广义H空间上的转化定理的应用及其逆问题

在１９９５年作者「西安交通大学学报２９（６）」给出了仿紧空间上从樊畿－Ｇｌｉｃｋｓｂｅｒｇ型不动点定理来直接推出广义ＫＫＭ定理的“转化定理”基础上，进一步研究该定量的应用问题，并讨论了该定理的逆问题。     

哈明距离下极大不一致支撑树的部分逆问题

给定一个简单无向赋权图和其中的一个森林,极大不一致支撑树的部分逆问题研究如何尽可能少地改变图中各边的权,使得在新的权值下存在一个极大不一致支撑树包含该森林.在赋权哈明距离下,得到了该问题的一些性质,并且给出了求解该问题的多项式时间算法.     

圈图上的两类组合优化问题

在圈图上研究了两类组合优化问题.第一类问题主要研究在要求图中各边的最大调整费用不能超过给定预算时,如何对各边权进行调整,使得其他各顶点到给定顶点的距离之和最大,得到了线性时间算法;第二类问题主要研究在要求圈图上的所有边的调整费用之和不超过给定预算时,如何对各边权进行调整,使得某一固定顶点到给定顶点的距离尽可能的大,得到了求解该问题的多项式时间算法.     

单磁偶极子源的逆问题解

通过检测到的心脏磁场强度数据对心脏建立源模型,求解模型参数有助于研究心脏电活动,对心脏疾病的临场诊断和医学研究具有极大的价值,提出一种心脏磁场等效单磁偶极子源求解的算法,通过对仿真结果的分析验证算法的正确性,实验表明,该方法可以较精确的求出等效单磁偶极子的位置和磁矩参数。     

Euler梁有限差分模型的振动逆问题

本文用变步长的二阶差分格式建立了Euler 梁的离散模型,并找出了与之等价的弹簧-质点-刚杆系统。在此基础上,研究了Euler 梁离散模型频谱的性质,讨论了由全频谱数据构造Euler 梁截面参数的问题,简化了已有的算法,并用这一算法计算了数值算例,对结果作了初步分析。     

非线性转子动力学半逆问题

讨论了转子动力学的主要逆问题——不平衡响应计算系统的最主要非线性环节（油膜轴承）的动态特性参数。由于具体工程应用所遇到的一些限制条件，在求解逆问题时，需要首先求解刚性简支转子的正问题，本文所处理的是一类半逆问题。     

压电材料变分原理逆问题的研究——动力学中的逆问题

研究了压电材料耦合动态场中Hamilton 型和Gurtin 型变分原理的逆问题。采用变积方法, 建立了各级变分原理和广义变分原理, 为建立横观各向同性压电材料的动力学有限元分析模型提供了依据。      

考虑摩擦的机械手逆动力学问题的研究

机械手关节通常包括径向转动关节﹑止推转动关节﹑径向止推转动关节和滑移关节这四种类型。本文针对机械手各类关节的结构特征,分别建立了与之相应的关节库仑摩擦和粘性摩擦的数学模型,并将这些模型应用于机械手逆动力学问题的研究中,给出了既考虑关节库仑摩擦又考虑粘性摩擦的机械手逆动力学问题的算法。最后,以STANFORD机械手为算例,分别计算了计入摩擦和不计入摩擦两种情形下的关节驱动力矩(或驱动力)的时间历程。计算结果表明两种情形下得到的关节驱动力矩(或驱动力)之间存在着明显的差异。     

拓展导热逆问题原理测算物体导热系数方法的最优化问题再探讨

对拓展导热逆问题原理测算物体导热系数方法的最优化问题进行了更广泛、深入的研究，提示了敏感度系数Ｘ＾＋ｋ、Ｘ＾＋ｈ的变化规律，得到了最优化判别式和判据。实验测算中，探讨并确定了实测环境与条件、参数优选及最优化测算程序。对于导热系数ｋ值数量级为１０＾－２－１０Ｗ／（ｍ．℃）的三种不同试材测量与计算结果表明，本方法所测算的ｋ值与传统方法所测值相比，相对误差在１．５９％－４．００％之内：而本方法简单、可靠     

Inverse problem of controlling the interface velocity in Stefan problems by conjugate gradient method

Abstract

The conjugate gradient method of minimization with adjoint equation is used successfully to solve the inverse problem in estimating an appropriate boundary control function such that the phase front moves at a desired velocity in the Stefan problem.

It is assumed that no prior information is available on the functional form of the unknown control function, therefore, it is classified as the function estimation in inverse calculation. The stability and accuracy of the inverse analysis using present algorithm are examined by comparing the results of the previous work by Voller [12].

