Element‐wise a posteriori estimates based on hierarchical bases for non‐linear parabolic problems

We show that the issue of a posteriori estimate the errors in the numerical simulation of non‐linear parabolic equations can be reduced to a posteriori estimate the errors in the approximation of an elliptic problem with the right‐hand side depending on known data of the problem and the computed numerical solution. A procedure to obtain local error estimates for the p version of the finite element method by solving small discrete elliptic problems with right‐hand side the residual of the p‐FEM solution is introduced. The boundary conditions are inherited by those of the space of hierarchical bases to which the error estimator belongs. We prove that the error in the numerical solution can be reduced by adding the estimators that behave as a locally defined correction to the computed approximation. When the error being estimated is that of a elliptic problem constant free local lower bounds are obtained. The local error estimation procedure is applied to non‐linear parabolic differential equations in several space dimensions. Some numerical experiments for both the elliptic and the non‐linear parabolic cases are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

Plasticity effects in incremental slitting measurement of residual stresses

The effect of plasticity is investigated for the incremental slitting, or crack-compliance, method for measuring through-thickness profiles of residual stress. Based on finite element simulations, the errors can be strongly correlated with K_Irs, the stress-intensity factor caused by the cut extending into a residual stress field. 3-D simulations also show that the errors are strongly dependent on the amount of constraint provided by the part width. The simulations are used to develop a procedure for estimating errors from experimental data. Even with the possibility of plasticity errors in the measured residual stresses, the K_Irs can be simply calculated using only the experimentally measured strains. This K_Irs is called “apparent” because the calculation assumes elasticity. The apparent K_Irs can then be used to bound the errors in the measured residual stresses. The error bound is given as a function of non-dimensionalized apparent K_Irs and part width.     

A simple a-posteriori error estimation for adaptive BEM in elasticity

In this paper, the properties of various boundary integral operators are investigated for error estimation in adaptive BEM. It is found that the residual of the hyper-singular boundary integral equation (BIE) can be used for a-posteriori error estimation for different kinds of problems. Based on this result, a new a-posteriori error indicator is proposed which is a measure of the difference of two solutions for boundary stresses in elastic BEM. The first solution is obtained by the conventional boundary stress calculation method, and the second one by use of the regularized hyper-singular BIE for displacement derivative. The latter solution has recently been found to be of high accuracy and can be easily obtained under the most commonly used C ⁰ continuous elements. This new error indicator is defined by a L ₁ norm of the difference between the two solutions under Mises stress sense. Two typical numerical examples have been performed for two-dimensional (2D) elasticity problems and the results show that the proposed error indicator successfully tracks the real numerical errors and effectively leads a h-type mesh refinement procedure.     

Methods for Locating Stray-Signal Sources in Anechoic Chambers

Two complementary numerically efficient frequency-domain methods for locating stray-signal sources in anechoic chambers are investigated and applied in combination to actual measurement data. Both methods use single-frequency near-field data collected on a planar surface and process them to reconstruct field values (images) elsewhere. The first method, which is based on the fact that the probe output satisfies the Helmholtz equation, uses plane waves to backpropagate the scan-plane data and is well suited for fast-Fourier-transform (FFT)-based rapid reconstruction of images on planar surfaces parallel to the scan plane. The second method uses the simple spherical-wave focusing technique and is flexible, in that, it can be used to generate images on either planar or nonplanar surfaces from the data collected on either planar or nonplanar surfaces. When data and image points are both located on a regular grid, the method can be implemented using the FFT-based fast convolution technique. Both methods include a spatial filter for isolating selected plane-wave spectrum components. The two methods are used in combination to successfully locate the strong multiple-bounce stray signals that degrade the quiet zone of a near-field bistatic radar cross-section facility. Subsequent scan data confirm that the suppression of these stray signals indeed substantially improves the quality of the quiet zone. The spherical-focusing method is also used to evaluate the effectiveness of the various absorber configurations applied to selected edges of the reflector to control edge-diffracted fields. It is shown that the reduction of the edge-diffracted fields further improves the quiet zone.     

