QQ客服 官方微博 反馈留言

题名	电磁场形状、拓扑优化及其在核磁共振磁体设计中的应用; 电磁场形状、拓扑优化及其在核磁共振磁体设计中的应用
作者	1肖继军,电工研究所
学位类别	博士
答辩日期	2007-06-08
授予单位	中国科学院电工研究所
导师	1张一鸣,电工研究所
关键词	形状优化 拓扑优化 灵敏度分析 水平集法 核磁共振 Shape optimization topology optimization Sensitivity analysis Level set method NMR
其他题名	电磁场形状、拓扑优化及其在核磁共振磁体设计中的应用
中文摘要	随着计算机计算能力的快速发展和有限元法在电磁系统分析中的有效应用，人们对科学研究和工业应用中，利用数值方法优化设计电磁系统表现出浓厚的兴趣。本文致力于研究静磁场问题中的形状、拓扑优化问题的理论及其数值计算方法，讨论了数值优化技术、灵敏度分析、几何形状的参数描述方法，重点研究了利用伴随变量法高效求解形状、拓扑优化问题中的敏度信息和最近引入的水平集方法，同时研究了形状、拓扑优化技术在核磁共振磁体设计中的应用。 从描述数值优化技术入手，介绍了优化方法分类和常用的确定类优化算法，分析了电磁场形状、拓扑优化面临的特殊问题，然后，分析了不同的求解电磁系统一阶灵敏度的方法。在电磁场优化设计中敏度信息的求解精度和效率对优化过程和结果影响很大。这些方法包括： ·有限差分法； ·解析法和半解析法； ·连续性方法。 本文从计算效率的角度对几种灵敏度的计算方法进行了比较。电磁装置形状优化受电磁装置几何形状参数选择方法的影响。本文介绍了电磁装置形状优化中几何形状参数选取的三种常用方法，包括：使用有限元模型中边界节点坐标作为设计变量的简单方法，使用多项式插值和B样条曲线来描述边界形状的方法，然后，引入一种替代方法--水平集法描述边界形状，这是一种区域表示法，边界形状嵌入高一维的标量函数，作为该函数的等位线（面）。形状的改变通过求解Hamilton-Jacobi偏微分方程实现。Hamilton-Jacobi方程中的速度向量和形状优化中的灵敏度信息有非常紧密的关系，因此，水平集法提供了一种将几何形状参数和形状优化过程自然结合的方法。 最后，将电磁场形状、拓扑优化方法应用到具体问题中，包括：利用水平集法和连续性灵敏度分析方法优化设计永磁型核磁共振磁体磁极极面形状；利用密度法和拓扑灵敏度信息对核磁共振Halbach磁体主动补偿；在连续性拓扑灵敏度分析的基础上，利用罚函数法来优化单边核磁共振仪器永磁磁体的磁化方向。数值结果表明了以上提出的电磁装置的形状、拓扑优化方法的有效性。 In Parallel to the rapid development of computational power and efficient finite element methods used for modeling electromagnetic systems, numerical solution of optimal design of electromagnetic systems in science and industry are becoming an interesting research topic. This thesis is concerned with theoretical and computational aspects of optimal shape and topology design problems that are governed by magnetostatics. The aim is to provide an overview of components necessary to optimal design of electromagnetic device which compose of numerical optimization techniques, design sensitivity analysis, geometric parametrization techniques. The main emphasis is put on an efficient implementation of numerical methods for shape and topology optimization which exploits an effectively sensitivity analysis by the adjoint method and a just recently introduced level set methods. The classification of optimization problems are outlined, various solving methods of optimization problems are presented. The methods used in computer aided solving of electromagnetic optimization problems are emphasized. Different numerical methods of computing the first order sensitivity are present. Several numerical methods are presented and compared from the point of view of efficiency: · the finite difference method; · the analytical and semi-analytical methods; · the continuum approach. It is well known that the success of optimization procedure is strongly influenced by the appropriate choice of the design variable and by the method used for the parametrization of electromagnetic device geometry. Several ways of define the electromagnetic device geometry are presented such as one-to-one correspondence with node points of finite element model and B-spline method. A level set method is adopted as an alternative approach to the parametrization of electromagnetic device geometry.. Change of the shape is governed by Hamilton-Jacobi partial differential equation. The velocity vector of the Hamilton-Jacobi PDE is shown to be naturally related to the shape sensitivity analysis. Thus, the level set method provides a natural setting to combine the shape variations into the optimization process. Finally, Practical applications of optimal shape and topology design methods are discussed. Optimization the shape of pole for permanent-type Nuclear magnetic resonance(NMR) using level set method combined with continuum sensitivity analysis is performed. The use of density method and continuum sensitivity analysis for the active shim in the Halbach NMR is presented. A permanent magnet array for singled-sided NMR is designed. In order to obtain a constant gradient magnetic field alone a direction in a rectangular resonant region outside the surface of magnet, penalty-function method utilizing topology design sensitivity information is employed to find an optimized distribution of the direction of magnetization of the permanent magnets. Numerical results verified the validity of the overall methods.
语种	中文
公开日期	2010-10-18
页码	119
分类号	TM1
内容类型	学位论文
源URL	[http://ir.iee.ac.cn/handle/311042/6714]
专题	电工研究所_其他部门_其他部门_博士学位论文
推荐引用方式 GB/T 7714	1肖继军,电工研究所. 电磁场形状、拓扑优化及其在核磁共振磁体设计中的应用, 电磁场形状、拓扑优化及其在核磁共振磁体设计中的应用[D]. 中国科学院电工研究所. 2007.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。