Cardiac magnetic source imaging based on current multipole model

It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares (MNLS) method, the optimal weighted pseudoinverse method (OWPIM), and the optimal constrained linear inverse method (OCLIM) are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared.     

Fluid-Structure Interaction in Microchannel Using Lattice Boltzmann Method and Size-Dependent Beam Element

Fluid-structure interaction (FSI) problems in microchannels play prominent roles in many engineering applications. The present study is an effort towards the simulation of flow in microchannel considering FSI. Top boundary of the microchannel is assumed to be rigid and the bottom boundary, which is modeled as a Bernoulli-Euler beam, is simulated by size-dependent beam elements for finite element method (FEM) based on a modified couple stress theory. The lattice Boltzmann method (LBM) using D2Q13 LB model is coupled to the FEM in order to solve fluid part of FSI problem. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.     

基于平面问题的位移压力混合配点法

引入压力变量,将弹性力学控制方程表达为位移和压力的耦合偏微分方程组,采用重心插值近似未知量,利用重心插值微分矩阵得到平面问题控制方程的矩阵形式离散表达式.采用重心插值离散位移和应力边界条件,采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,采用最小二乘法求解过约束方程组,得到平面问题位移数值解.数值算例验证了所提方法的有效性和计算精度.     

导热几何形状反演的变分原理及边界条件的确立

本文采用变域变分原理,建立了导热几何形状反演问题的变分原理,同时获得了该问题所需满足的边界条件和附加条件.该变分原理能将未知形状的几何变量及控制方程结合在一个变分泛函中,使得数学描述简洁、紧凑,且几何变量及控制方程的求解能耦合地进行.介绍了运用该变分原理并结合有限元方法进行数值计算的方法. 关键词： 几何形状反演 变分原理 有限元 导热     

求解跨音速粘性流反问题的有限体积法

1前言叶轮机械气动热力学研究的最终目的之一，是为工程师提供可用以设计高性能、高效率叶轮机械的思想与方法。而在过去叶轮机械气动热力学的研究大都集中求解正问题上，即在给定几何形状的叶片的条件下来求解流场上的气动参数。因此，为了设计出高性能的叶型，通常是凭设计者的经验，通过试验或正问题流场的分析计算，对一系列几何形状相差不大的叶型进行筛选。用这种方法是非常耗时并导致昂贵的设计费用，而且这样也并不总能得到预期的效果。所以，正问题计算虽然在预测性能和筛选试验方案等方面具有重要价值，但对于叶栅设计，应该具有…     

Image quality improvement in ultrasonic nondestructive testing by the maximum entropy method

We consider the possibility of solving the inverse scattering problem in the linear approximation (in the form of a convolution equation) by reducing it to a system of linear algebraic equations and minimizing the residual. Since the problem is an ill-posed one, the Tikhonov regularization proves useful. The possibility of using the entropy of the image estimate as a stabilizing functional is considered, which is the key idea of the maximum entropy method. The single-frequency and multifrequency versions of the method are realized. The advantage of the maximum entropy method over the conventional linear methods of solving the inverse scattering problem is shown. The superresolution and sidelobe suppression abilities of the maximum entropy method are demonstrated. The method is shown to be stable to measurement noise and multiplicative interference in the form of aperture decimation. Examples of the image reconstruction by the maximum entropy method from model and experimental data are presented.     

Simulation of fluid-structure interaction in a microchannel using the lattice Boltzmann method and size-dependent beam element on a graphics processing unit

Fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The bottom boundary of the microchannel is simulated by size-dependent beam elements for the finite element method （FEM） based on a modified cou- ple stress theory. The lattice Boltzmann method （LBM） using the D2Q13 LB model is coupled to the FEM in order to solve the fluid part of the FSI problem. Because of the fact that the LBM generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallel computing. The simulations are carried out on graphics processing units （GPUs） using computed unified device architecture （CUDA）. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.     

