带面积约束的光顺曲面造型算法

讨论了带有面积约束的光顺曲面造型方法，通过用Bezier曲面来拟合空间数据点，并且满足相应的面积约束，光顺标准及误差要求，通过泛函的极小化计算得到相关参数，并进行加权分析得到相关曲面，文后通过对花瓶的拟合，对算法进行了各种定量计算。     

C-Bézier曲线的光顺

在工业设计和反求工程中,曲线是形状设计和数据拟合的重要对象。曲线的光顺性对最终产品的外观质量有着直接影响。文章利用文献[1]构造出带有参数调配函数的模型,用其生成三次C-Bézier曲线。在能量法的基础上,研究了控制参数α对这种新曲线形态的影响,通过调整α和控制顶点使得曲线的能量最小,得到最优的光顺逼近曲线。通过最小二乘法和非线性泛函的极小值优化计算,对平面数据点进行光顺逼近,达到光顺的目的。该算法既可以对曲线进行全局光顺又可以进行局部光顺。最后给出了由数据拟合的C-Bézier曲线光顺的实例。     

基于插值与逼近的复杂曲面拟合

工程图纸和实物模型提供的曲面原始数据通常具有分布不均匀的特点，如果直接使用四边域或三边域曲面进行拟合，曲面的光顺性将无法保证。针对这种情况，笔者利用插值与逼近相结合的曲面拟合思路，构造了由初始曲面拟合、曲面逼近、及曲面细化等3个步骤组成的曲面造型方法。实践表明，这种方法能较好地解决原始数据点分布不均匀的曲面造型问题。     

非均匀背景下的红外图像曲面拟合分割

红外图像往往存在着背景不一致的特点,因此在分割时无法有效地提取出目标。本文针对这一问题提出了一种基于曲面拟合的图像分割方法,以分割非均匀背景下的红外目标。这种方法首先对背景进行光顺限制的曲面拟合,再通过设置一个偏移量来形成阈值曲面。通过研究发现,曲面拟合时的偏离项和光顺项的权重系数比是由图像背景的双拉普拉斯变换以及噪声均方差共同决定的,从而在估计噪声均方差的基础上实现了对权重系数的自适应选取。从仿真结果可以看出,本文提出的曲面拟合分割法在背景去除和目标提取上要优于传统的Ostu法和局部阈值法。     

快速求解点到自由曲面的距离的方法

在拟合曲面细分基础上,提出切平面法快速求解点到自由曲面距离。首先对点云数据中邻域不在同一直线的三个点进行局部二次曲面拟合,并求取该拟合曲面的切平面,同时求得细分曲面片任意一点处的切平面,最后在两个切平面上进行点对迭代运算,得到点到曲面片的最短距离。此法只需分割较少曲面片就能得到较高的计算精度,提高了计算速度。     

C1连续曲面重构与光顺的有限元算法

提出了一种基于离散的测量数据重建光顺自由曲面的有限元新方法。根据最佳逼近与能量光顺原理，建立正定的目标泛函，采用18自由度三角形板单元对泛函离散，进行极小化，求得最优解。根据有限元插值计算，重新构造出全场C^1连续的自由曲面。这种方法结合了能量光顺技术，有效地抑制了输入数据上误差噪声的影响，曲面重建的精度高、光顺性好，而且能给出合理的一阶导数。该方法计算简单、便于应用，所需的输入数据点少，并可用于处理曲线边界区域的问题。     

基于广义能量法的截面曲线光顺

对于气动流形曲面,除了满足对原始数据的逼近精度要求之外,通常还要求曲面具有较高的光顺性能。笔者在综合分析现有光顺方法不足的基础上,提出了同时考虑曲面几何及物理等多项光顺准则的基于广义能量法的曲面整体光顺思路,建立了包含曲面截线族粗光顺、曲面精光顺两个步骤的曲面光顺方法。这种方法对于提高曲面的整体光顺性能具有良好的效果。     

LCD Mura缺陷的B样条曲面拟合背景抑制

针对机器视觉检测TFT-LCD Mura缺陷时存在的图像整体亮度不均匀、背景复杂等影响检测准确性的问题,提出一种基于B样条曲面拟合的背景抑制方法。在最小二乘法准则的约束下,采用双三次B样条曲面拟合算法拟合出背景,并添加光顺项调整拟合精度,用原始图像减去拟合背景,从而消除亮度不均匀背景对缺陷分割造成的影响。为提高算法速度,对原始图像进行分块拟合,并将双三次B样条函数分解为一元函数求解,减小了计算量,同时避免了对原函数求解时容易出现的病态解问题。实验结果表明,该算法准确、高效。     

