对抛物方程使用新显格式的区域分解算法

我们提出了两个具有改进稳定性限制条件的新显格式．与经典显格式相比,稳定性限制条 件分别对两维抛物问题放宽了4倍,对一维问题放宽了2倍,同时它的精度与经典全隐格式 的相同．然后,我们通过在内边界点使用大步长的这种新显格式,在内点使用全隐格式,设计 了一个有限差分区域分解算法,稳定性限制条件分别对一维抛物问题放宽了2m2倍,对二维 问题放宽了4m2倍．从而我们能使用一个大的时间步长,这使我们在并行求解抛物问题时能 节省大量的计算量．     

连铸方坯的二冷水控制问题

对连铸过程的二冷水控制问题进行了讨论;将二维凝固温度场的边界控制问题,用线性化方法将原问题等价地转化为在几个Ｒａｎｄｏｎ测试空间求最优测度的有限维线性优化问题,从而得到全局最优控制律。数值试验显示此方法是有效的。     

Design of servo systems for distributed parameter systems by finite dimensional dynamic compensator

The design problem of servo systems for distributed parameter systems is investigated. The output regulator of integral type is designed in order to guarantee internal stability and output regulation. The design procedure based on a dynamic stabilizing compensator is discussed. The output regulation of a wide class of distributed parameter systems is proved under the condition that a closed-loop system is stabilized by a dynamic compensator of general type. Then a closed-loop system can be stabilized by a finite dimensional dynamic compensator under some additional conditions. The reducabitity of the design procedure to a purely finite dimensional one is discussed.     

Numerische Erfahrungen bei der Lösung des dreidimensionalen Transportproblems

To find an initial basic feasible solution is a special problem on solving the three dimensional transportation problem. It is not possible to do this work in a similar simple way as it can be done in the usual transportation problem. In [3] Haley proposes to solve a new problem that is essentionally the old one with the addition of a set of artificial variables. However, numerical investigations have shown that this procedure enlarges the amount of computing very much. This paper now gives another procedure for finding an initial basic solution for the three dimensional transportation problem. A great number of examples is discussed which demonstrate the efficiency of this procedure.     

Optimum design of plano-milling machine structure using finite element analysis

The problem of optimum design of plano-milling machine structure is formulated as a nonlinear mathematical programming problem with the objective of minimizing the structural weight. The plano-milling machine structure is idealized with triangular plate elements and three dimensional frame elements based on finite element displacement method. Constraints are placed on static deflections and principal stresses in the problem formulation. The optimization problem is solved by using an interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique and cubic interpolation method of one dimensional search are employed. A numerical example is presented for demonstrating the effectiveness of the procedure outlined. The results of sensitivity analysis conducted with respect to design variables and fixed parameters about the optimum point are also reported.     

A dimensional decomposition approach to identifying efficient units in large-scale DEA models

In this paper, we propose the use of a dimensional decomposition procedure together with lexicographic parametric programming to reduce computational burden when identifying the efficient decision making units in data envelopment analysis (DEA). The use of lexicographic parametric programming makes it possible to develop an efficient algorithm for the problems with few inputs and outputs. Based on this we propose the procedure which first partitions the original problem dimensionally into sub-problems and then identifies the efficient units of the sub-problems. Since those units are a subset of the weakly efficient solutions of the original problem, they are used as an initial approximation for the efficient units of the original problem. The efficiency of the approach is illustrated by numerical results.     

The determination of optimum accelerating factors for successive overrelaxation on an equidistant and non-equidistant rectangular net

A modification to the successive overrelaxation iterative procedure for solving elliptic partial differential equations is presented. The modified method is based on an extension of Brazier's nodal overrelaxation method in one dimension, characterised by the use of a different overrelaxation factor for each point in the net. The extension to several dimensions make use of the separability of the variables for the error distribution. Thus the optimum one dimensional results are directly used in the several dimensional problem.The present method has been examined in one and two dimensions, for equidistant and non-equidistant nets. The computational time required to obtain a given accuracy for a solution was found for all two dimensional cases to be half (or less) of that required by conventional methods.     

Sensors and controllers location in distributed systems—A survey

A survey of the field of optimal sensors and/or controllers location for dynamical distributed parameter systems modelled by partial differential equations is presented. The recent contributions in this field are grouped according to the main goal for which the location problem is developed, namely: system identification, state estimation, and optimal control. In order to pose the sensors and controllers location problem, the semigroup approach for modelling distributed linear systems is briefly reviewed together with its equivalent (infinite dimensional) and approximate (finite dimensional) Fourier expansion representations. After presenting a concise general review of the several methods considered in the current literature, a classification of methods is also proposed. The main classifying factor concerns the use of N-modal approximation schemes, and the different stages of the optimization procedure in which they are required.     

Near-optimum regulator design of singularly perturbed systems via Chandrasekhar equations

The singular perturbation theory provides a powerful design and analysis approach for model order reduction. Another method of simplifying the calculation of feedback gains in an LQG problem is the Chandrasekhar algorithm, which replaces the usual Riccati approach. The method presented in this paper combines the advantages inherent in the singular perturbation theory with those of the Chandrasekhar algorithm. This is accomplished by using lower dimensional Chandrasekhar equations for calculating the asymptotic expansion terms of the feedback gains. Two alternative design procedures are given. In one procedure the fast or boundary layer gains are calculated first followed by the slow or reduced gains. In the other procedure a more conventional design sequence is adopted. That is, first the reduced problem is solved and the boundary layer correction terms are added later on if needed.     

