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Nonlinear conjugate gradient method for identifying Young's modulus of the elasticity imaging inverse problem 弹性成像反问题杨氏模量的非线性共轭梯度辨识方法
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-04-02 DOI: 10.1080/17415977.2021.1905638
Talaat Abdelhamid, Rongliang Chen, M. Alam
Application of elasticity imaging inverse problem to identify Young's modulus in the elasticity problems in human's life is an interesting research area. In this study, we identify the modulus of elasticity for solving elasticity imaging inverse problem using a modified output least-squares method. Numerical convergence in the displacements of the direct problem for elasticity is investigated. To study the elasticity imaging inverse problem in an optimization framework, we utilize the sensitivity and adjoint problems to conceptualize a new model for computing the gradient of the minimizer. Discrete formulae in the model are then used to devise a scheme for an efficient computation gradient of the modified output least-squares objective function using the nonlinear conjugate gradient method. Numerical experiments demonstrate the effectiveness of the proposed technique.
应用弹性成像逆问题来识别杨氏模量在人类生活中的弹性问题中是一个有趣的研究领域。在这项研究中,我们使用一种改进的输出最小二乘法来确定弹性成像逆问题的弹性模量。研究了弹性力学直接问题位移的数值收敛性。为了在优化框架下研究弹性成像逆问题,我们利用灵敏度和伴随问题来概念化一个计算极小值梯度的新模型。然后,使用模型中的离散公式,使用非线性共轭梯度方法,设计了一种有效计算修正输出最小二乘目标函数梯度的方案。数值实验证明了该方法的有效性。
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引用次数: 2
Estimation method for inverse problems with linear forward operator and its application to magnetization estimation from magnetic force microscopy images using deep learning 线性正演算子反问题估计方法及其在深度学习磁力显微镜图像磁化估计中的应用
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-29 DOI: 10.1080/17415977.2021.1905637
Hajime Kawakami, H. Kudo
ABSTRACT This study considers an inverse problem, where the corresponding forward problem is given by a finite-dimensional linear operator T. The inverse problem has the following form: It is assumed that the number of patterns that the unknown quantity can take is finite. Then, even if the unknown quantity may be uniquely determined from the data. This case is the subject of this study. We propose a method for solving this inverse problem using numerical calculations. A famous inverse problem requires the estimation of the unknown magnetization distribution or magnetic charge distribution in an anisotropic permanent magnet sample from the magnetic force microscopy images. It is known that the solution of this problem is not unique in general. In this work, we consider the case where a magnetic sample comprises cubic cells, and the unknown magnetic moment is oriented either upward or downward in each cell. This discretized problem is an example of the above-mentioned inverse problem: Numerical calculations were carried out to solve this model problem employing our method and deep learning. The experimental results show that the magnetization can be estimated roughly up to a certain depth.
摘要本研究考虑一个反问题,其中相应的正问题由有限维线性算子T给出。反问题具有以下形式:假设未知量可以采用的模式数量是有限的。然后,即使可以根据数据唯一地确定未知量。这个案例就是本研究的主题。我们提出了一种使用数值计算来解决这个反问题的方法。一个著名的反问题需要从磁力显微镜图像中估计各向异性永磁体样品中未知的磁化分布或磁电荷分布。众所周知,这个问题的解决方案在一般情况下并不是唯一的。在这项工作中,我们考虑了磁性样品包括立方单元的情况,并且未知磁矩在每个单元中向上或向下定向。这个离散化问题是上述逆问题的一个例子:使用我们的方法和深度学习进行了数值计算来解决这个模型问题。实验结果表明,磁化强度可以大致估计到一定的深度。
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引用次数: 0
Inverse singular value problem for nonsymmetric ahead arrow matrix 非对称前进箭头矩阵的奇异值逆问题
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-29 DOI: 10.1080/17415977.2021.1902515
F. Fathi, M. A. Fariborzi Araghi, S. A. Shahzadeh Fazeli
ABSTRACT Constructing a matrix by its spectral information including singular values is called inverse singular value problem (ISVP). In this paper, an ISVP for nonsymmetric ahead arrow matrix by two eigenpairs of the required matrix and one singular value of each leading principal submatrices is investigated. To solve the problem, the recurrence relation of characteristic polynomial of the block Jordan–Weilant matrix associated with the aim matrix is obtained. The conditions of solvability of the problem are derived. Finally a numerical algorithm and an example are given.
利用包含奇异值的谱信息构造矩阵称为逆奇异值问题。本文研究了由所需矩阵的两个本征对和每个前导主子矩阵的一个奇异值组成的非对称前矢矩阵的ISVP。为了解决这个问题,得到了块Jordan–Weilant矩阵的特征多项式与目标矩阵的递推关系。导出了该问题可解的条件。最后给出了一个数值算法和算例。
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引用次数: 1
A modified quasi-reversibility method for inverse source problem of Poisson equation 泊松方程逆源问题的一种修正拟可逆性方法
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-22 DOI: 10.1080/17415977.2021.1902516
Jin Wen, Li-Ming Huang, Zhuan-Xia Liu
ABSTRACT In this article, we consider an inverse source problem for Poisson equation in a strip domain. That is to determine source term in the Poisson equation from a noisy boundary data. This is an ill-posed problem in the sense of Hadamard, i.e., small changes in the data can cause arbitrarily large changes in the results. Before we give the main results about our proposed problem, we display some useful lemmas at first. Then we propose a modified quasi-reversibility regularization method to deal with the inverse source problem and obtain a convergence rate by using an a priori regularization parameter choice rule. Numerical examples are provided to show the effectiveness of the proposed method.