基于激光点云数据的叶片型面三维重构

在四坐标叶片型面检测基础上,提出基于激光点云数据的叶片型面三维重构方法。激光位移传感器对叶片型面进行多视角扫描采样,快速采集叶片型面海量点云数据。运用由点到线到面的数学建模原理,先基于端点一阶导矢连续法拟合出光顺NURBS曲线,再依据分片能量法构建辅助曲面拟合出光顺NURBS曲面,最后对分片NURBS曲面进行统一描述,构造出精确光滑的叶片型面,实现叶片型面的三维重构。实验结果表明：采用该方法实现对各类叶片复杂型面的三维重构,重构误差均<0.015 mm,能够满足精密零件的测量需求。     

基于图像的曲面光顺算法

针对目前曲面光顺算法存在的问题,提出了一种由平滑曲面在平行光照射下图像达到光顺的思想而形成的曲面光顺算法。该算法直接平滑曲面在平行光照射下的图像,然后通过光度立体技术反求出光顺后的曲面。由于能直接平滑曲面在平行光照射下的图像,使得光顺后的曲面在基于光照模型的曲面光顺准则下具有很的好光顺性质。应用实例显示,该算法能在保持原曲面形态的基础上达到很好的光顺效果。     

Reconstruction of time-dependent boundary heat flux by a BEM-based inverse algorithm

The objective of this study is to reconstruct an unknown time-dependent heat flux distribution at a surface whose temperature history is provided by a broad-band thermochromic liquid crystal (TLC) thermographic technique. The information given for this inverse problem is the surface temperature history. Although this is not an inverse problem, it is solved as such in order to filter the errors in input temperatures which are reflected in errors in heat fluxes. We minimize a quadratic functional which measures the sum of the squares of the deviation of estimated (computed) temperatures relative to measured temperatures provided by the TLC thermography. The objective function is minimized using the Levenberg–Marquardt method, and we develop an explicit scheme to compute the required sensitivity coefficients. The unknown flux is allowed to vary in space and time. Results are presented for a simulation in which a spatially varying and time-dependent flux is reconstructed over an airfoil.     

Inverse Problem of Evaluation of the Coefficient of Friction of Layers According to the Data of Measurements of the Surface Displacements

We consider a one-dimensional model of friction contact of two layers of different nature. The lower surface of the first layer is elastically fixed and the second layer is pressed to the upper surface of the first layer and moves along this surface with variable velocity. As a result of friction, heat is produced on the contact surface according to the Amonton's law. For known boundary and initial conditions, we pose the problem of evaluation of the friction coefficient and the intensity of friction heat flux according to given values of the vertical displacements of the upper surface of the second layer. The posed problem is reduced to the inverse contact problem of thermoelasticity described by the Volterra integral equation of the first kind. The solution of the problem obtained by the method of averaging of functional corrections enables us to study the time behavior of the indicated quantities for the entire period of interaction of the bodies and establish the dependence of the friction coefficient on the basic parameters of the process (sliding velocity, contact pressure, and temperature of the contact surface). The solution of the direct contact problem of thermoelasticity is used to perform the numerical verification of the proposed method for the solution of the inverse problem.     

A mixed non-linear boundary value problem appearing in gas dynamics: generalized solutions and numerical results

Considering the class of mixed non-linear elliptic-hyperbolic problems, the paper deals with the significant case given by the model of Karman and Guderley. An entropy condition is also taken into account. The problem is ill-posed. This unfavourable situation leads first to construct an approach of the problem then to state numerical and functional methods. Involving suitable arguments, we show that the gradient method works to obtain a numerical solution in accordance with results of previous authors. Furthermore it is proved by a functional method that the solution of the problem reduces to the finite dimensional case.     

Interface Edge Crack in a Bimaterial Elastic Half-Plane

The plane strain elastic half-plane problem of an edge crack lying along the interface of two perfectly bonded dissimilar quarter-planes is considered. Moreover, on the boundaries of the two quarter-planes concentrated forces are acting. For the correct formulation of the crack problem at hand, we consider the existence of a small slippage zone near the crack tip where closing stresses act. The mixed boundary value problem is subsequently reduced to a system of two functional equations of the Wiener–Hopf type which are effectively solved. The exact analytical solution of the problem is presented in series form. Numerical results, as well as asymptotic solutions for the most important physical quantities, are also presented. It is shown that there exist certain modes of surface loading of the homogeneous half-space, that result to the formation of two distinct zones at the crack tip region, one where the crack opening occurs and another adjacent to it, where frictionless contact of crack lips takes place. Also, it is demonstrated that in the case of high contrast of Young's moduli of the two quarter-planes, two opening-contact intervals appear consecutively along the crack. This revised version was published online in August 2006 with corrections to the Cover Date.     

