D-Optimal Designs for Trigonometric Regression Models on a Partial Circle

In the common trigonometric regression model we investigate the D-optimal design problem, where the design space is a partial circle. It is demonstrated that the structure of the optimal design depends only on the length of the design space and that the support points (and weights) are analytic functions of this parameter. By means of a Taylor expansion we provide a recursive algorithm such that the D-optimal designs for Fourier regression models on a partial circle can be determined in all cases. In the linear and quadratic case the D-optimal design can be determined explicitly.     

There is no (46, 6, 1) block design*

Abstact: In this paper we show that a (46, 6, 1) design does not exist. This result was obtained by a computer search. In the incidence matrix of such a design, there must exist a “c4” configuration—6 rows and 4 columns, in which each pair of columns intersect exactly once, in distinct rows. There can also exist a “c5” configuration with 10 rows and 5 columns, in which each pair of columns intersect exactly once, in distinct rows. Thus the search for (46, 6, 1) designs can be subdivided into two cases, the first of which assumes there is no “c5”, and the second of which assumes there is a “c5”. After completing the searches for both cases, we found no (46, 6, 1) design. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 60–71, 2001     

On reductions for the Steiner Problem in Graphs

Several authors have demonstrated how reductions can be used to improve the efficiency with which the Steiner Problem in Graphs can be solved. Previous reduction algorithms have been largely ad hoc in nature. This paper uses a theory of confluence to show that, in many cases, all maximal reduction sequences are equivalent, gaining insights into the design of reduction algorithms that obtain a maximum degree of reduction.     

部分纯净主效应设计

纯净效应准则是选择最优设计的一个重要准则,实际中往往部分二阶交互效应是可忽略的,此时对主效应的估计,可以允许主效应与可忽略二阶交互效应混杂.文章首先回顾了部分纯净主效应设计的相关理论、进展、以及二水平情形下的结果.然后以三水平为例,给出了高水平下部分纯净主效应设计的若干结果.相比二水平情形,其存在更多类的高水平部分纯净主效应设计.最后通过随机模拟比较,验证了三水平部分纯净主效应设计在估计参数上的优势.     

Designing approximation minimal parametric surfaces with geodesics

Geodesic is an important curve in practical application, especially in shoe design and garment design. In practical applications, we not only hope the shoe and garment surfaces possess characteristic curves, but also we hope minimal cost of material to build surfaces. In this paper, we combine the geodesic and minimal surface. We study the approximation minimal surface with geodesics by using Dirichlet function. The extremal of such a function can be easily computed as the solutions of linear systems, which avoid the high nonlinearity of the area function. They are not extremal of the area function but they are a fine approximation in some cases.     

单源模糊数的模糊随机有限元方程的解法

在工程实际情况下,有时候可以利用单源模糊数的运算法则,来减少模糊随机有限元方程的计算量.通过推导证明,其计算量仅相当于求解普通的随机有限元方程.为了更好地适应现代工程设计的需要,还提出用模糊随机有限元方程计算结果求结构模糊失效概率的近似方法.     

Grasp Embedded Scatter Search for the Multicommodity Capacitated Network Design Problem

A GRASP embedded Scatter Search is developed for the multicommodity capacitated network design problem. Difficulty for this problem arises from the fact that selection of the optimal network design is an NP-complete combinatorial problem. There exist no polynomial exact algorithms which can solve this problem in a reasonable period of time for realistically sized instances. In such cases, heuristic procedures are commonly used. Two strategies were designed for GRASP: a traditional approach and a memory based technique. As for Scatter Search, 5 different strategies were used to update the reference set. Computational results on a large set of randomly generated instances show the convenience of the proposed procedures.     

Case-cohort analysis with general additive-multiplicative hazard models

The case-cohort design is widely used in large epidemiological studies and prevention trials for cost reduction. In such a design, covariates are assembled only for a subcohort which is a random subset of the entire cohort and any additional cases outside the subcohort. In this paper, we discuss the case-cohort analysis with a class of general additive-multiplicative hazard models which includes the commonly used Cox model and additive hazard model as special cases. Two sampling schemes for the subcohort, Bernoulli sampling with arbitrary selection probabilities and stratified simple random sampling with fixed subcohort sizes, are discussed. In each setting, an estimating function is constructed to estimate the regression parameters. The resulting estimator is shown to be consistent and asymptotically normally distributed. The limiting variance-covariance matrix can be consistently estimated by the case-cohort data. A simulation study is conducted to assess the finite sample performances of the proposed method and a real example is provided.     

