三次拟Bézier曲线的光顺逼近

利用 Friedman的 URN模型构造出带有参数的调配函数 ,用其生成三次拟Bézier曲线 .通过对这种新曲线进行分析 ,利用最小二乘法和非线性泛函的极小值优化计算 ,来对平面数据点进行光顺逼近 ,得到最优的光顺逼近曲线 .     

线性流量阀内筒孔的设计

从理论上证明了不存在使过流面积与移动距离成线性关系的图形,同时得到了内筒孔形状的特点.并给出了两种具体设计方案.方案I中,简化曲线段设计,直接使每一个曲线段与圆上对应的弧相同,在满足线性区间最大面积达到最大范围的85%的条件下求得内筒孔形状的初始宽度为a=0.372r,这时线性区间达到最大范围区间的77.3%.方案II中用位图离散化表示外筒孔和待设计的内筒孔,用matlab编程模拟两个图形相对运动时过流面积的变化的同时描绘出内筒孔的形状.内筒孔的初始宽度a=0.196r,此时得到的连续线性区间达到最大范围区间的98.55%,线性区间的最大面积达到最大范围的99.02%.文章的最后比较了两种方案的优缺点.     

线性流量阀内筒孔形状设计问题研究

对于双筒式线性流量阀,内筒孔形状设计是关系到线性流量阀的过流面积能否"线性变化"的核心问题.从工程实际应用出发,对线性流量阀的内筒孔进行了分段地形状设计.经设计的内筒设计能够使线性流量阀的线性控制区达到90%以上,"过流面积"也完全能够达到"最大范围".设计的内筒孔主体形状为矩形和简单曲线组成,易于加工制造.     

Perzyna粘塑性模型的参变量变分原理*

Perzyna模型是粘塑性本构关系的主要形式之一,本文给出该模型的参变量变分原理,该原理将原问题化为求解带约束条件的泛函极值,其约束条件就是由粘塑性本构关系推导出的系统状态方程,所讨论的问题其塑性流动不受Drucker假定的限制,文中给出原理的证明,并研究弹塑性蠕变问题.     

梁的弹性最优设计*

本文根据最小余能原理建立了弹性梁最优强度设计问题的数学形式,它为一个具有等式和不等式约束的泛函极值问题。进而应用拉格朗日乘子法得到了极值的必要条件,并由此导出最优解所必须满足的一组关系式,这组关系式可以用来检验等强度设计或任一可行弹性设计的最优性。当等强度设计不是最优设计时文中还建议了一个迭代寻优的数值解法。     

不等式约束条件下部分线性回归模型的参数估计

本文研究了不等式约束条件下部分线性回归模型的参数估计问题，利用最优化方法和贝叶斯方法，给出了不等式约束条件下部分线性回归模型的最小二乘核估计和最佳贝叶斯估计，并且证明了在一定条件下，带约束条件的最小二乘核估计在均方误差意义下要优于无约束条件的最小二乘核估计。     

带Hermite插值条件的最小二乘估计

提出了带Hermite插值条件的最小二乘拟合问题,并给出了带Hermite插值条件的最小二乘拟合的拟合曲线的具体表达式.利用Lingo建模语言设计了求解带Hermite插值条件的最小二乘拟合的拟合曲线的Lingo程序,并通过Excel软件得到了求解带Hermite插值条件的最小二乘拟合的拟合曲线的应用软件.     

总体最小二乘准则下非线性EV模型的参数拟合方法

在非线性回归模型参数拟合问题中,当数据中的每个变量都存在不可忽略的误差时,在普通的最小二乘准则下拟合出的参数不是最优的.按照总体最小二乘准则,以观测点到拟合曲线或拟合曲面垂直距离平方和为目标函数,然后用最优化方法搜索出使目标函数值取最小值的参数和数据点估计,从而给出求最优模型参数的算法,最后,通过计算机仿真和与文献比较,验证了提出方法的正确性.     