Types of stationary points in a variational formulation of shallow-water flows

Summary Free-surface gravity flows are stationary points of a functional J when the problem is formulated variationally.Here we are concerned with the problem of determining the nature of the stationary point, that is, whether it is a minimum, a maximum, a saddle point or whether a singularity occurs. This is a problem of both theoretical and computational importance.Within a variational approximation of shallow-water type developed by the authors, we prove some new results on the problem. The analysis is carried out by studying the second variation of the functional J and the corresponding Jacobi's equation.Reference is also made to numerical experiments which confirm the findings. The experiments also suggest that such findings may well extend to flows outside the class of shallow-water flows governed by the model used in the analysis.     

A numerical method for determining a quasi solution of a backward time-fractional diffusion equation

In this study, we present existence and uniqueness theorems of a quasi solution to backward time-fractional diffusion equation. To do that, we consider a methodology, involving minimization of a least squares cost functional, to identify the unknown initial data. Firstly, we prove the continuous dependence on the initial data for the corresponding forward problem and then we obtain a stability estimate. Based on this, we give the existence theorem of a quasi solution in an appropriate class of admissible initial data. Secondly, it is shown that the cost functional is Fréchet-differentiable and its derivative can be formulated via the solution of an adjoint problem. These results help us to prove the convexity of cost functional and subsequently the uniqueness theorem of the quasi solution. In addition, in order to approximate the quasi solution, WEB-spline finite element method is used. Since the obtained system of linear equations is ill-posed, we apply the Levenberg-Marquardt regularization. Finally, a numerical example is given to show the validation of the introduced method.     

The Dagum and auxiliary covariance families: Towards reconciling two-parameter models that separate fractal dimension and the Hurst effect

The functional statistical framework is considered to address the problem of least-squares estimation of the realizations of fractal and long-range dependence Gaussian random signals, from the observation of the corresponding response surface. The statistical methodology applied is based on the functional regression model. The geometrical properties of the separable Hilbert spaces of functions, where the response surface and the signal of interest lie, are considered for removing the ill-posed nature of the estimation problem, due to the non-locality of the integro-pseudodifferential operators involved. Specifically, the local and asymptotic properties of the spectra of fractal and long-range dependence random fields in the Linnik-type, Dagum-type and auxiliary families are analyzed to derive a stable solution to the associated functional estimation problem. Their pseudodifferential representation and Reproducing Kernel Hilbert Space (RKHS) characterization are also derived for describing the geometrical properties of the spaces where the functional random variables involved in the corresponding regression problem can be found.     

利用氧化石墨烯复合膜吸附去除水中重金属离子的研究进展

氧化石墨烯作为一种独特的碳纳米材料,具有很高的比表面积,且其表面含有丰富的羟基、羧基等含氧基团,被认为是一种得天独厚的吸附材料,在净化水体方面有着广阔的发展前景。目前,为进一步提高氧化石墨烯对重金属离子的选择吸附性,氧化石墨烯被辅之以其他功能化材料,来制备复合材料。此外,膜分离技术在解决水环境问题上效果显著,因此将氧化石墨烯复合材料与膜分离技术相结合,来制备氧化石墨烯复合膜,对净化水体起到了事半功倍的效果。本文综述了氧化石墨烯复合膜材料的制备方法,并对其去除水中重金属离子的研究进展与吸附机理进行了综述,也对后续研究方向进行了展望。     

On the optimal cooling strategy for variable‐speed continuous casting

In this paper, we consider the inverse problem of determining the optimal cooling parameters for continuous casting under changing casting speed. We rely on automatic differentiation to support different search methods for the parameter values that will minimize a given cost functional, which can include a variety of criteria: surface temperature evolution and variation, interface position, full solidification point. In the direct problem we use a fixed‐domain transformation to solve the corresponding free‐boundary problem to high accuracy. Numerical experiments are provided to illustrate and support the effectiveness of the present concept. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑合力作用点位置的主动土压力计算

从滑动土体整体静力平衡方程出发,推导了坡面起伏,且有不均匀超载,墙背倾斜,黏性填土等一般情况下的主动土压力泛函极值的等周模型。在此基础上,引入拉格朗日乘子,将主动土压力问题转化为确定含有两个函数自变量的泛函极值问题。依据泛函取极值时必须满足的欧拉方程,得到了对数螺旋线的滑裂面函数和沿滑裂面分布的法向应力函数。结合边界条件和横截条件,主动土压力泛函极值问题进一步转化为以两个拉格朗日常数为未知量的函数优化问题。通过算例表明,对于一般土体,在作用点位置系数下界限处,主动土压力最小,滑裂面为平面;随着作用点位置的上移,主动土压力呈非线性增长,相应滑裂面为对数螺旋面,在作用点位置系数上界限处,主动土压力达到最大。在作用点位置系数上下界限处所对应的主动土压力构成的数值范围,包含了各种挡墙变位模式下的主动土压力。通过算例对比分析,采用库仑土压力理论进行的抗倾覆设计存在安全系数偏低的缺点,应该根据主动土压力和作用点位置的区间估计来指导设计。