三维燃烧介质和壁面温度的非接触联合重建研究

温度分布在线实时测量对于燃烧过程优化和污染物控制具有重要意义, 针对以往非接触三维温度分布重建过程的耗时性问题和忽略壁面辐射的不足, 本文提出了一种新的离散重建模型, 用于三维吸收、 发射和散射性高温燃烧介质以及壁面温度的快速联合非接触测量. 该模型以四个CCD(Charge Coupled Device) 为测量传感器, 通过构建辐射逆问题求解方程, 从CCD输出的辐射投影图像重建温度分布. 介质中不同投影方向内的辐射传递过程通过离散传递法来描述, 介质的散射和壁面反射则通过离散坐标法来近似. 离散后计算局部辐射强度的病态方程通过最小二乘余量法来求解, 论文对其计算速度进行了优化. 通过非对称温度分布测量算例分析了该模型的有效性, 讨论了测量噪音、 介质和壁面辐射特性对重建精度的影响, 并与其他方法对比分析了模型的重建速度. 计算结果表明本文提出的离散模型可以有效地用于大型高温燃烧介质和壁面温度分布的联合非接触测量. 即使在有噪声的情况下, 该模型也能获得准确的测量结果, 与其他计算方法相比, 采用改进的最小二乘余量法, 能有效地提高温度分布的重建计算速度.     

管道内壁侵蚀形状识别的无网格法研究

本文使用直接配点无网格法结合共轭梯度法对管道内壁面侵蚀状况进行了反演识别。直接配点无网格法使用节点离散求解区域,采用移动最小二乘近似构造试函数,直接配点法构造线性方程组进行导热正问题求解;反演过程采用共轭梯度法使目标函数最小化,Akima三次样条插值将连续的几何边界反演问题转化为离散点几何位置的反演,并最终将这些离散点拟合成为光滑曲线。文中选择两个典型算例对数值方法进行验证,模拟结果表明使用直接配点无网格法结合共轭梯度法进行管道内壁几何边界识别具有较高精度。     

Forward and inverse problem for cardiac magnetic field and electric potential using two boundary element methods

This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials.A torso-heart model established by boundary element method(BEM) is used for studying the distributions of cardiac magnetic fields and electric potentials.Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions,their properties and influences are compared.Then based on constructed torso-heart model and supposed current source functional model-current dipole array,the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time.Through figure and reconstructing parameter comparison,though the magnetic current dipole array imaging possesses better reconstructing effect,however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.     

一维梯度折射率介质光学特性的反演

在单个方波脉冲入射情况下,利用共轭梯度法对一维梯度折射率介质的折射率、吸收系数以及散射系数进行了反演.正问题采用间断有限元法求解,反问题的解则在正问题的基础上通过共轭梯度法得到.研究结果表明,利用单个方波脉冲入射情况下的时域半球反射率以及时域半球透射率作为测试值能够有效地反演一维梯度折射率介质的光学特性及其分布情况.     

Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite-difference Newton method

An inverse radiation problem was considered to estimate boundary conditions such as temperature distribution and emissivity in axisymmetric absorbing, emitting, and scattering medium, given the measured incident radiative heat fluxes. The finite-volume method was employed to solve a direct radiative transfer equation for a two-dimensional axisymmetric geometry. Various parameter estimators, such as conjugate-gradient method, hybrid genetic algorithm, and finite-difference Newton method, were employed to solve the inverse problems, while discussing their performances in terms of estimation accuracy and computational efficiency. Based on this, we proposed, as a best inverse analysis tool, a new combined method that adopted the hybrid genetic algorithm as an initial value selector and used the finite-difference Newton method as a parameter estimator.     

基于支持向量机的电磁逆散射方法

为解决电磁逆散射问题,提出了一种实时逆散射方法,该方法利用支持向量机(SVM)将逆散射问题转化为一个回归估计问题. 基于SVM的电磁逆散射方法成功地解决了逆散射问题中的非线性和不适定性.利用穿墙问题测试了该方法的可行性和有效性, 测试结果表明,不论是无噪声还是有噪声的情况,该方法都能很好地对墙后目标进行探测与定位.此外, 在穿墙环境下用SVM预测模型讨论了接收天线的采样位置数对预测结果的影响.最后对多源设置下的预测误差进行了分析和研究, 研究表明,相比于单源情况多源设置有利于对墙后目标的识别.     