高阶拉氏乘子法和弹性理论中更一般的广义变分原理

作者曾指出[1],弹性理论的最小位能原理和最小余能原理都是有约束条件限制下的变分原理采用拉格朗日乘子法,我们可以把这些约束条件乘上待定的拉氏乘子,计入有关变分原理的泛函内,从而将这些有约束条件的极值变分原理,化为无条件的驻值变分原理.如果把这些待定拉氏乘子和原来的变量都看作是独立变量而进行变分,则从有关泛函的驻值条件就可以求得这些拉氏乘子用原有物理变量表示的表达式.把这些表达式代入待定的拉氏乘子中,即可求所谓广义变分原理的驻值变分泛函.但是某些情况下,待定的拉氏乘子在变分中证明恒等于零.这是一种临界的变分状态.在这种临界状态中,我们无法用待定拉氏乘子法把变分约束条件吸收入泛函,从而解除这个约束条件.从最小余能原理出发,利用待定拉氏乘子法,企图把应力应变关系这个约束条件吸收入有关泛函时,就发生这种临界状态,用拉氏乘子法,从余能原理只能导出Hellinger-Reissner变分原理[2],[3],这个原理中只有应力和位移两类独立变量,而应力应变关系则仍是变分约束条件,人们利用这个条件,从变分求得的应力中求应变.所以Hellinger-Reissner变分原理仍是一种有条件的变分原理.     

六关节机械臂运动路径设计

就关节式机械臂指尖在任意两点间移动、沿固定曲线移动、机械臂绕开障碍物执行任务以及参数优化等问题展开研究.首先确定了自由度组合到指尖空间位置的映射,建立了求解上述问题的最小二乘模型、泛函条件极值模型,并给出了数值解法.最后,结合图像处理等技术,对各参数的优化设计提出了改进措施.     

Optimal Thickness of a Cylindrical Shell Under a Time-Dependent Force

We discuss thickness optimization problems for cylindrical tubes that are loaded by time-dependent applied force. This is a problem of shape optimization that leads to optimal control in linear elasticity theory. We determine the optimal thickness of a cylindrical tube by minimizing the deformation of the tube under the influence of an external force. The main difficulty is that the state equation is a hyperbolic partial differential equation of the fourth order. The first order necessary conditions for the optimal solution are derived. Based on them, a numerical method is set up and numerical examples are presented.     

Shape functional optimization with restrictions boosted with machine learning techniques

Shape optimization is a widely used technique in the design phase of a product. Current ongoing improvement policies require a product to fulfill a series of conditions from the perspective of mechanical resistance, fatigue, natural frequency, impact resistance, etc. All these conditions are translated into equality or inequality restrictions which must be satisfied during the optimization process that is necessary in order to determine the optimal shape. This article describes a new method for shape optimization that considers any regular shape as a possible shape, thereby improving on traditional methods limited to straight profiles or profiles established a priori. Our focus is based on using functional techniques and this approach is, based on representing the shape of the object by means of functions belonging to a finite-dimension functional space. In order to resolve this problem, the article proposes an optimization method that uses machine learning techniques for functional data in order to represent the perimeter of the set of feasible functions and to speed up the process of evaluating the restrictions in each iteration of the algorithm. The results demonstrate that the functional approach produces better results in the shape optimization process and that speeding up the algorithm using machine learning techniques ensures that this approach does not negatively affect design process response times.     

Control the Fibre Orientation Distribution at the Outlet of Contraction

A two dimensional model of the orientation distribution of fibres in a paper machine headbox is studied. The goal is to control the fibre orientation distribution at the outlet of contraction by changing its shape. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Then, the problem is expressed as an optimal control problem governed by variational forms. By using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to shape variation design to a one dimensional headbox. The usefulness of this idea is that the method is not iterative and it does not need any initial guess of the solution.      

