基于等参元的三维电阻抗成像的数值模拟和分析

对于电阻抗成像的数学模型,本文用等参元方法将对应的椭圆型方程离散化,把成像问题转化为非线性优化问题,给出了目标函数梯度及近似Hesee阵的计算公式；提出了伪单元刚度矩阵的概念,给出了利用其在迭代过程中的不变性来提高计算效率的方法：分别用BFGS校正拟Newton算法和Goldfeld修正Gauss-Newton算法对三维成像问题进行了一系列数值模拟实验,证实了算法的有效性,指出了其中存在的问题。     

Finite element analysis of transient free convection flow over vertical plate

A finite element method is used to study the heat-transfer response of an incompressible, laminar, transient free convection flow over a semi-infinite vertical plate. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved using the Newton–Raphson iteration. The resulting first-order ordinary differential equations with respect to time are solved using the implicit Euler scheme. Numerical results for the details of the velocity and temperature contours and profiles as well as heat transfer rate in terms of Nusselt number which are shown on graphs have been presented.     

一种基于高斯-牛顿法的光电经纬仪交会测量算法

针对靶场光电测量中使用的双站交会方法需要切换交会公式、交会精度不高的问题,提出了一种在直角发射坐标系中,基于高斯-牛顿法的多站交会方法。通过仿真试验将其与传统双站交会方法进行比较,证明了这种多站交会方法具有良好的收敛性和较高的交会精度。     

Optimal maintenance scheduling of power producers considering unexpected unit failure

A novel unit maintenance scheduling (UMS) problem formulation for a generation producer is presented, to maximise its benefit while thoroughly considering the risk associated with unexpected unit failures. First, the unit failure is characterised by a more practical bathtub-shaped failure behaviour from the modified superposed power law process. Its parameters are estimated from the historical data by solving a nonlinear least-squares-fitting problem via Gauss-Newton iteration method. On the basis of the unit failure analysis, the new UMS formulation is solved by a combination of linear programming and genetic algorithms (GAs), and its impact on the producer-s benefit is analysed in detail, including expected profit of selling energy, expected renewal cost of damaged components and maintenance cost. Compared with the current models, the proposed UMS model takes into consideration the influences of market factors as well as unexpected unit failures to strike the right balance between profits and costs related with potential unit failures. Numerical examples on a four-unit producer are utilised to demonstrate the effectiveness of the proposed scheme.     

Combined effect of thermal dispersion and radiation on free convection in a fluid saturated, optically thick porous medium

The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton–Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.     

基于C#编程实现高斯牛顿法求解激光跟踪干涉仪基站空间坐标

为了实现利用C#语言编程求解激光跟踪干涉仪基站空间坐标,对基站空间坐标的标定原理进行了研究,指出本质上基站空间坐标求解问题可转化为非线性最小二乘问题,为此分析了高斯牛顿法求解原理。进一步采用C#与MATLAB混合编程、仅依靠C#语言编程两种方式实现高斯牛顿法求解。对两种编程的关键技术进行了介绍,指出了混合编程存在的不足之处。通过坐标测量机及激光跟踪干涉仪组成实验系统,在3个不同的基站站位下开展了标定实验,实验结果表明C#编程计算结果与C#调用MATLAB的计算结果相比,差值在10^-7数量级,并且效率更高,验证了C#实现高斯牛顿法求解激光跟踪干涉仪基站空间坐标的准确性,为后续激光跟踪干涉仪数据采集及处理软件的开发打下了基础。     

一种改进的DDTFA方法及其在齿轮箱故障诊断中的应用

针对数据驱动时频分析(DDTFA)方法的初始相位函数选取问题,提出一种可准确、快速且自适应优选初始相位函数的改进DDTFA方法。引入数学中函数求极值的思想,将信号的初始相位函数选取问题转换为初始解集的连续寻优问题,通过对DDTFA中的高斯牛顿迭代算法进行精简,以初始解集中的初始相位函数迭代一次斜率的变化量为导数获得初始解集的连续导数集,进而求得局部极大值,并以局部极大值对应信号分量的能量最强为准则优选信号的初始相位函数,进而完成信号分解。仿真分析与齿轮箱故障诊断实例表明,该方法可准确、快速且自适应地优选初始相位函数,并有效提取故障特征,且具有一定抗噪性。     