Results show that the estimated control function by using conjugate gradient method did not exhibit oscillatory behavior in the inverse calculations for a broad range of front velocity while in [12] the inverse solutions are very sensitive to phase front velocity, therefore the application of future time stepping [2] is necessary in [12].

The advantage of applying this algorithm in inverse analysis lies in its stability as compared to the conventional minimization process [12]. Artificial future time stepping is unnecessary during the inverse calculation, since it is still an uncertainty in the inverse analysis. Furthermore, the inverse solutions obtained by the present method are found to be more accurate than the solutions obtained by the conventional minimization process.     

用遗传算法计算几个地球物理反问题

本文考察了用遗传算法计算多电极电阻率测井,二维大地电磁勘探和地下水含水层渗透系数三个地球物理反问题的方法和效果。只要适当选取遗传算子和相应的控制参数并将遗传算法和其他辅助手段适当结合,就可以得到满意的结果,克服其它优化方法遇到的一些困难。     

Inverse spectral problem for Dirac operator with discontinuous coefficient and polynomials in boundary condition

In this work, the inverse scattering problem for Dirac equations system with discontinuous coefficient and higher order polynomials of spectral parameter in the boundary condition is considered. The scattering function of the problem is defined, and its properties are investigated. The Marchenko-type main equation is obtained and it is shown that the potential is uniquely recovered by the scattering function. A generalization of Marchenko method is given for a class of Dirac operator.     

Inverse geometry heat transfer problem based on a radial basis functions geometry representation

We present a methodology for solving a non‐linear inverse geometry heat transfer problem where the observations are temperature measurements at points inside the object and the unknown is the geometry of the volume where the problem is defined. The representation of the geometry is based on radial basis functions (RBFs) and the non‐linear inverse problem is solved using the iteratively regularized Gauss–Newton method. In our work, we consider not only the problem with no geometry restrictions but also the bound‐constrained problem. The methodology is used for the industrial application of estimating the location of the 1150°C isotherm in a blast furnace hearth, based on measurements of the thermocouples located inside it. We validate the solution of the algorithm against simulated measurements with different levels of noise and study its behaviour on different regularization matrices. Finally, we analyse the error behaviour of the solution. Copyright © 2005 John Wiley & Sons, Ltd.     

非均匀圆膜轴对称振动的离散模型的振动反问题

本文研究圆膜的振动反问题。首先，采用二阶中心差分格式，导出了圆膜做轴对称振动的差分离散模型. 阐明了这一离散模型属于雅可比正系统，进而获得了该系统的振动定性性质. 在此基础上，本文提出了周边固定或周边弹性支承膜的离散系统的模态反问题以及周边固定和周边弹性支承膜的离散系统的频率反问题. 借助Jacobi矩阵反问题的已有成果，成功地求解了上述两个新的反问题. 最后给出了反问题的三个计算实例，验证了反问题的提法和解法的正确性.     

On the half inverse spectral problem for an integro-differential operator

We consider the Sturm–Liouville differential operator on a finite interval with Dirichlet boundary conditions perturbed with a convolution integral operator. The inverse problem is studied of recovering the convolution kernel from a half spectrum, provided that the kernel function on the first half of the interval as well as the Sturm–Liouville potential on the entire interval are known a priori. Besides the uniqueness of a solution of this half inverse problem, we also obtain necessary and sufficient conditions of its solvability. A constructive procedure for solving the inverse problem is also provided.     

Inverse diffraction problems for buried objects in the layered elastic media: the anti-plane problem

The authors study direct and inverse scattering problems for buried objects in the stratified layered elastic media. It is assumed that a source load is applied on the upper boundary surface, to generate a certain wave field inside the medium. Then we build the solutions to the direct problems through specially constructed Green’s functions for every considered case. Using the known measured amplitude of the upper boundary oscillations over a certain finite-length interval, the inverse problems in a one-mode frequency range are solved. Some numerical examples demonstrate the stability of the proposed algorithm for the formulated inverse problems.     

一类对称正交反对称矩阵反问题

设P是n阶对称正交矩阵,如果n阶矩阵A满足AT=-A和(PA)T=-PA,则称A为对称正交反对称矩阵。讨论了问题IPLS:给定n阶矩阵 A,n×m矩阵X和B,求n阶对称正交反对称矩阵A使得‖AX-B‖F=min和‖ A-A‖F=min。给出了该问题解的表达式及其数值方法,并将所得结果应用于研究对称正交反对称矩阵特征值反问题。     

杆结构探伤的逆特征值方法

本文基于逆特征值问题研究了均匀杆的结构探伤问题,包括确定损伤的位置和损伤程度。杆的几何参数建立的有限元模型能够由系统未发生结构损伤状态和发生结构损伤状态的各一个特征对重构。本文基于这种重构给出了杆结构探伤的逆特征值方法,进行了理论分析,并给出了数值算法。