Vibrations of an elastic strip with a rough boundary

A plane problem of steady-state forced vibrations of an elastic strip whose lower boundary contains a rough segment is considered. Using Green’s functions for a strip, the problem is reduced to a system of integral equations with integrals over the rough boundary, which is solved by the boundary-element method. The inverse problem of determining the shape of the rough boundary segment from the data on the displacement field of a certain part of the upper boundary is formulated. By the linearization procedure, the inverse problem is reduced to a Fredholm integral equation of the first kind with a smooth kernel, which is solved by Tikhonov’s regularization method.     

Determination of the crack configuration in an anisotropic elastic medium

The problem of the identification of a single internal crack in an anisotropic elastic body is investigated. Using the dislocation theory approach, a system of boundary integral equations for the crack opening functions is constructed and studied by the boundary element method. A crack identification method is developed on the basis of the crack parametrization by a finite number of parameters, with their subsequent determination through the minimization of a certain nonquadratic residual functional. The problem of identifying a transverse tunnel crack in an orthotropic layer is solved for the cases of plane and antiplane deformations.     

A new inverse approach for the equivalent gray radiative property of a non-gray medium using a modified zonal method and the complex-variable-differentiation method

Non-gray radiative properties of an absorbing, emitting, non-gray participating medium significantly increase the difficulty of solving the radiative transfer equation. This paper presents a new inverse approach for the equivalent gray radiative property of a non-gray medium. In this approach, the unknown equivalent gray radiative properties are treated as the optimization variables, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. The measured data are simulated by solving the direct problem, in which a modified zonal method together with the Edwards exponential wide-band model is employed. In the inverse problem, the sensitivity coefficients are first calculated by the complex-variable-differentiation method, and then the least-square method and the Newton-Raphson iterative method are employed to minimize the target function. The effectiveness and efficiency of the inverse problem are demonstrated in an example, and another case is given to show the accuracy and potential of the proposed algorithm. The effects of the measurement error and the number of measurement points on the accuracy of the inverse analysis are also investigated in detail.     

一种新的求解脑磁逆问题的搜索方法

给出一种新的求解真实头模型下脑磁逆问题的搜索方法.通过不同位置的源的相互关系，由上一个搜索源的计算结果通过简单计算，直接得到下一个搜索源的结果，避免了繁琐耗时的边界元积分方法，简化了求解过程，提高了求解速度. 关键词： 脑磁图 逆问题 搜索方法     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

Field reconstruction in an anisotropic elastic medium

For steady-state vibrations of an anisotropic elastic body of finite dimensions, a method of the determination of the vibration energy flows in the body is proposed. The method is based on the measurements of the surface values of the stress and displacement vectors at a part of the boundary. The proposed algorithm of the wave field reconstruction is reduced to solving nonclassical boundary integral equations of the first kind with smooth kernels. The formulation of these equations does not require the determination of fundamental solutions, but represents a conditionally well-posed problem. The numerical realization of the proposed method is based on the Tikhonov regularization method and the idea of the boundary element method. Numerical experiments consisting in the reconstruction of the displacements and stresses at the boundary of a rectangular and a circular domains of austenitic steel are performed in the framework of a planar problem of the orthothropic elasticity theory.     

A method to solve an acoustic inverse scattering problem involving smart obstacles

A time-harmonic acoustic inverse scattering problem involving smart obstacles is formulated and a method to solve it is proposed. A smart obstacle is an obstacle that, when hit by an incoming acoustic wave, tries to pursue a given goal circulating a suitable pressure current on its boundary. A pressure current is a quantity whose physical dimension is pressure divided by time. The goals pursued by the smart obstacles that we have considered are the following ones: to be undetectable or to appear with a shape and/or acoustic boundary impedance different from its actual ones eventually in a location in space different from the actual location. The following time-harmonic inverse scattering problem is considered: from the knowledge of several far fields generated by the smart obstacle when hit by known time-harmonic waves, the knowledge of the goal pursued by the smart obstacle and of its acoustic boundary impedance reconstruct the boundary of the obstacle. A method to solve this inverse problem that generalizes the so-called Herglotz function method is proposed. Some numerical experiments that validate the method proposed are presented. The website http://www.econ.univpm.it/recchioni/w13 contains some auxiliary material that helps the understanding of the current paper.