A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media

Classical plasticity and damage models for porous quasi-brittle media usually suffer from mathematical defects such as non-convergence and non-uniqueness. Yield or damage functions for porous quasi-brittle media often have yield functions with contours so distorted that following those contours to the yield surface in a return algorithm can take the solution to a false elastic domain. A steepest-descent return algorithm must include iterative corrections; otherwise, the solution is non-unique because contours of any yield function are non-unique. A multi-stage algorithm has been developed to address both spurious convergence and non-uniqueness, as well as to improve efficiency. The region of pathological isosurfaces is masked by first returning the stress state to the Drucker–Prager surface circumscribing the actual yield surface. From there, steepest-descent is used to locate a point on the yield surface. This first-stage solution, which is extremely efficient because it is applied in a 2D subspace, is generally not the correct solution, but it is used to estimate the correct return direction. The first-stage solution is projected onto the estimated correct return direction in 6D stress space. Third invariant dependence and anisotropy are accommodated in this second-stage correction. The projection operation introduces errors associated with yield surface curvature, so the two-stage iteration is applied repeatedly to converge. Regions of extremely high curvature are detected and handled separately using an approximation to vertex theory. The multi-stage return is applied holding internal variables constant to produce a non-hardening solution. To account for hardening from pore collapse (or softening from damage), geometrical arguments are used to clearly illustrate the appropriate scaling of the non-hardening solution needed to obtain the hardening (or softening) solution.     

Application of the Method of Singular Integral Equations to the Determination of the Contours of Equistrong Holes in Plates

We propose a procedure for the determination of the contours of equistrong holes in elastic plates based on the method of singular integral equations. The problem is reduced to the solution of inverse two-dimensional problems of the theory of elasticity with unknown boundaries. The singular integral equations of the direct problems are solved numerically by the method of mechanical quadratures. For plates with one, two, or a system of periodic holes loaded by biaxial tension at infinity and internal pressure on the contours of holes, we determine the parameters of the contours of equistrong holes. Some numerical results are compared with the available data obtained by using different methods. Good accuracy of numerical results is attained even for small numbers of the parameters of shape of the holes and nodal points on their contours, which confirms the efficiency of the proposed procedure.     

Robust Parameter Estimation in Dynamic Systems

In this paper we present a practical method for robust parameter estimation in dynamic systems. In our study we follow the very successful approach for solving optimization problems in dynamic systems, namely the boundary value problem (BVP) approach. The suggested method combines multiple shooting for parameterizing dynamics, a flexible realization of the BVP principle, with a fast Gauss-Newton algorithm for solving the resulting constrained l ₁ problem. We give an overview of the theoretical background as well as the details of a numerical implementation. We discuss why the Gauss-Newton algorithm, which is known to perform well mainly on well-conditioned problems, is appropriate for parameter estimation problems, while quasi-Newton methods have only limited use for parameter estimation. The method is implemented on the basis of the direct multiple shooting method as implemented in PARFIT, thus inheriting all basic properties of PARFIT such as numerical stability, reliability and efficiency. The new code has been successfully applied to real-life parameter estimation problems in enzyme and chemical kinetics.     

The accelerated power method

An algorithm is presented to accelerate the convergence of the inverse iteration method for the solution of algebraic symmetric eigensystems. The algorithm is based on the use of the Ritz analysis during inverse iteration to generate improved trial vectors at virtually no extra cost. Examples are shown to illustrate the computational advantages of the method. The results are compared with those obtained using the subspace iteration method, the determinant search method and the accelerated subspace iteration method.     

Non-interferometric methods of phase estimation for application in optical tomography

Abstract

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.     

静力荷载作用下结构参数识别及状态评估的统计分析

基于静态结构识别方法,提出了服役结构损伤探测及状态评估的概率分析方法。首先通过有限元法把结构离散成用基本参数及核心矩阵表示的分析模型,根据两种分析模型和实际结构间的误差定义,用 Gauss-Newton法推导了在不完全测量情况下两种参数识别方法。在设计的测量情况下,进一步采用 Monte Carlo 法模拟测量数据,详细分析和比较这两种算法在有测量误差时的有效性和稳定性问题。第一种算法中的敏感矩阵不受测量误差的影响而具有比较好的性能,在确定了其识别结果的概率特性后,引入假设试验,探测和评估损伤的位置及程度。数字模拟显示了这一方法的有效性和准确性。     