Integer linear programming models for topology optimization in sheet metal design

The process of designing new industrial products is in many cases solely based on the intuition and experience of the responsible design engineer. The aid of computers is restricted to visualization and manual manipulation tools. We demonstrate that the design process for conduits, which are made out of sheet metal plates, can be supported by mathematical optimization models and solution techniques, leading to challenging optimization problems. The design goal is to find a topology that consists of several channels with a given cross section area using a minimum amount of sheet metal and, at the same time, maximizing its stiffness. We consider a mixed integer linear programming model to describe the topology of two dimensional slices of a three dimensional sheet metal product. We give different model formulations, based on cuts and on multicommodity flows. Numerical results for various test instances are presented.     

A note on partially balanced ternary designs

Two new methods of constructing a series of partially balanced ternary designs are presented. One from a BIB design and a PBIB design, and the second from a PBIB design alone, obtained by method of differences in both the cases.     

Numerical instabilities in structural optimization – analogy between topology & shape design problems

The formulation of structural optimization problems on the basis of the finite–element–method often leads to numerical instabilities resulting in non–optimal designs, which turn out to be difficult to realize from the engineering point of view. In the case of topology optimization problems the formation of designs characterized by oscillating density distributions such as the well–known “checkerboard–patterns” can be observed, whereas the solution of shape optimization problems often results in unfavourable designs with non–smooth boundary shapes caused by high–frequency oscillations of the boundary shape functions. Furthermore a strong dependence of the obtained designs on the finite–element–mesh can be observed in both cases. In this context we have already shown, that the topology design problem can be regularized by penalizing spatial oscillations of the density function by means of a penalty–approach based on the density gradient. In the present paper we apply the idea of problem regularization by penalizing oscillations of the design variable to overcome the numerical difficulties related to the shape design problem, where an analogous approach restricting the boundary surface can be introduced. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于iSIGHT平台的三维机翼气动优化设计

基于iSIGHT设计平台,结合CFD软件Fluent对三维机翼进行多目标优化设计,以提高其气动性能．设计过程中采用NCGA(neighborhood cultivation)——邻域培植遗传算法,NSGA-Ⅱ(non-dominated sorting)——非支配解排序遗传算法为优化算法,以N-S方程作为主控方程,对三维机翼优化．经过优化设计后结果表明,机翼的气动性能有了显著改善,该优化方法可推广用于多种翼型和机翼优化．     

Analysis and synthesis of switched nonlinear systems using the T–S fuzzy model

In this paper, the methods based on Lyapunov stability theorem to study the stability and switching law design for the T–S fuzzy switched systems with state-driven switching method are presented. Furthermore, these methods can be applied to cases when all individual systems are unstable. The PDC is employed to design fuzzy controllers from the T–S fuzzy models. The stabilization analysis is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Finally, a numerical example and an illustrative example based on the chemical process example are given to show the merits of the proposed approach, respectively.     

Complementary design theory for sliced equidistance designs

The complementary design theory is powerful for searching for an optimal design when its complementary design is smaller. This paper introduces a new class of sliced equidistance designs and develops the corresponding complementary design theory under the generalized minimum aberration criterion. Two rules are established to search for a generalized minimum aberration design through its complementary design in a sliced equidistance design. As a result, the developed theory covers the related results for the whole designs being saturated designs as special cases. Some examples are presented to illustrate its usefulness.     

Sensitivity analysis for product design selection with an implicit value function

In product design selection the decision maker (DM) often does not have enough information about the end users’ needs to state the “preferences” with precision, as is required by many of the existing selection methods. We present, for the case where the DM gives estimates of the preferences, a concept for calculating a “robustness index.” The concept can be used with any iterative selection method that chooses a trial design for each iteration, and uses the DM’s preference parameters at that trial design to eliminate some design options which have lower value than the trial design. Such methods, like our previously published method, are applicable to cases where the DM’s value function is implicit. Our robustness index is a metric of the allowed variation between the actual and estimated preferences for which the set of non-eliminated trial designs (which could be singleton) will not change. The DM, through experience, can use the robustness index and other information generated in calculating the index to determine what action to take: make a final selection from the present set of non-eliminated designs; improve the precision of the preference estimates; or otherwise cope with the imprecision. We present an algorithm for finding the robustness index, and demonstrate and verify the algorithm with an engineering example and a numerical example.     

