无网格Galerkin法的理论进展及其应用研究

无网格Galerkin(Element-free Galerkin,EFG)法是无网格方法中应用比较广泛的一种,在介绍其基本特点和原理的基础上,对其移动最小二乘近似过程中涉及到的基函数、权函数的选择、影响域半径的确定等方面取得的新进展进行了介绍.并针对本征边界条件的满足,离散和积分方案的实施,自适应分析及误差分析的应用等一系列相关问题的研究现状及取得的成果进行了详细阐述.同时以受均布载荷的悬臂梁为例,编制了EFG平面弹性程序,验证了EFG法的可行性.最后针对EFG法存在的不足,提出了几个研究方向.     

热机载荷作用下拐折裂纹问题的通用权函数法分析

根据Betti互易原理,推导出二维拐折裂纹问题通用权函数法的普遍表达式,并利用虚拟裂纹扩展技术以及刚度阵导数法,将通用权函数法与有限元法直接耦合,给出了二维拐折裂纹问题通用权函数法的有限元格式。通过实例计算比较,验证了此方法的可靠性和准确性。分析结果表明:通用权函数法可以极大地简化计算过程,具有极高的计算效率。在此基础上应用此方法讨论了拐折裂纹长度、拐折角度对应力强度因子过渡过程的影响。     

模型参考自适应恒张力控制系统研究

为解决不适张力对带材供送的影响,通过放卷辊的动力学分析,建立了张力数学模型,分析了影响张力的因素。针对放卷过程中半径变小,而常规PI控制难以实现参数在线调整,提出模型参考自适应张力控制方法,建立了参考模型,采用梯度法推导了自适应率。建立了控制系统模型,并进行了仿真。结果表明,利用该方法系统可以有效的跟随半径减小调节控制器参数,保证了系统的稳定性,缩短了调节时间,减小了超调量。     

自适应插值算法在图像修复中的应用研究

针对BSCB模型速度慢、整体变分模型易产生阶梯效应的缺点,提出了一种基于扩散率函数的自适应插值算法。该算法利用待修复像素点周围的已知像素点的梯度权函数和距离权函数,对未知像素点进行赋值。实验结果显示: 将该算法应用到灰度图像和彩色图像的修复中,与传统算法相比所需运算时间短,视觉效果较好,定量评价指标(峰值信噪比)也证明了该算法的有效性。     

一个自动确定信赖域半径的信赖域方法

本文对无约束优化问题提出一个自适应的信赖域方法,每次迭代都充分利用当前迭代点包含的二次信息自动产生一个信赖域半径,所用的计算信赖域半径的策略没有增加额外的计算量。在通常条件下,证明了全局收敛性及局部超线性收敛结果,数值结果验证了新方法的有效性。     

表面裂纹应力强度因子计算及扩展跟踪的权函数法

 介绍了一种显式的权函数法,并将这种方法用于圆柱形容器接管外拐角表面裂纹的应力强度因子计算和扩展跟踪上.结果表明,权函数法可以用于分析各种载荷下不同形状的裂纹.就一般的工程问题而言,权函数法不失为一种与有限元法互补的方便有效的分析方法.     

基于权函数正交基展开的过程神经元网络学习算法

针对过程神经元输入和网络连接权均可以是过程或时变函数,为解决过程神经元网络训练涉及的时域聚合运算问题,提出了基于权函数基展开的过程神经元网络学习算法。在网络输入函数空间中引入权函数正交基,将输入函数和网络连接权函数表示为该组正交基的有限项展开形式,利用函数基的正交性,可简化过程神经元在时间聚合运算中的复杂性,提高网络学习效率。     

数值方法进展:从连续介质到离散粒子模型

数值方法经历了由连续介质到离散粒子模型的进展过程。无网格粒子方法正是离散粒子模型发展的产物,它在纳米时代显示出具大的发展潜能。介绍了无网格粒子方法的背景、原理及其与其他数值方法的区别,探讨了无网格法的基函数、权函数、影响半径、本质边界条件、积分与离散方案等热点问题,列举了这种数值方法的应用现状。最后,介绍了自然单元法、多尺度计算概念、中值定理与局部边界积分方程等,并对无网格粒子方法在未来的发展进行展望。     

一个瞬态温度场区间上下界估计的数值方法

提出一种求解带有区间不确定性参数的瞬态热传导问题的数值方法。利用Taylor展开和区间分析技术,建立温度区间量与不确定参数区间量的确定性关系,然后采用时域分段自适应算法和有限元技术,递推计算温度场的区间半径及区间中值,以估算温度场不确定区间的上下界。自适应计算可根据时间步长的变化,使计算在各离散时段达到给定的计算精度,从而保证整个时域的计算精度。在算例分析中,通过与组合方法、概率方法的比较,说明了所提方法的有效性,并探讨了Taylor展开阶次与计算步长对计算结果的影响。     