Aberrator integration error in adaptive imaging

Tissue speed of sound inhomogeneities cause significant degradation of medical ultrasound images. In some cases these inhomogeneities may be modeled as a thin time delay screen located at the face of the transducer. The effects of such near-field aberrations can be reduced by adding compensating time delays to the normal system focusing delays. Unfortunately array elements are generally large in at least one dimension when compared to variations in the aberrator, thus correction of the mean time delay on an element leaves residual variations in the time delay profile across that element. This paper presents theoretical expressions and simulation results describing the magnitude of this aberrator integration error. Simulations results are also presented which show the distortion of received pulses and degradation of point spread functions which results from aberrator integration error. These results indicate that aberrator integration error may be the dominant source of error in the implementation of adaptive imaging techniques and in phase aberration measurements. Thus, correction of near-field aberrations may be significantly more difficult than previously suspected     

Signal Identification Using a Least L1 Norm Algorithm

In many important applications a signal consists of a sum of exponential terms. The signal is measured at a discrete set of points in time, with possible errors in the measurements. The Signal Identification (SI) problem is to recover the correct exponents and amplitudes from the noisy data. An algorithm (SNTLN) has been developed which can be used to solve the SI problem by minimizing the residual error in the L₁ norm. In this paper the convergence of the SNTLN algorithm is shown, and computational results for two different types of signal are presented, one of which is the sum of complex exponentials with complex amplitudes. For comparison, the test problems were also solved by VarPro, which is based on minimizing the L₂ norm of the residual error. It is shown that the SNTLN algorithm is very robust in recovering correct values, in spite of some large errors in the measured data and the initial estimates of the exponents. For the test problems solved, the errors in the exponents and amplitudes obtained by SNTLN1 were essentially independent of the largest errors in the measured data, while the corresponding errors in the VarPro solutions were proportional to these largest data errors.     

高空光测系统误差的恒星法修正

在高空目标光学测量中,由于设备和环境条件的影响,数据存在一定的系统误差,系统误差修正是获取高精度位置参数的关键.针对高空光测系统误差修正问题,首先分析了80 km 以上目标光测数据的系统误差来源,建立了高空目标光测数据的系统误差模型,提出了基于恒星的修正方法,对大气折射误差和设备轴系误差进行联合修正.为验证方法的有效性,将该方法应用于实际高空光学测量,实验结果表明修正效果明显,可使系统误差修正精度提高到2″.     

Three-dimensional measurement and imaging based on multicameras randomly distributed on the circumference

We present a three-dimensional (3D) measurement and imaging based on a multicamera system. In the presented system, projected images of 3D objects are taken by cameras located at random positions on a circumference, and then the 3D objects can be reconstructed numerically. We introduce an angle correction function to improve the quality of the reconstructed object. The angle correction function can correct the angle error caused by the position errors in the projected images due to the finite pixel size of the image sensor. The numerical results show that the point source was reconstructed successfully by introducing the angle correction function. We also demonstrate experiments: the two objects are located on a rotary stage controlled by a computer, the projected images are taken by a single camera, and by using 33 projected images, the two objects are reconstructed successfully.     

Analysis of the complex phase error introduced by the application of the Fourier transform method

Abstract

The relation between modulus and phase errors introduced by the application of the Fourier transform method to fringe pattern analysis has been established. The theoretical results obtained are proposed for the reconstructed phase error correction. Numerical verification for a one-dimensional fringe pattern, comparison of corrected and non-corrected results obtained for different basic spatial frequencies and an example of application of the proposed correction for real data are given.     

The Correction Capability of the Berlekamp–Massey–Sakata Algorithm with Majority Voting

Sakata’s generalization of the Berlekamp–Massey algorithm applies to a broad class of codes defined by an evaluation map on an order domain. In order to decode up to the minimum distance bound, Sakata’s algorithm must be combined with the majority voting algorithm of Feng, Rao and Duursma. This combined algorithm can often decode far more than (d _min −1)/2 errors, provided the errors are in general position. We give a precise characterization of the error correction capability of the combined algorithm. We also extend the concept behind Feng and Rao’s improved codes to decoding of errors in general position. The analysis leads to a new characterization of Arf numerical semigroups.     

