A combined approach for goal‐oriented error estimation and adaptivity using operator‐customized finite element wavelets

We describe how wavelets constructed out of finite element interpolation functions provide a simple and convenient mechanism for both goal‐oriented error estimation and adaptivity in finite element analysis. This is done by posing an adaptive refinement problem as one of compactly representing a signal (the solution to the governing partial differential equation) in a multiresolution basis. To compress the solution in an efficient manner, we first approximately compute the details to be added to the solution on a coarse mesh in order to obtain the solution on a finer mesh (the estimation step) and then compute exactly the coefficients corresponding to only those basis functions contributing significantly to a functional of interest (the adaptation step). In this sense, therefore, the proposed approach is unified, since unlike many contemporary error estimation and adaptive refinement methods, the basis functions used for error estimation are the same as those used for adaptive refinement. We illustrate the application of the proposed technique for goal‐oriented error estimation and adaptivity for second and fourth‐order linear, elliptic PDEs and demonstrate its advantages over existing methods. Copyright © 2005 John Wiley & Sons, Ltd.     

起伏背景下目标噪声线谱检测与频率估计

针对传统的水下目标辐射噪声线谱检测与频率估计方法所存在的不足,提出一种起伏背景下的水下目标辐射噪声线谱检测与线谱频率估计的方法。通过对观测数据的预处理,滤除目标辐射噪声起伏趋势项,再分别使用FFT方法和修正的Newton-Raphson迭代法来实现对目标辐射噪声线谱频率的粗略估计和精确估计。仿真结罘表明,该方法计算量较少,提高了检测概率和频率估计精度,且频率估计值的均方根误差较传统的周期图方法更接近Cramer-Rao界。     

Overdrive in the ramp histogram test of ADCs

This paper presents a study about the amount of overdrive to use when analog-to-digital converters (ADCs) are tested with the ramp histogram method. Overdrive is used to limit the error induced by input-equivalent noise in the estimation of the ADC transition voltages. This study has direct application in the new coarse ramp static test.     

液体黏性软启动装置输出轴的有限元分析

针对液体黏性软启动装置的工作特点,要求输出轴传动力矩和输出转速变化范围较大,轴变形应该保持在较小范围内,输出轴的性能对液体黏性软启动装置正常工作有重要影响,需要对输出轴的结构作进一步分析.通过建立液体黏性软启动装置输出轴的Pro/E三维模型,采用有限元软件ANSYS Workbench对启动装置的输出轴进行有限元分析,确定输出轴的变形和应力状况,计算输出轴的模态和疲劳损伤.仿真结果表明：输出轴损伤最大部位位于较粗轴端键槽一侧.提出了一些改进措施,为液体黏性软启动装置输出轴的结构设计和疲劳寿命估算提供参考依据.     

Intersymbol interference channels with signal-dependent non-Gaussian noise: estimation of achievable information rates

In this letter, we calculate the achievable information rates for the intersymbol interference channels with general signal-dependent correlated noise under the constraint that the inputs are chosen from a finite alphabet. The proposed method employs canonical multivariate density estimation techniques. This method is important in that it can be used for accurate estimation of the achievable information rates for magnetic recording channels with media noise, where higher order media noise models can be taken into account instead of the first-order model.     

A theoretical framework for performance characterization of elastography: the strain filter

This paper presents a theoretical framework for performance characterization in strain estimation, which includes the effect of signal decorrelation, quantization errors due to the finite temporal sampling rate, and electronic noise. An upper bound on the performance of the strain estimator in elastography is obtained from a strain filter constructed using these limits. The strain filter is a term used to describe the nonlinear filtering process in the strain domain (due to the ultrasound system and signal processing parameters) that allows the elastographic depiction of a limited range of strains from the compressed tissue. The strain filter predicts the elastogram quality by specifying the elastographic signal-to-noise ratio (SNR(e)), sensitivity, and the strain dynamic range at a given resolution. The dynamic range is limited by decorrelation errors for large tissue strain values, and electronic noise for low strain values. Tradeoffs between different techniques used to enhance elastogram image quality may also be analyzed using the strain filter.     

Smart computational fracture of materials and structures

The use of the finite element method for complex engineering problems is now common. To ease the burden on the engineer the development of smart or adaptive computational methods is now required to model complex problems. In this paper we investigate the development of an adaptive finite element method for fracture-related problems. The adaptive method involves various stages which include the finite element analysis, error estimation/indication, mesh refinement and fracture/failure analysis in a loop. Some simple error estimators, based on stress projection, are used to investigate the adaptive finite element process. Element refinement is based on three schemes; the first and second are a simple and hierarchical refinement scheme with transitioning which avoids the need for constraint equations between element boundaries. Another scheme based on constraint equations between elements is also examined. The energy norm is used to estimate the element error. The software has the ability to introduce a discrete fracture in the structure according to standard fracture analysis practice. Crack tip parameters are calculated using a least-squares fit of the displacements into the asymptotic crack tip displacement field. Some simple examples are used to investigate the adaptive process, its behavior and some of the practical problems encountered. The convergence and equilibrium of the adaptive process, in terms of global error in the energy norm, are investigated. In the example the same problem is analyzed using both a fine computational grid and a coarse one. The coarse mesh is then adapted using the three different procedures available. The estimated error in the solution and the stress intensity are shown against the number of elements and number of iterations. Some further areas of research in adaptive finite element analysis are discussed.     

