渐进结构优化方法失效机理分析与改进策略

针对ESO方法在Zhou-Rozvany算例中失效的根本机理进行了深入的分析,提出有效的改进策略。指出ESO方法失效的根本原因既不是网格划分的数目过少,也不是优化策略的不合理,而是对于各单元内材料有效性评估的误差所致。针对ESO方法的失效机理引入奇异单元的概念,并提出了一种基于奇异单元的改进策略,改进后的ESO方法能够在网格较为稀疏的情况下保证0-1优化结果的合理性。     

二阶扩张状态观测器的误差分析

本文利用分片光滑的Ｌｙａｐｕｎｏｖ函数来进行扩张状态观测器的误差分析,指出了非线性扩张状态观测器有更好的估计精度能力,给出了为提高估计精度扩张状态观测器的参数所满足的条件．     

The optimal execution strategy of employee stock options

In this paper, we develop an optimal execution strategy for employee stock options by means of the fluid model, in which a voluntary turnover is considered. We show that the value function is the viscosity solution of the Hamilton-Jacobi-Bellman variational inequality and prove the uniqueness of the viscosity solution. Finally, we present numerical illustrative examples and numerical solutions of optimal strategies which are computed by the finite difference method.     

基于自抗扰控制器的力矩电机伺服系统控制

自抗扰控制器能将被控对象的内、外“总扰动”进行估计并用前馈补偿的方法将其抵消,适于力矩电机因直接驱动所带来干扰的补偿与控制。针对测量噪声对线性自抗扰控制器观测器带宽的限制,提出了二阶线性自抗扰的相似结构,并结合三阶积分链式微分器对其效果进行了对比仿真验证。力矩电机的控制仿真实验表明,与二阶线性自抗扰算法相比,基于相似结构的改进的力矩电机控制,能在有测量噪声情况下兼顾系统跟踪精度、突加负载时抗扰动性与抗噪性。     

Synthesis and characterization of itaconic‐based epoxy resins

A trifunctional epoxy resin from itaconic acid (TEIA) was synthesized from a renewable resource‐based itaconic acid by allylation of itaconic acid to form diallyl itaconate by using m‐chloroperoxybenzoic acid as oxidizing agents followed by epoxidation of allylic C═C bond of diallyl itaconate methylhexahydropthalic anhydride as curing agent in the presence of 2‐methyl imidazole as a catalyst. The chemical structure of the synthesized resins was confirmed by Fourier transform infrared and nuclear magnetic resonance (¹H‐NMR and ¹³C‐NMR) spectroscopy analysis. The mechanical, thermal, and rheological performances of the TEIA were also investigated and compared with diglycidyl ether of bisphenol A and a plant‐based epoxidized soybean oil bioresin cured with the same curing agent. The higher epoxy value of 1.02, lower viscosity (0.96 Pa s at 25°C), higher mechanical, and higher curing reactivity toward methylhexahydropthalic anhydride of TEIA as compared with epoxidized soybean oil and comparable with diglycidyl ether of bisphenol A demonstrated significant evidence to design and develop a novel bio‐based epoxy resin with high performance to substitute the petroleum‐based epoxy resin.     

基于虚拟材料的T-B梁拓扑优化ESO方法

自从Zhou和Rozvany于2001年以T-B梁(Tie-Beam)问题质疑渐进结构优化方法ESO(Evolutionary Structural Optimization)的算法收敛性以来,结构最优化领域的研究者提出了多种算法以求解决这一问题。T-B梁问题仍是当前结构拓扑优化领域的研究热点,因为现有的各种T-B梁解法或是存有不足或是无法获得满意解答。本文在传统ESO算法中,将虚拟材料引入待删除单元,用以检测结构传力路径是否受到破坏,进而确定单元删除的合理性。算例表明,本文算法可有效防止ESO方法求解T-B梁问题时的失效并获得最优解,且本文算法只需在ESO迭代中附加一次检测,不改变ESO方法的迭代进程和寻优能力。     

Valuing executive stock options: A quadratic approximation

This paper develops a continuous-time model for valuing executive stock options (ESOs) with features of early exercise, delayed vesting and forfeiture. Applying the quadratic approximation established for valuing American options into ESOs, we obtain an explicit formula for the fair ESO value at its grant date. We show that the approximation formula is consistent with the exact results for two special cases either with no dividend or infinite maturity, and also that the perpetual value for the latter case gives an upper bound of the ESO value. To see the performance of the formula, we numerically examine it with benchmark results generated by a binomial-tree model for some particular cases. Numerical experiments show that there is a complementary relation between the vesting and trading periods with respect to exit rate of ESO holders.     

基于一种动态删除率的ESO方法

渐进结构优化方法 ESO(Evolutionary Structural Optimization)的基本思想是基于单元灵敏度,通过把无效或低效的单元逐步从结构中删除,从而得到优化的拓扑结构。经过20年的发展,其算法结构、理论研究以及实际工程应用领域已经取得了大量成果。在原始ESO算法中删除单元的数目是由固定删除率RR的取值决定的,设计者无法预期每一个迭代步删除单元的数量。对于一个初始满设计区域,合理的删除策略为随着迭代的进行,随着结构应力分布越均布,应该逐渐减少单元删除数量。基于此,本文构造了一种动态删除率,使得随着迭代的进行单元的删除数量逐渐减少,相对于前人构造的动态删除率更为简单明了,人为控制参数更少,并且通过算例证明该方法相比原始删除策略具有更好的优化效果。     

多功能结构拓扑形态优化数值方法

对建筑结构设计的多功能要求,以平面问题为研究对象,对改进进化论方法进行了功能上的改进,增强了方法对复杂空间条件的适应性,提高了计算效率和所生成结构体的质量。针对建筑对空间的限制,将方法的允许空间拓展为自由边界允许空间,并引进临时允许空间的概念;针对结构功能需求,研究了能够适应支座改变、荷载组合等多工况情况的合理结构形态创构方法;考虑到材料的受力特性,研究了相应（如指定构件纯受压或纯受拉）的结构拓扑形态优化方法。文中还通过算例分析了方法的特点,探讨了方法所得到结构形态的一些力学特性。该方法所得结构为以均匀拉压应力形式来抵抗荷载,其形式可为结构概念设计提供参考。     

渐进结构优化法(ESO)和双向渐进结构优化法(BESO)的近期发展

本文介绍渐进结构优化法和双向渐进结构优化法的近期发展和主要研究成果.从理论层面对该方法的合理性、连续体拓扑优化在多种工程问题中的应用,以及计算机软件的具体实现, 进行了阐述及算例演示.这些结果充分展示了渐进结构优化法解决实际工程优化设计问题的能力,以及其通过现有成熟建模界面广泛应用于日常建筑和机械结构设计的可行性.