Level set based robust shape and topology optimization under random field uncertainties

A robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material properties is developed in this work. The proposed approach integrates the state-of-the-art level set methods for shape and topology optimization and the latest research development in design under uncertainty. To characterize the high-dimensional random-field uncertainty with a reduced set of random variables, the Karhunen–Loeve expansion is employed. The univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is then employed for calculating statistical moments of the design response. The combination of the above techniques greatly reduces the computational cost in evaluating the statistical moments and enables a semi-analytical approach that evaluates the shape sensitivity of the statistical moments using shape sensitivity at each quadrature node. The applications of our approach to structure and compliant mechanism designs show that the proposed RSTO method can lead to designs with completely different topologies and superior robustness.     

高阶高斯型积分计算机求解算法

提出一种新颖的高阶高斯积分算法.该算法不仅可以高效地求解高阶高斯积分问题,而且无论权函数是否为标准正交多项式均能统一处理,因而具有更广泛的工程应用价值和适用性.所提算法通过借助Hankel矩阵高效地解决了与高斯积分相关的非线性方程组的求解问题.算法只涉及矩阵乘法、求逆及求特征值等初等矩阵运算,而传统的方法需要应用到选代搜索等数值方法.因此新的算法具有更高的计算效率和精度.     

Robust optimization of supply chain network design in fuzzy decision system

This paper presents a new robust optimization method for supply chain network design problem by employing variable possibility distributions. Due to the variability of market conditions and demands, there exist some impreciseness and ambiguousness in developing procurement and distribution plans. The proposed optimization method incorporates the uncertainties encountered in the manufacturing industry. The main motivation for building this optimization model is to make tools available for producers to develop robust supply chain network design. The modeling approach selected is a fuzzy value-at-risk (VaR) optimization model, in which the uncertain demands and transportation costs are characterized by variable possibility distributions. The variable possibility distributions are obtained by using the method of possibility critical value reduction to the secondary possibility distributions of uncertain demands and costs. We also discuss the equivalent parametric representation of credibility constraints and VaR objective function. Furthermore, we take the advantage of structural characteristics of the equivalent optimization model to design a parameter-based domain decomposition method. Using the proposed method, the original optimization problem is decomposed to two equivalent mixed-integer parametric programming sub-models so that we can solve the original optimization problem indirectly by solving its sub-models. Finally, we present an application example about a food processing company with four suppliers, five plants, five distribution centers and five customer zones. We formulate our application example as parametric optimization models and conduct our numerical experiments in the cases when the input data (demands and costs) are deterministic, have fixed possibility distributions and have variable possibility distributions. Experimental results show that our parametric optimization method can provide an effective and flexible way for decision makers to design a supply chain network.     

Robust performance optimization based on stochastic model errors: the stable case

Robust control aims to account for model uncertainty in design. Traditional methods for robust control typically assume knowledge of hard bounds on the system frequency response. However, this does not match well with system identification procedures which typically yield statistical confidence bounds on the estimated model. This paper explores a new procedure for obtaining a better match between robust control and system identification by using stochastic confidence bounds for robust control design. Given a nominal design, we set up an optimization problem which is aimed at reducing the statistical variability, measured in a mean square sense, from the nominal sensitivity. The proposed procedure is straightforward and leads to an easily computable solution for the final robust controller in the case of a stable plant and modest plant uncertainty. An illustrative example is provided which shows the advantages of the method. Copyright © 2002 John Wiley & Sons, Ltd.     

Comments on the accurate evaluation of integrals arising from the bulk electron densities in quantum wells

The calculation of bulk electron densities in high electron mobility transistors calls for the accurate numerical evaluation of the variants of the Fermi-Dirac integral. Mamedov reduces these integrals to a series involving gamma functions. These integrals are more efficiently evaluated by a DE quadrature scheme.     

一种新型非线性滤波的多特征融合跟踪算法

为有效解决非线性系统的状态估计问题,提出一种新型非线性滤波算法。该算法通过在积分卡尔曼滤波中引入修正因子,对积分点进行优化重组,并采用修正后的积分卡尔曼滤波产生优选建议分布函数,较好地克服了粒子退化现象。在新算法的框架内,利用颜色和运动边缘特征作为观测模型进行视频目标跟踪,并通过D-S证据理论的方法进行权值融合,较好地克服了单一颜色特征在姿态改变、相似背景遮挡等情况下跟踪稳定性较差的问题。实验表明本方法对复杂条件下的目标跟踪问题在保持较强鲁棒性的同时,跟踪精度提升了近32%。     

Fast convergence of inviscid fluid dynamic design problems

A new procedure for robust and efficient design optimization of inviscid flow problems has been developed and implemented on a wide variety of test problems. The methodology involves the use of an accurate flow solver to calculate the objective function and an approximate, dissipative flow solver, which is used only in the solution of the discrete quasi-time-dependent adjoint problem. The resulting design sensitivities are very robust even in the presence of noise or other non-smoothness associated with objective functions in many high-speed flow problems. The design problem is solved using what we term progressive optimization, whereby a sequence of a partially converged flow solution, followed by a partially converged adjoint solution followed by an optimization step is performed. This procedure is performed using a sequence of progressively finer grids for the solution of the flow field, while only using coarser grids for the adjoint equation solution.This approach has been tested on numerous inverse and direct (constrained) design problems involving two- and three-dimensional transonic nozzles and airfoils as well as supersonic blunt bodies. The methodology is shown to be robust and highly efficient, with a converged design optimization produced in no more than the amount of computational work to perform from 0.5 to 2.5 fine-mesh flow analyses.     

基于微分求积法的互连线灵敏度分析

提出一种基于微分求积法、对互连线的响应波形进行灵敏度分析的新方法．以传输线时域模型对互连 线进行建模,在此基础上导出灵敏度分析模型．由于利用了所有离散点的信息,微分求积法通常只需要较少的采样 点就能达到较高的精度．数值算例证明了该方法的有效性．     

Pseudospectral methods for optimal motion planning of differentially flat systems

The article presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization. We show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to Fliess' implicit state variable representation of dynamical systems. The optimal motion planning problem for differentially flat systems is equivalent to a classic Bolza problem of the calculus of variations. We exploit the notion that derivatives of flat outputs given in terms of Lagrange polynomials at Legendre-Gauss-Lobatto points can be quickly computed using pseudospectral differentiation matrices. Additionally, the Legendre pseudospectral method approximates integrals by Gauss-type quadrature rules. The application of this method to the two-dimensional crane model reveals how differential flatness may be readily exploited.