Fractional finite Fourier transform

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.     

Resonance ejection from the paul trap: a theoretical treatment incorporating a weak octapole field

In response to the growing experimental evidence of the importance of nonlinear phenomena in ion trap operation, a new theoretical model of ion ejection is developed. The pseudopotential well approximation for forced ion oscillations in an ion trap under the conditions of ion-molecule collisions is modified to include octapole perturbations on the quadrupole field. Ion ejection is investigated using the first-order Mitropol'skii asymptotic method for both infinitesimal and finite scan rates. It is shown that the combined action of collisional damping and nonlinearity distorts the resonance curve in such a way that "quenching" of oscillations takes place. As a result, with appropriate excitation and direction of scanning, the amplitude increases as if no damping exists! The main characteristics of the jump are derived as functions of scan rate and used for analytical estimation of mass resolution, mass peak width, and excitation voltage. Satisfactory agreement between calculated and experimental peak widths is demonstrated for the range of scanning rates in excess of 6 orders of magnitude.     

Goal‐oriented adaptive refinement for phase field modeling with finite elements

Phase field modeling is very often performed with the finite‐difference method for equally spaced grids. Typically its solutions are highly non‐homogenous; and, therefore, non‐equally spaced grids with dense meshes at interfaces between different phases and coarse meshes in homogenous regions would be more advantageous with respect to both, efficiency and reliability of the numerical solutions. To this end, in the present work, an adaptive strategy with finite elements for phase field modeling is adopted, where the time step and the grid size are selected on the basis of goal‐oriented error estimation. In order to account for nonlinearity of the variational equations, we introduce a secant form for the dual problem, which for practical purposes is approximated by a tangent form. In a numerical example, we investigate transformation and retransformation for a two‐phase system in a square region subjected to thermal loading. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental evaluation of velocity and power estimation forultrasound blood flow imaging, by means of a two-dimensionalautocorrelation approach

This paper evaluates experimentally the performance of a novel axial velocity estimator, the 2D autocorrelator, and its Doppler power estimation counterpart, the 2D zero-lag autocorrelator, in the context of ultrasound color flow mapping. The evaluation also encompasses the well-established 1D autocorrelation technique for velocity estimation and its corresponding power estimator (1D zero-lag autocorrelator), to allow performance comparisons under identical conditions. Clutter-suppressed in vitro data sets from a steady-flow system are used to document the effect of the range gate and ensemble length, noise level and angle of insonation on the precision of the velocity estimates. The same data sets are used to examine issues related to the estimation of the Doppler signal's power. The first-order statistics of power estimates from regions corresponding to flow and noise are determined experimentally and the ability of power-based thresholding to separate flow signals from noise is characterized by means of ROC analysis. In summary, the results of the in vitro evaluation show that the proposed 2D-autocorrelation form of processing is consistently better than the corresponding 1D-autocorrelation techniques, in terms of both velocity and power estimation. Therefore, given their relatively modest implementation requirements, the 2D-autocorrelation algorithms for velocity and power estimation appear to represent a superior, yet realistic, alternative to conventional Doppler processing for color flow mapping     

一种估计船舶线谱的联合分析法

线谱是船舶辐射噪声中重要的特征信息，线谱提取是水中目标识别的关键技术。文章简述了船舶辐射噪声的物理成因和频谱特征，利用经典谱估计法与现代谱估计法在短时序列谱估计中的特点，结合Matlab仿真试验的结果，提出了一种对船舶辐射噪声0．100Hz低频段线谱估计的联合分析法。并用该方法对两艘实船噪声进行了谱分析，提取了A型船在中速航行时5．25Hz的特征线谱，B型船存在65．5Hz和69．2Hz两条特征线谱。实验结果表明该方法对低频段的线谱特征提取有明显的实用效果。     

An adaptive MsFEM for nonperiodic viscoelastic composites

We present a modification of the multiscale finite element method (MsFEM) for modeling of heterogeneous viscoelastic materials and an enhancement of this method by the adaptive generation of both meshes, ie, a macroscale coarse one and a microscale fine one. The fine mesh refinements are performed independently within coarse elements adjusting the microscale discretization to the microstructure, whereas the coarse mesh adaptation optimizes the macroscale approximation. Besides the coupling of the hp‐adaptive finite element method with the MsFEM we propose a modification of the MsFEM to accommodate for the analysis of transient nonlinear problems. We illustrate the efficiency and accuracy of the new approach for a number of benchmark examples, including the modeling of functionally graded material, and demonstrate the potential of our improvement for upscaling nonperiodic and nonlinear composites.     

