Comparison of techniques for solving the Laser Intensity Modulation Method (LIMM) equation

The Laser Intensity Modulation Method (LIMM) is a technique for the determination of polarization and/or space charge profiles in the thickness direction of ceramic and polymeric samples. The experimental data are analyzed by means of a Fredholm integral equation of the first kind. This equation admits to multiple and very different solutions. A number of techniques have been developed in order to obtain the most physically reasonable profile. Several techniques based on the regularization method have been proposed. A recent version, polynomial regularization, was developed by Lang. A completely different approach is the Monte Carlo method of Tuncer and Lang. Several sets of both simulated and experimental data are analyzed by the two methods in this paper. Conclusions concerning speed and accuracy are presented.     

An analysis of the integral equation of the surface laser intensitymodulation method using the constrained regularization method

The SLIMM (surface laser intensity modulation method) is used for the determination of polarization distributions near the surfaces of ferroelectric samples. The experimental data measured are pyroelectric currents as functions of frequency. The data analysis requires the solution of a Fredholm integral equation of the 1st kind. This is an ill-posed problem which has multiple and very different solutions. The constrained regularization method can be used to solve this problem. However, the choice of the proper regularization parameter is normally somewhat arbitrary and this can affect the solution drastically. In the technique used here, an optimal regularization parameter is found using a set of simulated data. These data are based on a polarization distribution constructed from a simple frequency-to-space transformation. It is shown that the conventional minimization of the deviations between experimental data and the predicted values according to the principles of least-squares gives meaningless results in an ill-posed problem of this type. Experimental data on lanthanum-doped lead-zirconate-titanate ceramics and LiNbO₃ are analyzed     

热脉冲法数据处理的反问题求解研究

应用热脉冲法测量聚合物薄膜电介质内空间电荷分布的数据分析过程涉及第一类Fredholm积分方程,过往先求解电场分布后微分的传统做法,会使反问题求解的不适定性带来的误差进一步放大。该文提出一种用于热脉冲法数据分析中反问题求解的直接计算空间电荷分布方法。结合一维热传导方程,推导得到了能够直接求解获取空间电荷分布的热响应电流方程。以Tikhonov正则化与尺度变换法2种数值求解算法为例,研究了不同信噪比对热脉冲法测量方法中直接计算电荷分布结果的影响,并讨论了2种数值算法直接进行空间电荷分布计算的优缺点。仿真结果表明,应用2种数值方法对含有一定噪声的数据处理时,直接计算空间电荷分布的方式相较于传统对电场分布微分的方式而言,能够很好地克服第一类Fredholm积分方程的不适定性,使解分布曲线中的振荡减少,且对仿真电流信号的噪声敏感程度更低,能更好地契合预设分布曲线,提高了空间电荷计算结果的准确性。     

Laser intensity modulation method (LIMM): review of the fundamentals and a new method for data analysis

The laser intensity modulation method (LIMM) is widely used for the determination of the spatial distribution of polarization in ceramics, single crystals and polymers. A brief history of the origin and development of LIMM during the past 20 years is presented. The experimental technique and the derivation of the LIMM equation are described. The data analysis requires the numerical solution of a Fredholm integral equation of the 1st kind. This is an illposed problem that has multiple and very different solutions. In this paper, a new technique is proposed that gives the polarization distribution in the form of a special 8th-degree polynomial. Both simulated and experimental data are analyzed with the new technique.     

Novel numerical methods for measuring distributions of space charge and electric field in solid dielectrics with deconvolution algorithm

The deconvolution algorithm for measuring the distribution of space charge under DC by the pressure wave propagation (PWP) method is studied in this paper. A new Fredholm integral equation of the first kind, including a space charge distribution without a partial differential operator is presented. Numerical methods based on Tikhonov regularization for solving this integral equation and the original PWP equation are studied. Numerical simulation is studied for the effect of signal-to-noise ratio (SNR), and comparison with other algorithms is discussed. The numerical solution of an electric field distribution from measurements of a LDPE specimen is obtained successfully.     

基于双参数模型的ECT图像重构混合算法

为了提高电容层析成像重构图像的精度和速度,本文提出了一种基于双参数模型的电容层析成像图像重构混和算法。该算法利用Morozov偏差原理确定Tikhonov正则参数,能使正则参数的选取与初始数据的误差相匹配,同时基于Morozov偏差方程导出了一种双参数模型,并进一步与牛顿法相结合用于快速得到最优的正则参数。数值实验表明:与线形反投影算法(LBP)、Landweber迭代算法和L-曲线法相比,所提出的混合算法具有图像重构速度快、精度高的优点。     

BTV图像超分辨率重建改进算法

在双边滤波正则化算法的基础上,结合自然图像自身结构相似性,提出一种基于BTV的改进算法.通过在代价方程中引入表达图像非局部结构相似性的正则化项,对重建图像的解空间进一步加以限制和优化,最后通过最陡下降法求得代价方程最优解,从而完成重建.实验证明,与BTV算法相比,改进后的算法不仅能很好地抑制噪声,同时也更好地保留了图像...     