移动最小二乘方法中影响半径的选取

在移动最小二乘法中,影响半径r的选取是一个急待解决的重要问题。如果r太大,不能充分体现其局部性;如果r太小,则需求解的线性方程组系数矩阵A不可逆或条件数太大。本文首先推导出矩阵A可逆的充分必要条件,其次研究了影响半径r的选取对矩阵A的条件数的影响,最后讨论了影响半径的选取方法。节点均匀分布时,对于线性基,影响半径r可取为1．2h（h为步长）;对于二次基,如果x到边界的距离大于h,影响半径r可取为1．9h,否则影响半径r可取为2．5h。     

A Quadratic Adapative Method for Aberration Correction

Abstract

A new non-merit function based lens design algorithm has been developed which combines a quadratic approximation to the individual aberration variations with adaptive aberration control. This results in an increase in the magnitude of the applied parameter changes and a reduction in the computing load compared to the linear adaptive method. Examples given verify that the method described can diagnoze specific aberrational problems. This feature, together with the increased magnitude of the applied parameter changes, enhances the radius of convergence in computer-aided lens design.     

一种时空权重和边缘自适应的扫描格式转换

为实现隔行扫描到逐行扫描的视频扫描格式转换,提出了一种时空权重和边缘自适应的去隔行算法,主要包括运动估计、小角度边缘搜索、时空权重计算、自适应插值等。该算法通过4场相邻像素的最大灰度变化与运动阈值比较实现对当前像素的运动估计,采用自适应搜索半径和并行搜索树的方法实现小角度边缘检测,并且增加对半像素边缘的考虑实现最小6°边缘的检测,最后通过时空权重自适应的插值算法实现去隔行处理,取得很好的处理效果。     

An adaptive species conservation genetic algorithm for multimodal optimization

This paper introduces an adaptive species conservation genetic algorithm (ASCGA) by defining a species with three parameters: species seed, species radius and species boundary fitness. A species is defined as a group of individuals that have similar characteristics and that are dominated by the best individual in the species, called the species seed. Species radius defines the species' upper boundary and the species boundary fitness is the lowest value of fitness in the boundary. Some heuristic algorithms have been developed to adjust these parameters and an ASCGA has been proposed to solve multimodal optimization problems. With heuristic techniques, ASCGA can automatically adjust species parameters and allow the species to adapt to an optimization problem. Experimental results presented demonstrate that the proposed algorithm is capable of finding the global and local optima of test multimodal optimization problems with a higher efficiency than the methods from the literature. ASCGA has also successfully found a significantly different solution of a 25‐bar space truss design and identified 761 local solutions of the 2‐D Shubert function. Copyright © 2009 John Wiley & Sons, Ltd.     

An adaptive metamodel-based global optimization algorithm for black-box type problems

In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.     

Analysis of thermal stress intensity factors for cracked cylinders using weight function method

In this paper a general weight function was derived to evaluate the thermal stress intensity factors of a circumferential crack in cylinders. The weight function derived is valid for a wide range of thin- to thick-walled cylinders and relative crack depth. Closed-form stress intensity factor based on the weight function method was derived as a function of the Biot number and relative depth and various inner-to-outer radius ratios of cylinders. The accuracy of the analysis has been examined using the finite element method results and were compared to existing solutions for uniform loading in the literature for special geometries, indicating an excellent agreement.     

Weight Function Method for Stress Intensity Factor of Internal Surface Semi-elliptical Crack in Elliptical Holes

The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.     

Unequal-area facility layout by genetic search

This paper applies genetic optimization with an adaptive penalty function to the shape-constrained unequal-area facility layout problem. We implement a genetic search for unequal-area facility layout, and show how optimal solutions are affected by constraints on permitted department shapes, as specified by a maximum allowable aspect ratio for each department. We show how an adaptive penalty function can be used to find good feasible solutions to even the most highly constrained problems. We describe our genetic encoding, reproduction and mutation operators, and penalty evolution strategy. We provide results from several test problems that demonstrate the robustness of this approach across different problems and parameter settings.     

Adaptive trochoidal toolpath for complex pockets machining

This work proposes a novel adaptive trochoidal (TR) toolpath model for complex pocket machining. The proposed model is able to adjust its TR radius, while simultaneously offers an adaptive trochoidal step for generation of each toolpath cycle. With the varying radius, complex regions can be machined by a single strip of TR toolpath. Moreover, the step of each TR cycle can be adjusted with reference to the varied radius so as to maintain a constant radial depth of cut, and hence more stable material removal rate among all TR cycles can be achieved. For the pocket machining cases with complex inner and outer boundaries, experimental study has shown that the proposed TR toolpath can effectively minimise the fluctuation of cutting forces, and achieve better toolpath efficiency.