Comparison of magnetic Barkhausen noise and ultrasonic velocity measurements for microstructure evaluation of SAE 1040 and SAE 4140 steels

The aim of this study is to compare the performance of magnetic Barkhausen noise and ultrasonic methods for the evaluation of the microstructure of commercial steels. Following the austenitization of the specimens made of SAE 1040 and SAE 4140, various heat treatments were carried out to obtain microstructures consisting of martensite, tempered martensite, fine pearlite–ferrite, and coarse pearlite–ferrite. The microstructures were initially characterized by SEM investigation and hardness measurements. The magnitude and position of Barkhausen noise peaks were determined via a commercial system. The propagation rates of longitudinal waves were determined with the ultrasonic pulse-echo technique. Barkhausen noise response and sound velocity goes to minimum for the as-quenched martensite, and both tend to increase in the following sequence: tempered martensite, fine pearlite–ferrite, and coarse pearlite–ferrite. However, the magnetic features are more sensitive to the microstructure variations than to the sound velocity.     

A Coarse Alignment Based on the Sliding Fixed-Interval Least Squares Denoising Method

The observation vectors in traditional coarse alignment contain random noise caused by the errors of inertial instruments, which will slow down the convergence rate. To solve the above problem, a real-time noise reduction method, sliding fixed-interval least squares (SFI-LS), is devised to depress the noise in the observation vectors. In this paper, the least square method, improved by a sliding fixed-interval approach, is applied for the real-time noise reduction. In order to achieve a better-performed coarse alignment, the proposed method is utilized to de-noise the random noise in observation vectors. First, the principles of proposed SFI-LS algorithm and coarse alignment are devised. A simulation test and turntable experiment were executed to demonstrate the availability of the designed method. It is indicated that, from the results of the simulation and turntable tests, the designed algorithm can effectively reduce the random noise in observation vectors. Therefore, the proposed method can enhance the performance of coarse alignment availably.     

噪声谱估计算法对语音可懂度的影响

噪声谱估计是单通道语音增强算法的关键步骤,当前大部分语音增强算法旨在提高语音质量,提高语音可懂度的算法却很少。在传统的单通道语音增强算法中,语音质量的提高往往是以牺牲语音的可懂度为代价的。对目前主流的几种噪声谱估计算法对语音可懂度影响进行分析。在不同噪声背景、不同信噪比情况下进行噪声谱估计,并采用谱减法对含噪语音信号作去噪处理,对比分析不同噪声、不同信噪比下增强前后语音的短时客观可懂度(Short-Time Objective Intelligibility,STOI)值,最后根据信噪比,对比分析了不同噪声环境下,语音增强前后语音能量高于噪声能量的时频块所占比例。实验表明,相比其他噪声估计算法,最小统计(Minima Statistics,MS)算法由于保留了更多的以语音能量为主的时频块,使得去噪后的语音有较高的可懂度。     

Wideband on-wafer noise measurement setup for noisecharacterization of active devices in the low VHF band

This paper addresses a new wideband on-wafer measurement test set designed for noise characterization of microwave active devices over the frequency range of 300 kHz to 150 MHz. Noise parameters obtained from the multiple impedance technique on a GaAlAs/GaAs heterojunction bipolar transistor (HBT) from 300 kHz to 70 MHz are reported and compared with low-frequency noise data. Investigation of the excess noise sources of III-V HBT's is performed well above the 100 kHz frequency limit of standard dynamic signal analyzers and noise modeling of these devices is reported     

基于遗传算法和有限混合分布的应力谱多模态建模

该文提出了一种基于遗传算法(genetic algorithm, GA)的有限混合分布参数估计方法, 应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先, 采用小波变换消除原始应变监测数据中的温度影响, 利用雨流计数法将应变时程曲线转化为日应力谱, 考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响, 建立标准日应力谱。然后, 采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模, 根据赤池信息准则(Akaike’s information criterion, AIC)确定最佳的有限混合模型。最后, 采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明, 该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。     

一种快速自适应噪声谱估计方法

提出了一种快速自适应的噪声谱估计方法。该方法在Doblinger和Cohen的噪声谱估计方法基础上,提出了改进算法,修正了带噪语音子带中语音存在的判断门限和噪声谱更新公式,估计的噪声谱既能快速适应背景噪声变化,又能保证准确性。实验结果表明,结合文中噪声谱估计方法构成的语音增强系统能有效抑制带噪语音中平稳和非平稳噪声,对于噪声突变的情况也适用。     

Reduction of Noise‐Induced Bias in Displacement Estimation by Linear Off‐Pixel Digital Image Correlation

Abstract: A linear digital image correlation algorithm is proposed to eliminate noise‐induced bias in one‐dimensional translation estimation using noisy images. The algorithm uses linear interpolation for both initial and current images at off‐pixel positions and solves directly the displacement parameter by minimizing a sum‐of‐squared‐differences coefficient. Both analytical results and numerical simulations using synthetic image sets show that there is indeed no noise‐induced bias in the displacement estimation using the proposed algorithm if the off‐pixel positions in both images are chosen properly according to the relative displacement between two images. When the displacement is only known initially within a range of ±0.5 pixels from the actual displacement, an iterative procedure using the algorithm is able to obtain the displacement estimation with a residual bias that converges to the noiseless subpixel approximation bias. A further refinement of the off‐pixel analysis algorithm will be needed so the remaining residual bias due to subpixel approximation can also be significantly reduced.