2D shape optimization under proximity constraints by CFD and response surface methodology

In this paper we consider two-dimensional CFD-based shape optimization in the presence of obstacles, which introduce nontrivial proximity constraints to the optimization problem. Built on Gregory’s piecewise rational cubic splines, the main contribution of this paper is the introduction of such parametric deformations to a nominal shape that are guaranteed to satisfy the proximity constraints. These deformed shape candidates are then used in the identification of a multivariate polynomial response surface; proximity-constrained shape optimization thus reduces to parametric optimization on this polynomial model, with simple interval bounds on the design variables. We illustrate the proposed approach by carrying out lift and/or drag optimization for the NACA 0012 airfoil containing a rectangular fuel tank: By identifying polynomial response surfaces using a large batch of 1800 design candidates, we conclude that the lift coefficient can be optimized by a linear model, whereas the drag coefficient can be optimized by using a quadratic model. Higher order polynomial models yield no improvement in the optimization.     

基于CVaR的债券投资组合模型

针对债券投资组合中的风险度量难题,用CVaR作为风险度量方法,构建了基于CVaR的债券投资组合优化模型.采用历史模拟算法处理模型中的随机收益率向量,将随机优化模型转化为确定性优化模型,并且证明了算法的收敛性.通过线性化技术处理CVaR中的非光滑函数,将该模型转化为一般的线性规划模型.结合10只债券的组合投资实例,验证了模型与算法的有效性.     

高速公路网络上行车时间估计和最优路线的选取

首先建立交通流动力学模型求解问题Ⅰ.在不考虑流量和考虑流量的两种情况下,该模型都能够解出在任意给定的时刻t位于第一个传感器的车辆到达第5个感应器的行车时间.我们还从四个方面给出了判断交通堵塞的衡量标准,并且利用神经网络方法准确地对未来的车流状态进行了预测.问题Ⅱ建立了交通网络的加权有向图模型,引入协方差矩阵描述网络中道路之间的相关性,并设计了查找最优路径的动态Dijkstra算法.问题Ⅲ构建了统计多目标规划模型,利用车比雪夫不等式,成功找到了从端点3到14和14到3的最优路径,并估算出了对应的行车时间.     

Risk averse elastic shape optimization with parametrized fine scale geometry

Shape optimization of the fine scale geometry of elastic objects is investigated under stochastic loading. Thus, the object geometry is described via parametrized geometric details placed on a regular lattice. Here, in a two dimensional set up we focus on ellipsoidal holes as the fine scale geometric details described by the semiaxes and their orientation. Optimization of a deterministic cost functional as well as stochastic loading with risk neutral and risk averse stochastic cost functionals are discussed. Under the assumption of linear elasticity and quadratic objective functions the computational cost scales linearly in the number of basis loads spanning the possibly large set of all realizations of the stochastic loading. The resulting shape optimization algorithm consists of a finite dimensional, constraint optimization scheme where the cost functional and its gradient are evaluated applying a boundary element method on the fine scale geometry. Various numerical results show the spatial variation of the geometric domain structures and the appearance of strongly anisotropic patterns.     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

The inverse scattering problem for a partially coated cavity with interior measurements

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.     

Adjacency based method for generating maximal efficient faces in multiobjective linear programming

Multiobjective linear optimization problems (MOLPs) arise when several linear objective functions have to be optimized over a convex polyhedron. In this paper, we propose a new method for generating the entire efficient set for MOLPs in the outcome space. This method is based on the concept of adjacencies between efficient extreme points. It uses a local exploration approach to generate simultaneously efficient extreme points and maximal efficient faces. We therefore define an efficient face as the combination of adjacent efficient extreme points that define its border. We propose to use an iterative simplex pivoting algorithm to find adjacent efficient extreme points. Concurrently, maximal efficient faces are generated by testing relative interior points. The proposed method is constructive such that each extreme point, while searching for incident faces, can transmit some local informations to its adjacent efficient extreme points in order to complete the faces’ construction. The performance of our method is reported and the computational results based on randomly generated MOLPs are discussed.