摘要在本文中,我们考虑了条域中Poisson方程的一个反源问题。也就是说,从有噪声的边界数据中确定泊松方程中的源项。在Hadamard的意义上,这是一个不适定的问题,即数据的微小变化可能导致结果的任意大的变化。在给出我们提出的问题的主要结果之前,我们首先展示了一些有用的引理。然后,我们提出了一种改进的拟可逆正则化方法来处理逆源问题,并通过使用先验正则化参数选择规则来获得收敛速度。通过算例验证了该方法的有效性。
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引用次数: 5
Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method 时空分数阶扩散方程的未知源识别问题:最优误差界分析和正则化方法
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-19 DOI: 10.1080/17415977.2021.1900841
Fan Yang, Qian-Chao Wang, Xiao-Xiao Li
In this paper, the problem of unknown source identification for the space-time fractional diffusion equation is studied. In this equation, the time fractional derivative used is a new fractional derivative, namely, Caputo-Fabrizio fractional derivative. We have illustrated that this problem is an ill-posed problem. Under the assumption of a priori bound, we obtain the optimal error bound analysis of the problem under the source condition. Moreover, we use a modified quasi-boundary regularization method and Landweber iterative regularization method to solve this ill-posed problem. Based on a priori and a posteriori regularization parameter selection rules, the corresponding convergence error estimates of the two regularization methods are obtained, respectively. Compared with the modified quasi-boundary regularization method, the convergence error estimate of Landweber iterative regularization method is order-optimal. Finally, the advantages, stability and effectiveness of the two regularization methods are illustrated by examples with different properties.
本文研究了时空分数阶扩散方程的未知源辨识问题。在这个方程中,使用的时间分数导数是一个新的分数导数,即Caputo-Fabrizio分数导数。我们已经说明,这个问题是一个不适定的问题。在先验界的假设下,我们得到了源条件下问题的最优误差界分析。此外,我们使用一种改进的准边界正则化方法和Landweber迭代正则化方法来解决这个不适定问题。基于先验和后验正则化参数选择规则,分别获得了两种正则化方法的收敛误差估计。与改进的拟边界正则化方法相比,Landweber迭代正则化方法的收敛误差估计是阶最优的。最后,通过不同性质的例子说明了这两种正则化方法的优点、稳定性和有效性。
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引用次数: 6
The generalized flexibility matrix method for structural damage detection with incomplete mode shape data 不完全振型数据下结构损伤检测的广义柔度矩阵法
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-15 DOI: 10.1080/17415977.2021.1900840
Haifeng Liu, Baisheng Wu, Zhengguang Li
Achieving complete data of measured mode shapes is costly during the process of structural dynamic test. This results in a challenge for the damage detection. This paper concentrates on structural damage detection problem with incomplete mode shape data. An efficient method to deal with this problem is proposed. The generalized flexibility matrix (GFM) is employed. By introducing a few new variables and partitioning the involved matrices, a nonnegative linear least square model is derived. Most of the variables in the model are the damage extents of structural elements. Our method does not involve mode shape expansion or reduction technique. Three numerical examples show that the performance of the proposed method is superior to that of the GFM method combining with mode shape expansion, it is almost the same as that of the GFM approach with complete mode shapes data.
在结构动力试验过程中,获得完整的模态振型数据是代价高昂的。这就给损伤检测带来了挑战。本文主要研究不完全模态振型数据下的结构损伤检测问题。提出了一种处理该问题的有效方法。采用广义柔度矩阵(GFM)。通过引入一些新的变量并对所涉及的矩阵进行分块,得到了一个非负线性最小二乘模型。模型中的大部分变量是结构构件的损伤程度。我们的方法不涉及模态振型展开或缩减技术。三个数值算例表明,该方法的性能优于结合模态振型展开的GFM方法,与具有完整模态振型数据的GFM方法的性能基本相同。
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引用次数: 5
Inverse source problem of heat conduction equation with time-dependent diffusivity on a spherical symmetric domain 球对称域上含时扩散率热传导方程的反源问题
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-13 DOI: 10.1080/17415977.2021.1899172
Xiaoxiao Geng, Hao Cheng, Mian Liu
In this paper, we consider the inverse source problem of heat conduction equation with time-dependent diffusivity on a spherical symmetric domain. This problem is ill-posed, i.e. the solution of the problem does not depend continuously on the measured data. To solve this problem, we propose an iterative regularization method and obtain the Hölder type error estimates. Numerical examples are presented to demonstrate the effectiveness of the proposed method.
