two-dimensional NM-TTFCEs on regular and irregular distribution points with several computational domains. The numerical results vouch for the accuracy and high efficiency of the proposed method. Finally, we will conclude that the ISBM/DRM method can be considered a potential alternative to existing meshless strong form approaches in solving multi-term fractional equation problems with complex geometries.

A novel isogeometric boundary element approach for solving phase change problems with the level set method

In this study a new algorithm is proposed for numerically solving phase change problems. The algorithm (PTE-IGBEM) integrates the precise time domain expanding method (PTE) and the isogeometric boundary element method (IGBEM). The governing equations are transformed into recursive form by expanding the variables within the time period. The domain integral is transformed into boundary integral by the dual reciprocity method (DRM). An adaptive checking scheme is used to determine the number of expanding items required for a time period. In addition, the level set method (LSM) is used to capture the trajectory of the front separating the solid and liquid phases. Several classical examples are given to demonstrate the accuracy and robustness of the algorithm.

SOFTWARE FOR SIMULATION OF NON-STATIONARY HEAT TRANSFER IN ANISOTROPIC SOLIDS

The software «AnisotropicHeatTransfer3D» for the numerical solution of three-dimensional non-stationary heat conduction problems in anisotropic solids of complex domain by meshless method [1] was developed. The numerical solution of the non-stationary anisotropic heat conduction problem in the software «AnisotropicHeatTransfer3D» is based on a combination of the dual reciprocity method [2] with anisotropic radial basis functions [3] and the method of fundamental solutions [4]. The dual reciprocity method with anisotropic radial basis functions is used to obtain particular solution, and the method of fundamental solutions is used to obtain a homogeneous solution of boundary-value problem.

The localized method of fundamental solutions for 2D and 3D inhomogeneous problems

In this paper, the newly-developed localized method of fundamental solutions (LMFS) is extended to analyze multi-dimensional boundary value problems governed by inhomogeneous partial differential equations (PDEs). The LMFS can acquire highly accurate numerical results for the homogeneous PDEs with an incredible improvement of the computational speed. However, the LMFS cannot be directly used for inhomogeneous PDEs. Traditional two-steps scheme has difficulties in finding the particular solutions, and will lead to a loss of the accuracy and efficiency. In this paper, the recursive composite multiple reciprocity method (RC-MRM) is adopted to re-formulate the inhomogeneous PDEs to higher-order homogeneous PDEs with additional boundary conditions, which can be solved by the LMFS efficiently and accurately. The proposed combination of the RC-MRM and the LMFS can analyze inhomogeneous governing equation directly and avoid troublesome caused by the two-steps schemes. The details of the numerical discretization of the RC-MRM and the LMFS are elaborated. Some numerical examples are provided to demonstrate the accuracy and efficiency of the proposed scheme. Furthermore, some key factors of the LMFS are systematically investigated to show the merits of the proposed meshless scheme.

Localized Method of Fundamental Solutions for Two-Dimensional Inhomogeneous Inverse Cauchy Problems

Due to the fundamental solutions are employed as basis functions, the localized method of fundamental solution can obtain more accurate numerical results than other localized methods in the homogeneous problems. Since the inverse Cauchy problem is ill posed, a small disturbance will lead to great errors in the numerical simulations. More accurate numerical methods are needed in the inverse Cauchy problem. In this work, the LMFS is firstly proposed to analyze the inhomogeneous inverse Cauchy problem. The recursive composite multiple reciprocity method (RC-MRM) is adopted to change original inhomogeneous problem into a higher-order homogeneous problem. Then, the high-order homogeneous problem can be solved directly by the LMFS. Several numerical experiments are carried out to demonstrate the efficiency of the LMFS for the inhomogeneous inverse Cauchy problems.