连续体结构的参数化水平集统一优化

针对传统分步式结构优化设计的不足,提出一种同时进行结构拓扑、形状和尺寸统一优化的设计方法.首先采用水平集函数描述统一的结构优化模型和几何尺寸边界,通过引入紧支径向插值基函数将结构拓扑优化变量、形状优化变量和尺寸优化变量变换为基函数的扩展系数;然后取该扩展系数为设计变量,借助一种参数的变化表达3种优化要素对结构性能的影响,将复杂的多变量优化问题变换为相对简单的参数优化问题,有利于与相对成熟的优化算法相结合提高求解效率;进一步用R函数将其融合为一个整体,构造出统一优化模型,并用最优化准则法进行求解.最后通过数值案例证明了该方法的有效性和精确性.     

Self-consistent gradient flow for shape optimization

We present a model for image segmentation and describe a gradient-descent method for level-set based shape optimization. It is commonly known that gradient-descent methods converge slowly due to zig–zag movement. This can also be observed for our problem, especially when sharp edges are present in the image. We interpret this in our specific context to gain a better understanding of the involved difficulties. One way to overcome slow convergence is the use of second-order methods. For our situation, they require derivatives of the potentially noisy image data and are thus undesirable. Hence, we propose a new method that can be interpreted as a self-consistent gradient flow and does not need any derivatives of the image data. It works very well in practice and leads to a far more efficient optimization algorithm. A related idea can also be used to describe the mean-curvature flow of a mean-convex surface. For this, we formulate a mean-curvature Eikonal equation, which allows a numerical propagation of the mean-curvature flow of a surface without explicit time stepping.     

Image magnification method using joint diffusion

In this paper a new algorithm for image magnification is presented. Because linear magnification/interpolation techniques diminish the contrast and produce sawtooth effects, in recent years, many nonlinear interpolation methods, especially nonlinear diffusion based approaches, have been proposed to solve these problems. Two recently proposed techniques for interpolation by diffusion, forward and backward diffusion (FAB) and level-set reconstruction (LSR), cannot enhance the contrast and smooth edges simultaneously. In this article, a novel Partial Differential Equations (PDE) based approach is presented. The contributions of the paper include: firstly, a unified form of diffusion joining FAB and LSR is constructed to have all of their virtues; secondly, to eliminate artifacts of the joint diffusion, soft constraint takes the place of hard constraint presented by LSR; thirdly, the determination of joint coefficients, criterion for stopping time and color image processing are also discussed. The results d     

一种视频目标轮廓跟踪的新算法

对双前沿活动轮廓模型进行了改进，提出一种鲁棒的视频目标轮廓跟踪新方法。通过限制支撑区域的大小，提高了演化速度。拟气球力的引入，既解决了因支撑区域限制导致的均匀区域内演化停滞的问题，又使参数调整更加容易，跟踪更加灵活。能较好地跟踪运动速度变化较大和形变较严重的目标，处理速度较快、并能自动适应目标拓扑的变化，适用于动态背景的视频。实验结果证明了该算法的高效性和鲁棒性。     

基于水平集的多运动目标检测和分割

针对视频图像的运动分割问题，提出了一种基于水平集方法的多运动目标检测和分割新方法.通过一种基于帧间差分的算法,自动提取初始背景图像，并使用相减法，检测出当前图像中的运动像素.定义了一种新的基于差分图像的局部梯度、目标的方差和背景的方差的速度函数，得到了改进的分割曲线的演化方程，分割出不同的运动目标.在水平集的求解过程，设定了控制演化曲线最终停止在目标边界上的条件，得到了运动目标的边界.实验结果表明，与其他传统方法相比，该运动目标检测和分割方法更有效和具有更好的鲁棒性，能够正确地提取运动目标边界.     

基于圆形约束快速水平集的原生质体细胞分割

原生质体细胞的显微图像具有边界模糊、内部分布不均匀的特点,利用传统分割方法较难取得理想分割效果.针对原生质体细胞的圆形特点,在快速水平集分割算法中加入圆形先验知识,提出一种新的基于圆形约束的快速水平集模型.为解决多个原生质体细胞分割问题,首先对图像进行预分割,然后利用多个水平集表示的圆形约束快速模型进行再分割.对传统快速水平集进行改进得到一种基于直方图统计的快速水平集模型,利用该模型进行预分割可以取得较好的效果.对多个不粘连细胞和多个粘连细胞,分别采用八链码跟踪法和随机霍夫圆检测法对预分割后的目标区域进行分裂.实验结果表明,本文快速水平集算法可以有效地解决单个及多个原生质体细胞分割问题.     