Colour-Doppler echocardiography flow field velocity reconstruction using a streamfunction–vorticity formulation

We introduce a new method (Doppler Velocity Reconstruction or DoVeR), for reconstructing two-component velocity fields from colour Doppler scans. DoVeR employs the streamfunction–vorticity equation, which satisfies mass conservation while accurately approximating the flow rate of rotation. We validated DoVeR using artificial colour Doppler images generated from computational fluid dynamics models of left ventricle (LV) flow. We compare DoVeR against the conventional intraventricular vector flow mapping (iVFM_1D) and reformulated iVFM (iVFM_2D). LV model error analysis showed that DoVeR is more robust to noise and probe placement, with noise RMS errors (nRMSE) between 3.81% and 6.67%, while the iVFM methods delivered 4.16–24.17% for iVFM_1D and 4.06–400.21% for iVFM_2D. We test the DoVeR and iVFM methods using in vivo mouse LV ultrasound scans. DoVeR yielded more haemodynamically accurate reconstructions, suggesting that it can provide a more reliable approach for robust quantification of cardiac flow.     

用于光热反射显微热成像的位置漂移修正方法

光热反射显微热成像测试过程中需要采集若干被测图像,整个过程中图像各像素与被测表面位置的对应关系应保持不变,但是被测表面不可避免地会发生位置漂移,从而引起测量误差。结合光热反射显微热成像的具体应用场景和位置漂移的特性,设计了有针对性的亚像素图像配准算法,结合PID控制驱动三轴纳米位移台实现实时的位置漂移修正。实验验证了算法性能以及漂移修正效果,位移修正残差在5nm以内,与未补偿测量相比,位置漂移引入的误差得到了较好的抑制,提高了光热反射显微热成像测试的准确性。     

Analytical modeling for the ballistic perforation of planar plain-woven fabric target by projectile

This paper presents an analytical model to calculate decrease of kinetic energy and residual velocity of projectile penetrating targets composed of multi-layered planar plain-woven fabrics. Based on the energy conservation law, the absorbed kinetic energy of projectile equals to kinetic energy and strain energy of planar fabric in impact-deformed region if deformation of projectile and heat generated by interaction between projectile and target are neglected. Then the decrease of kinetic energy and residual velocity of projectile after the projectile perforating multi-layered planar fabric targets could be calculated. Owing to fibers in fabric are under a high strain rate state when fabric targets being perforated by a high velocity projectile, the mechanical properties of the two kinds of fibers, Twaron^® and Kuralon^®, respectively, at strain rate from 1.0×10⁻² to 1.5×10³ s⁻¹, are used to calculate the residual velocity of projectile. It is shown that the mechanical properties of fibers at high strain rate should be adopted in modeling rate-sensitivity materials. Prediction of the residual velocities and energy absorbed by the multi-layered planar fabrics show good agreement with experimental data. Compared with other models on the same subject, the perforating time in this model can be estimated from the time during which certain strain at a given strain rate is generated. This method of time estimation is feasible in pure theoretical modeling when the perforation time cannot be obtained from experiments or related empirical equations.     

A parameter for quantitative analysis of plasticity induced crack closure

Numerical models have been successfully developed to predict plasticity induced crack closure (PICC). However, despite the large research effort a full understanding of the links between physical parameters, residual plastic wake and PICC has not been achieved yet. The plastic extension of material behind crack tip, Δy_p, obtained by the integration of vertical plastic deformation perpendicularly to crack flank, is proposed here to quantify the residual plastic field. The values of Δy_p and PICC were obtained numerically in a M(T) specimen using the finite element method. An excellent correlation was found between PICC and Δy_p which indicates that this parameter controls the phenomenon, and can be used to quantify the effect of physical parameters. An empirical model was developed to predict PICC assuming that the residual plastic field is a set of vertical plastic wedges, that the linear superposition principle applies and that the influence of a particular wedge exponentially decreases with distance to crack tip. The model was applied successfully to predict PICC for different residual plastic fields which provided an additional validation of Δy_p as the parameter controlling PICC.     

Correction of instrument line-shape distortions in Fourier transform spectroscopy

A recovery procedure has been developed to correct instrument line-shape distortions observed in Fourier transform spectroscopy. The procedure can be described as a phase-error correction performed in the spectral domain to correct for path-difference-dependent phase errors observed in sharp spectral features. The technique has been applied successfully to high-resolution atmospheric emission spectra. The inherent broadening of the real features has been separated accurately from instrumental distortions. Using models for the path-difference-dependent error sources and data from two narrow window regions at 50 and 118 cm(-1), we show that the distortion has a simple dependence on the spectral frequency.     