Gamma自适应滤波器及其最小均方误差训练方法

本文提出了一种新的自适应滤波器－Ｇａｍｍａ滤波器及其基于最小均方程误差准则的训练方法，首先建立了最小均方误差准则下Ｇａｍｍａ滤波器的Ｗｉｅｎｅｒ－Ｈｏｐｆ方程，然后分别提出了３种训练算法：（１）新斯－牛顿算法；（２）确定性梯度算法；（３）ＬＭＳ算法。最后给出Ｇａｍｍａ滤波器在随机信号预测中的应用和仿真结果。     

陀螺系统辛子空间迭代法

转子系统的有限元分析可以导出陀螺系统的本征值问题．而陀螺本征值问题可在哈密顿体系下求解。基于辛子空间迭代法的思想，提出了一种求解陀螺系统本征值问题的算法。首先引入对偶变量，将陀螺动力系统导入哈密顿体系，将问题化为了哈密顿矩阵的本征值问题。由于稳定的陀螺系统其本征值必为纯虚数，利用这个特点。提出了对应陀螺系统的辛子空问迭代法，从而可以求出系统任意阶的本征值及其振型。算例证明了这种算法的有效性。     

Computer algorithms for calculating efficient initial vectors for subspace iteration method

In this paper, the effects of selecting initial vectors on computation efficiency for a subspace iteration method are investigated. Four algorithms are used for selecting the initial vectors. First, arbitrary starting iteration vectors are chosen according to Bathe and Wilson's algorithm.¹ In the other algorithms, the initial vectors are the retrieved eigenvectors from the Guyan and quadratic reduction methods. Improvement of the eigenvalue approximations of the subspace iteration method over reduction methods is presented. The computation effort is examined for the various algorithms used for initial iteration vectors.     

Computing equifrequency contours of two-dimensional photonic crystals by Dirichlet-to-Neumann maps

Equifrequency contours provide important information for designing special photonic crystal devices. In this paper, we present an efficient method to compute equifrequency contours for two-dimensional photonic crystals with triangular and honeycomb lattices. Our method is based on the Dirichlet-to-Neumann (DtN) operator of a unit cell in the photonic crystal. The DtN operator maps the wave field on the boundary of the unit cell to its normal derivatives. For photonic crystals with a triangular or honeycomb lattice, a small linear eigenvalue problem is formulated to calculate the dispersion relation. The formulation is based on the DtN map of the unit cell for a given angular frequency, and the eigenvalue is related to the wave vector. Our method is especially suitable for calculating the equifrequency contours, if a relatively small number of frequencies are involved.     

陀螺特征值问题的广义SRR子空间迭代法及其加速法

本文基于非Ｈｅｒｍｉｔｉａｎ矩阵的Ｓｃｈｕｒ－Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ加速的子空间迭代法，构造了状态空间表示的陀螺特征值问题广义ＳＲＲ子空间迭代法，这是与由质量阵和刚度阵构成的广义特征值问题的子空间迭代法平行的一种算法，在迭代中充分利用陀螺特征值问题的反对特征性，使得投影及ＳＲＲ特征值问题求解方法的本质是反对称Ｓｃｈｕｒ型的平方乃是对称Ｓｃｈｕｒ型。这一发现揭示了对称与反对称特征值问题之间的内在     

A new filter-bank configuration for harmonic measurement

In this paper a new adaptive filter-bank structure suitable for the accurate harmonic measurement in power supply systems is presented. This adaptive measurement technique is based on the resonator-in-a-loop filter-bank structure and includes a new modified Gauss-Newton gradient algorithm. Using this filter-bank structure and a least-squared-error approximation method, simulation results are presented to establish the performance of the technique. The effects of time-varying fundamental frequency are also investigated using this filter-bank structure. Simulation results show that the fundamental frequency can be tracked with very small error. The technique is also successfully applied to a measured voltage signal sampled from the mains to demonstrate performance     

双曲传热反问题研究

该文建立了双曲妈传热正/反问题求解模型,应用高斯-牛顿方法,对辐射边界进行了识别.空间上采用等参元进行离散,时域上采用时域精细算法进行离散,利用测量信息和计算信息构造最小二乘函数,将多宗量反演识别问题转化为一个优化问题,所建模型可对导热系数和辐射边界等宗量进行有效的单一和组合识别.给出了相关的数值验证,对信息测量误差作...