本文研究了球对称域上具有随时间扩散率的热传导方程的逆源问题。这个问题是不适定的,即问题的解不连续地依赖于测量数据。为了解决这一问题,我们提出了一种迭代正则化方法,并获得了Hölder型误差估计。数值算例验证了该方法的有效性。
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引用次数: 10
Sequential estimation of creatinine removal by a haemodialyser 血液透析器去除肌酸酐的顺序估计
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-11 DOI: 10.1080/17415977.2021.1897123
Felipe Y. Magalhães, H. Orlande, J. Suassuna
This work is focused on the transient analysis of a haemodialyser. The objective is to sequentially estimate the concentration of creatinine in the blood returning to the patient, by solving a state estimation problem with measurements of the outflow creatinine concentration in the dialysate. Simulated measurements containing Gaussian errors were used in the inverse analysis, which was based on the Sampling Importance Resampling (SIR) algorithm of the Particle Filter method. Accurate results reveal that this technique may possibly be used for online monitoring and control of the haemodialysis therapy.
这项工作的重点是血液透析的瞬态分析。目的是通过测量透析液中流出肌酸酐浓度来解决状态估计问题,从而依次估计返回患者血液中的肌酸酐浓度。基于粒子滤波方法中的采样重要性重采样(SIR)算法,利用含有高斯误差的模拟测量值进行反分析。准确的结果表明,该技术可能用于血液透析治疗的在线监测和控制。
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引用次数: 0
Identification of the air gap thermal resistance in the model of binary alloy solidification including the macrosegregation and the material shrinkage phenomena 包含宏观偏析和材料收缩现象的二元合金凝固模型中气隙热阻的识别
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-05 DOI: 10.1080/17415977.2021.1897584
A. Zielonka, E. Hetmaniok, D. Słota
Goal of this elaboration is to investigate the mathematical model of the inverse problem of binary alloy solidification within the casting mould, with the material shrinkage and the macrosegregation phenomena included simultaneously. Major result of this paper is the solution of the inverse problem consisting in reconstruction of the following elements: the thermal resistance of the air gap created between the cast and the mould in the course of solidification process and the heat transfer coefficient on the boundary of heat exchange between the mould and environment. The additional information, necessary to solve the inverse task, is delivered by the temperature measurements read in the control point located in the centre of the mould. The theoretical discussion is supported by the numerical examples executed for various sets of input data.
本文的目的是研究二元合金在铸模内凝固反问题的数学模型,同时包括材料收缩和宏观偏析现象。本文的主要结果是求解了由以下元素重构而成的反问题:凝固过程中铸件与模具之间产生的气隙热阻以及模具与环境之间热交换边界上的传热系数。解决反向任务所需的附加信息由位于模具中心的控制点中读取的温度测量值提供。对各种输入数据集执行的数值示例支持了理论讨论。
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引用次数: 0
Inverse design of 3D curved ducts using a 3D-upgraded ball-spine algorithm 使用三维升级的球脊算法进行三维弯曲管道的逆向设计
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-03-01 DOI: 10.1080/17415977.2021.1894143
A. Kariminia, M. Nili-Ahmadabadi, K. Kim
ABSTRACT Achieving a unique solution for the 3D inverse design of a curved duct is a challenging problem in aerodynamic design. The centre-line curvature, and cross-sections’ area and shape of a 3D curved duct influence the wall pressure distribution. All the previous developments on the ball-spine method were limited to 2D and quasi-3D ducts, in which only the upper and lower lines of the symmetry plane were modified based on the target pressure distribution. In the present work, the ball-spine method was three-dimensionally developed for the design of curved ducts while considering the effects of cross-sectional shape and area. To validate the method, all the nodes of a 3D duct wall were iteratively corrected under the modified ball-spine method to reach the target geometry. The effects of the ball movement directions (spines) and the grid generation scheme in achieving the unique solution in inverse design were evaluated. The results showed that the new method converges to a unique solution only if the streamline-based grids are applied for the flow numerical solution, and the horizontal spines are considered as the directions for the displacement of the nodes. Finally, the wall pressure distribution of a high-deflected 3D S-shaped diffuser was three-dimensionally modified to reduce the separation, secondary flow, and flow distortion.
摘要:在空气动力学设计中,为弯曲管道的三维逆向设计找到一个独特的解决方案是一个具有挑战性的问题。三维弯曲风管的中心线曲率、横截面面积和形状会影响壁面压力分布。球脊法之前的所有发展都局限于2D和准3D管道,其中只有对称平面的上下线根据目标压力分布进行了修改。在本工作中,在考虑横截面形状和面积影响的情况下,为弯曲管道的设计三维开发了球脊法。为了验证该方法,在改进的球脊方法下迭代校正三维风管壁的所有节点,以达到目标几何体。评估了球的运动方向(脊)和网格生成方案在反设计中实现唯一解的效果。结果表明,只有将基于流线的网格应用于流动数值解,并且将水平脊视为节点位移的方向,新方法才能收敛到唯一的解。最后,对高偏转三维S形扩压器的壁压分布进行了三维修正,以减少分离、二次流和流动畸变。
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引用次数: 1
期刊
Inverse Problems in Science and Engineering
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