Determination of the polarization distribution inelectron-beam-poled PVDF using heat wave and pressure pulse techniques

In the present paper, heat wave (LIMM) and pressure pulse measurements are reported of the polarization and electric field distribution in nonuniformly electron-beam poled PVDF. In order to obtain the spatial distributions from the LIMM spectra, the regularization technique is applied to the deconvolution. In this connection nonlinear grid distributions are discussed. The polarization profiles obtained by the two methods are compared over the whole thickness range, and a satisfactory agreement is found     

Modelling of electrically thick cylindrical antennas

Hallen's integral equation has been used as the basis for the formulation of cylindrical antenna theories for many years. Being a Fredholm integral equation of the first kind, its solution is mathematically an ill-posed problem. The stability of the numerical methods based on this integral equation is dependent on the singularity and the non-smoothness of the kernel function. For electrically thick cylindrical antennas, the dominance of the singular part of the kernel (logarithmic) is weakened and the kernel function becomes relatively smooth. This observation implies possible deteriorations of the stability of the numerical methods based on Hallen's integral equation. This paper describes the development of an alternative formulation for the electrically thick cylindrical antennas based on the singular integral equation of the first kind with a Cauchy-type kernel which eliminates the potential instability problem. A numerical method based on this formulation of the antenna problem has been implemented and case studies show that it is very stable and efficient for the numerical modelling of electrically thick cylindrical antennas.     

基于改进极小范数解的电容层析成像图像重建算法

提出了一种新的电容层析成像图像重建算法。在分析极小范数解的基础上，针对电容层析成像(ECT)逆问题的特点，利用正则技巧对其进行改进，并利用奇异值分解定理分析了这种改进的数值稳定作用。在此基础上，利用加权技巧建立新的目标泛函进一步改进极小范数解，并在求解该泛函的过程中采用正则技巧确保数值解的稳定性。数值实验表明，该算法是有效的，能够有效地克服ECT图像重建的数值不稳定性；而且该算法计算直接、无需任何复杂的技巧；就该文所考察的重建对象而言，其图像重建质量好于线性反投影算法(LBP)、标准Tikhonov 正则法和投影Landweber迭代法。从而为ECT图像重建提供了一种新的有效方法。     

融合动态演变信息的声学三维温度场重建

在声学层析成像方法测量锅炉温度场的应用中,温度场重建算法的精度和速度起着重要作用。建立了三维温度场声学重建的动态模型,提出了同时考虑声学测量信息和温度场动态演变信息的动态重建算法。建立了一个融合声学测量信息、温度场的空间约束及动态演化信息的目标函数,在光滑约束法的基础上构建了反映相邻空间像素位置关系的正则矩阵,采用Tikhonov正则化和优化相结合的方法求解目标函数。仿真模拟研究表明,与最小二乘、代数重建法和标准Tikhonov正则化算法等静态重建算法相比,融合动态演变信息的温度场重建算法的重建速度相仿,而重建精度有显著提高并对于测量数据误差具有更好的数值稳定性,为声学温度场重建提供了一种可行性极高的有效方法。     

Stromverteilung in wechselstromdurchflossenen massiven Leitern,berechnet mit Hilfe von Integralgleichung

Übersicht In der vorliegenden Arbeit wird die Stromverteilung in einer ebenen Anordnung zweier rechteckiger Leiter mit Hilfe der Fredholmschen Integralgleichung analysiert. Durch Einführung der nicht leitenden hochpermeablen Abschirmung wird die Integralgleichung als eine Integralgleichung mit degeneriertem Kern beschrieben und als Lösung eines linearen Gleichungssystems dargestellt.

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Calculation of current distribution in massive leads with alternating current with the help of integral equation

Contents Current distribution in space-flat set of two rectangular leads is analysed by integral Fredholm equation in this paper. Introducing non-conducting ferromagnetic screen allowed transforming integral equation to integral equation with degenerated kernel. Final solution appeared thanks to this as solution of linear equations set.

     

基于全球定位系统与积分方程的互感线路零序参数带电测量

首先简要回顾了通常获取输电线路参数的三种方法,然后在增量法的基础上提出了基于全球定位系统(Global Position System,GPS)和积分方程的互感线路参数带电测量方法(简称积分法).该方法将互感线路的伏安特性方程转化为积分形式,并采用了最小二乘法求解测量中出现的超定方程组,同时得出各线路的零序自阻抗及线路间的零序互阻抗.文中给出了详细的数学模型和数字仿真结果以及软件算法流程图与实际测量结果,并将积分法计算结果与增量法的计算结果进行了比较,比较结果表明积分法的测量结果是精确可信的.     