Accuracy verification of a simple local three-dimensional displacement measurement method of DIC with two images coordinates

There are two methods applied for three-dimensional digital image correlation method to measure three-dimensional displacement. One is to measure the spatial coordinates of measuring points by analyzing the images. Then, the displacement vectors of these points can be calculated using the spatial coordinates of these points obtained at different stages. The other is to calibrate the parameters for individual measuring points locally. Then, the local displacements of these points can be measured directly. This study proposes a simple local three-dimensional displacement measurement method. Without any complicated distortion correction processes, this method can be used to measure small displacement in the three-dimensional space through a simple calibration process. A laboratory experiment and field experiment are carried out to prove the accuracy of this proposed method. Laboratory test errors of one-dimensional experiment are similar to the accuracy of the XYZ table; the error in Z-direction is only 0.0025% of the object distance. The measurement error of laboratory test is about 0.0033% of the object distance for local three-dimensional displacement measurement test. Test and analysis results of field test display that in-plane displacement error is only 0.12 mm, and the out-of-plane error is 1.1 mm for 20 m × 30 m measuring range. The out-of-plane error is only about 10 PPM of the object distance. These test and analysis results show that this proposed method can achieve very high accuracy under small displacement for both of laboratory and field tests.     

Analysis of error-correction constraints in an optical disk

The compact disk read-only memory (CD-ROM) is a mature storage medium with complex error control. It comprises four levels of Reed Solomon codes allied to a sequence of sophisticated interleaving strategies and 8:14 modulation coding. New storage media are being developed and introduced that place still further demands on signal processing for error correction. It is therefore appropriate to explore thoroughly the limit of existing strategies to assess future requirements. We describe a simulation of all stages of the CD-ROM coding, modulation, and decoding. The results of decoding the burst error of a prescribed number of modulation bits are discussed in detail. Measures of residual uncorrected error within a sector are displayed by C1, C2, P, and Q error counts and by the status of the final cyclic redundancy check (CRC). Where each data sector is encoded separately, it is shown that error-correction performance against burst errors depends critically on the position of the burst within a sector. The C1 error measures the burst length, whereas C2 errors reflect the burst position. The performance of Reed Solomon product codes is shown by the P and Q statistics. It is shown that synchronization loss is critical near the limits of error correction. An example is given of miscorrection that is identified by the CRC check.     

声压基阵误差单辅助矢量水听器快速校准方法

针对方位依赖的声压基阵误差校正困难问题,提出了声压基阵误差单辅助矢量水听器快速校准方法。利用精确校正的单只矢量水听器,就可以对声源方位及方位依赖的声压基阵幅度相位误差,进行无模糊的联合估计。由于阵元位置误差、互耦及通道的幅度相位误差均可以等效为方位依赖的基阵幅度相位误差,所以可以对多种同时存在的基阵误差进行校正。该方法适用于任意的阵列结构,不存在参数联合估计的局部收敛问题,只需参数的一维搜索,运算量小可实时在线完成。通过计算机仿真实验验证了该方法的有效性。     

Error evaluation and correction of stray impedance during measurement and interpretation of AC impedance of cement-based materials

In this study, the error of stray impedance during measurement and interpretation of the AC impedance of cement-based materials was evaluated based on a proposed reasonable correction method. The results indicated that the stray impedance produces approximately 60% and 35% modulus errors at 15 MHz frequency, and 1.68–55.30% and 10.72–153.58% errors of the interpreted parameters for 210-d and 3-d curing concrete, respectively. The stray impedance of the two electrodes and the extra shorting wire introduced in the traditional correction method (Z_ei) produce approximately 45% and 15% modulus errors at 15 MHz frequency, and 0.94–82.81% and 49.03–96.71% errors of the interpreted parameters for 210-d and 3-d curing concrete, respectively. The proposed method eliminates the Z_ei and contains only extra introduced contact resistance between the shorting wire and the two electrodes (R_cls). However, the R_cls produce less than 1% modulus and the interpreted parameters errors, indicating that the proposed method is accurate.