On a marching level-set method for extended discontinuous Galerkin methods for incompressible two-phase flows: Application to two-dimensional settings

In this work a solver for two-dimensional, instationary two-phase flows on the basis of the extended discontinuous Galerkin (extended DG/XDG) method is presented. The XDG method adapts the approximation space conformal to the position of the interface. This allows a subcell accurate representation of the incompressible Navier-Stokes equations in their sharp interface formulation. The interface is described as the zero set of a signed-distance level-set function and discretized by a standard DG method. For the interface, resp. level-set, evolution an extension velocity field is used and a two-staged algorithm is presented for its construction on a narrow-band. On the cut-cells a monolithic elliptic extension velocity method is adapted and a fast-marching procedure on the neighboring cells. The spatial discretization is based on a symmetric interior penalty method and for the temporal discretization a moving interface approach is adapted. A cell agglomeration technique is utilized for handling small cut-cells and topology changes during the interface motion. The method is validated against a wide range of typical two-phase surface tension driven flow phenomena in a 2D setting including capillary waves, an oscillating droplet and the rising bubble benchmark.     

Level-set topology optimization for multimaterial and multifunctional mechanical metamaterials

Metamaterials are artificially engineered composites designed to have unusual properties. This article will develop a new level-set based topology optimization method for the computational design of multimaterial metamaterials with exotic thermomechanical properties. In order to generate metamaterials consisting of arrays of microstructures under periodicity, the numerical homogenization method is used to evaluate the effective properties of the microstructure, and a multiphase level-set model is used to evolve the boundaries of the multimaterial microstructure. The proposed method will produce material geometries with distinct interfaces and smoothed boundaries, which may facilitate the fabrication of the topologically optimized designs. Several numerical cases are used to demonstrate the effectiveness of the proposed method.     

基于HSI空间彩色差的快速水平集分割方法*

为提高分割速度、改善分割效果,从两方面进行改进:首先对传统的快速水平集分割进行改进,得到基于CV模型的快速水平集;其次,通过引入HSI空间中的彩色差概念,建立一种新的、尤其适合彩色图像的快速水平集分割方法。实验表明,新提出的基于HSI彩色差的快速水平集分割方法,对彩色图像具有良好的分割效果。与传统水平集分割相比,新方法在分割性能和运算时间两方面均有明显提高。     

On the Transient Numerical Simulation of Solid Rocket Motor by Coupling Quasi One-Dimension Internal Flow with Three- Dimension Propellant Grain Burnback

固体火箭发动机内三维药柱燃烧的瞬态拟一维流场仿真

段娟^1,2,熊永亮^1,2,胡宁东^1,2

（1．华中科技大学 力学系,武汉 430074;

2．湖北省工程结构分析与安全评定重点实验室,武汉 430074）

创新点说明：

开发了固体火箭发动机内弹道混合维度求解器——耦合三维水平集法与一维TVD-MacCormack法降阶求解三维固体药柱燃烧退移时的瞬态流场及主要性能参数,该求解器可计算出较高精度的流场参数。

研究目的：

利用拟一维可压缩流场代替三维瞬态流场,并耦合三维水平集法从而降低固体发动机瞬态仿真的计算量,为进一步研究与指导设计提供可行性指导。

研究方法：

文中利用水平集法来捕捉三维药柱的实时界面并以此确定流场计算域,同时利用一维流场代替三维流场可大大节省计算成本,其原理是因为在药柱燃烧过程中径向和周向的流场参数变化对内部流场的影响相对较小。水平集法利用五阶WENO格式的有限差分进行离散,一维流场使用TVD-MacCormack法进行求解。耦合方法中考虑了药柱燃烧速率和喉部烧蚀对流场参数的影响。

结果与结论：

使用三维水平集耦合一维流场法可以准确高效地计算出药柱退移过程中的流场参数。为实际三维发动机整体工作过程仿真提供可行性实施方案。

关键词：瞬态可压缩流场求解器,固体火箭发动机内弹道仿真,水平集法,固体火箭发动机