周期孔洞具平动位移的无限弹性平面问题

具单个周期洞的无限弹性平面问题在文献 [1]中给出了提法 ,并借鉴文献 [2 ]处理非周期孔洞问题的方法 ,作了一个WepMaH变换 ,把周期带中有多个洞的具平动位移的边值问题转化成一个Fredholm方程 ,并证明方程解的存在唯一     

Numerical modelling of viscous flow in silicon thermal oxidation with the boundary element method

This paper describes the application of the boundary element method to solving two-dimensional steady slow viscous flow problems (creeping flow) in thermal silicon oxidation. The proposed method used the velocity–pressure formulation. The use of the incompressibility condition as a boundary condition and the application of the second Green's identity to transform the domain integral into a boundary integral result in a system of three boundary integral equations for velocity components and pressure. Solution of this system to be an ill-posed problem because of the presence of boundary conditions of the first kind. Two methods of regularization are employed. The numerical results for trench oxidation process are presented.     

Computation of Frequency Response of Integrated Pyroelectric Infrared Detectors

Pyroelectric detectors of infrared radiation are fast-response thermal sensors operating at ambient temperature unlike semiconductor detectors, which require cooling. Their spectral response is uniform in a large range of wavelengths, including main band of IR transmission of the earth's atmosphere. Triglycine Sulfate (TGS) based pyroelectric detectors are the most sensitive among available ferroelectric materials. The effective sensitivity and performance depend not only on the sensor element material characteristics but also on the thermal performance of the complete structure of a detector such as substrate material, absorbing layer, and isolation layers. Thus we have solved one-dimension thermal diffusion equation for an n-layered structure. From which the performance of any number of layers of a detector structure can be derived, predicted, and optimized. Using viable single element sensor configurations and pyroelectric parameters of deuterated triglycine sulfate (DTGS) crystals grown in our laboratory; the calculated and predicted current responsivity and other parameters are presented. A one dimensional heat conduction equation was solved analytically and the detector parameters were calculated using MatLab 6.0. The results obtained are encouraging for the development of DTGS based thin film-based detectors.     

格林函数法在电磁层析成像技术中的应用

EMT的逆问题求解很困难但也是必要的,采用格林函数法可以得到表示EMT多层媒质传感系统逆问题的积分式。合理忽略某些媒质层,可以得到简化了的逆问题的积分表达式,从而可构造图像重建算法,并得到了较好的重建结果。     

Polarization and electric field distribution in thermally poledPVDF and FEP

In the present paper, heat wave (LIMM) and pressure step (PPS) measurements of the spatial polarization and electric field distributions in nonuniformly thermally poled α-PVDF and Teflon FEP films are reported. The spatial distributions obtained by the two methods are compared over the entire thickness range, and a satisfactory agreement is found. For PVDF the results of both methods are in accordance with literature data for similarly poled specimens of similar material, the so-called `thermal profile', a polarization peak near the anode. Furthermore, in the LIMM experiments we found a small peak near the cathode, which can be explained by a positive compensation charge layer extending ≈2 μm in depth. For the first time, LIMM spectra of FEP are published. The space charge distribution in the FEP sample is nearly homogeneous inside the sample. Near the anode side an accumulation of negative charges appear. Near both surfaces a positive compensation charge was found with a thickness of ~1 μm. It is demonstrated that by means of our deconvolution the spatial distribution can be determined simultaneously with two thermal parameters, the diffusivity of the sample material and the heat transfer coefficient between sample and sample holder     

基于改进L1/2正则化的电阻抗层析成像

碳纤维复合材料的结构安全健康检测至关重要。电阻抗层析成像技术利用碳纤维复合材料的导电特性,可实现对其结构损伤检测。此技术具有成本低、非侵入和操作简便等优点,近年来成为广大学者的研究热点。在EIT的图像重构过程中存在着严重的病态性问题,本文提出了一种改进L1/2正则化算子的电阻抗层析成像算法。该方法采用L1/2范数构建稀疏正则化罚函数,通过布雷格曼交替方向乘子法的迭代算法对新目标函数进行求解,提高算法的性能。为验证算法有效性,使用COMSOL软件设计四种典型CFRP层合板损伤类型并搭建16电极EIT测试系统验证。仿真与实际实验结果表明,与其它算法相比,采用BADMM迭代算法求解L1/2正则化方法提高了图像相关系数,降低了图像误差,有效改善了重建图像的精度,且该方法对噪声具有较强的鲁棒性。     

基于积分方程的互感线路参数带电测量研究

首先简要回顾了通常得到输电线路参数的三种方法,然后在增量法的基础上提出了基于GPS和积分方程的互感线路参数带电测量的新方法——积分法。该方法是将互感线路的伏安特性方程转化为积分形式, 并采用了最小二乘法求解方程组,同时得出各线路的零序自阻抗及线路间的零序互阻抗。文中给出了详细的数学模型和数字仿真结果以及软件算法流程图,介绍了模拟实验过程,并将积分法与增量法的计算结果进行时比,结果表明积分法的测量结果是精确可信的。与增量法相比,该方法具有一定的滤波作用,一定程度上可以抑制高频分量,进行测量时一般不需额外提供测量用电源,方式更为省时省力。