Approximation schemes for NP-hard geometric optimization problems: a survey

 Traveling Salesman, Steiner Tree, and many other famous geometric optimization problems are NP-hard. Since we do not expect to design efficient algorithms that solve these problems optimally, researchers have tried to design approximation algorithms, which can compute a provably near-optimal solution in polynomial time. We survey such algorithms, in particular a new technique developed over the past few years that allows us to design approximation schemes for many of these problems. For any fixed constant c> 0, the algorithm can compute a solution whose cost is at most (1 + c) times the optimum. (The running time is polynomial for every fixed c> 0, and in many cases is even nearly linear.) We describe how these schemes are designed, and survey the status of a large number of problems. Received: December 2, 2002 / Accepted: April 28, 2003 Published online: May 28, 2003 Supported by a David and Lucile Packard Fellowship, NSF grant CCR-0098180, NSF ITR grant CCR-0205594     

Trajectory tracking for a class of switched nonlinear systems: Application to PMSM

This paper proposes a state-dependent switching control for a class of switched nonlinear systems, whose model describes a permanent magnet synchronous machine (PMSM) fed by a three-phase voltage source inverter. Due to its high torque density, high efficiency and wide velocity range, this electrical drive is widely used for traction and several applications in robotics, aerospace, electric vehicles among others. The proposed design conditions are based on a non-quadratic Lyapunov function, dependent on the machine shaft displacement, and assure asymptotic tracking of a pre-specified time-varying rotational velocity profile with guaranteed performance. Properties of the nonlinear system under consideration are used to derive design conditions expressed in terms of linear matrix inequalities that can be solved efficiently. Special cases involving asymptotic stability toward step and ramp velocity profiles are presented. Experimental results are used to validate the proposed technique.     

Semiglobal practical integral input-to-state stability for a family of parameterized discrete-time interconnected systems with application to sampled-data control systems

Semiglobal practical integral input-to-state stability (SP-iISS) for a feedback interconnection of two discrete-time subsystems is given. We construct a Lyapunov function from the sum of nonlinearly-weighted Lyapunov functions of individual subsystems. In particular, we consider two main cases. The former gives SP-iISS for the interconnected system when both subsystems are semiglobally practically integral input-to-state stable. The latter investigates SP-iISS for the overall system when one of subsystems is allowed to be semiglobally practically input-to-state stable. Moreover, SP-iISS for discrete-time cascades and a feedback interconnection including a semiglobally practically integral input-to-state stable subsystem and a static subsystem are given. As an application of the results, these can be exploited in controller design for a sampled-data system in the framework proposed in Nešić et al. (1999) and Nešić and Angeli (2002). We illustrate such a controller design via an example.     

Robust optimization – methodology and applications

Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO as applied to uncertain linear, conic quadratic and semidefinite programming. For these cases, computationally tractable robust counterparts of uncertain problems are explicitly obtained, or good approximations of these counterparts are proposed, making RO a useful tool for real-world applications. We discuss some of these applications, specifically: antenna design, truss topology design and stability analysis/synthesis in uncertain dynamic systems. We also describe a case study of 90 LPs from the NETLIB collection. The study reveals that the feasibility properties of the usual solutions of real world LPs can be severely affected by small perturbations of the data and that the RO methodology can be successfully used to overcome this phenomenon. Received: May 24, 2000 / Accepted: September 12, 2001?Published online February 14, 2002     

Finite element simulation of a layout optimisation technique by photoelastic stress minimisation

Layout optimisation to minimise maximum Tresca stress by photoelastic stress minimisation technique is simulated by finite element method: elements in the design domain that are lowly stressed are slowly removed resulting in a structure having minimum Tresca stress. The FEM simulation consists of analysing-monitoring the Tresca stress of elements in the design domain and “removing” material by declaring the element stiffness matrix of those possessing small stress values as of negligible stiffness in the subsequent step of the optimisation process. The lower bounds and upper bounds of stress limits for the “removal” criterion have to be appropriately chosen and effects of sharp notches introduced by removing finite elements should be properly taken into account for successful optimisation. The FEM simulation can be made fully automatic and can be extended to cases of complex geometry, loading material properties as well as to other objective functions of the optimisation problem.