Synthesis of sparse planar antenna arrays with multiple constraints

Synthesis of symmetrical sparse planar antenna arrays is introduced in this paper. In order to reduce the peak sidelobe level of the radiation pattern, the element positions of the arrays are optimized by invasive weed optimization with complex boundary conditions. The proposed algorithm changes a two‐dimensional optimization problem into a linear problem, which will reduce the complexity of the optimization procedure. The optimization method can constrain the size of the array aperture, the element number of the array, and the minimum spacing of the adjacent elements simultaneously. The simulation results show the robustness and effectiveness of the proposed method.     

An automated approach to the design of decision tree classifiers

The classification of large dimensional data sets arising from the merging of remote sensing data with more traditional forms of ancillary data causes a significant computational problem. Decision tree classification is a popular approach to the problem. This type of classifier is characterized by the property that samples are subjected to a sequence of decision rules before they are assigned to a unique class. If a decision tree classifier is well designed, the result in many cases is a classification scheme which is accurate, flexible, and computationally efficient. This correspondence provides an automated technique for effective decision tree design which relies only on a priori statistics. This procedure utilizes canonical transforms and Bayes table look-up decision rules. An optimal design at each node is derived based on the associated decision table. A procedure for computing the global probability of correct classification is also provided. An example is given in which class statistics obtained from an actual Landsat scene are used as input to the program. The resulting decision tree design has an associated probability of correct classification of 0.75 compared to the theoretically optimum 0.79 probability of correct classification associated with a full dimensional Bayes classifier. Recommendations for future research are included.     

可满足性问题的三维DNA图结构算法

论文提出用三维图结构解决DNA分子计算问题,给出了解决3-SAT问题的方法。在所提出的方法中,算法所要求的步骤与公式中变量的数目相等。     

Output Regulation for a Class of Infinite Dimensional Systems with an Unknown Exosystem

This paper is about solving the output regulation problem for a class of infinite dimensional systems with an unknown exosystem. First, under the unit relative degree assumption, the infinite dimensional system is decomposed into a cascaded one composed of a one‐dimensional system and an infinite dimensional system. Then, the problem is solved by combining an adaptive internal model and an adaptive control. The presented results are illustrated via a periodic tracking problem of a heat equation.     

Adaptive mesh redistribution for the boundary element in elastostatics

An adaptive mesh redistribution strategy based on the grading function method is employed to solve the two dimensional elastostatic problem with the boundary element method. Three benchmark problems, one of which involves a crack or singularity, are treated to verify the overall procedure. The results are quite satisfactory, pointing to the fact that mesh redistribution can be used effectively along with the boundary element technique.     

Finite dimensional approximation and Newton-based algorithm for stochastic approximation in Hilbert space

This paper presents a finite dimensional approach to stochastic approximation in infinite dimensional Hilbert space. The problem was motivated by applications in the field of stochastic programming wherein we minimize a convex function defined on a Hilbert space. We define a finite dimensional approximation to the Hilbert space minimizer. A justification is provided for this finite dimensional approximation. Estimates of the dimensionality needed are also provided. The algorithm presented is a two time-scale Newton-based stochastic approximation scheme that lives in this finite dimensional space. Since the finite dimensional problem can be prohibitively large dimensional, we operate our Newton scheme in a projected, randomly chosen smaller dimensional subspace.     

Kriging-based convex subspace single linkage method with path-based clustering technique for approximation-based global optimization

This paper proposes an improved approach of the Kriging-based Convex Subspace Single Linkage Method (KCSSL method), which was reported as one of approximation-based global optimization methods. The KCSSL method consists of a convex subspace clustering procedure and a local optimization procedure. For the clustering procedure, previously, the cell-based clustering technique was employed. However, this approach will involve a huge number of convexity estimations in case of a higher dimensional problem. This will cause a very high computational cost, therefore, a path-based clustering procedure is newly developed. At first, a procedure for the convexity estimation with the Kriging method is introduced. Next, outline and detailed procedure of the proposed path-based clustering technique are explained. Also, the proposed method is applied to solving some approximate optimization problems. From the numerical results, validity and effectiveness of the proposed method are discussed.     

State-space models for infinite-dimensional systems

Distributed effects are present in almost all physical systems. In some cases these can be safely ignored but there are many interesting problems where these effects must be taken into account. Most infinite dimensional systems which are important in control theory are specifiable in terms of a finite number of parameters and hence are, in principle, amenable to identification. The state-space theory of infinite dimensional systems has advanced greatly in the last few years and is now at a point where real applications can be contemplated. The realizability criteria provided by this work can be employed effectively in the first step of the identification procedure, i.e., in the selection of an appropriate infinite dimensional model. We show that there exists a natural classification of nonrational transfer functions, which is based on the character of their singularities. This classification has important implications for the problem of finite dimensional approximations of infinite dimensional systems. In addition, it reveals the class of transfer functions for which there exist models with spectral properties closely reflecting the properties of the singularities of the transfer functions. The study of models with infinitesimal generators having a connected resolvent sheds light on some open problems in classical frequency response methods. Finally, the methods used here allow one to see the finite dimensional theory itself more clearly as the result of placing it in the context of a larger theory.     

Algorithms for the circular two‐dimensional open dimension problem

In this paper, we propose three heuristics for the circular two‐dimensional open dimension problem, also known as the circular strip cutting/packing problem. We first propose an open strip generation solution procedure that uses the best local position rule into the open strip. Second, we propose a simple augmented version of the first heuristic by introducing an exchange‐order strategy. Third, we propose a hybrid heuristic that combines beam search and a series of target values belonging to a predetermined interval search. We evaluate the performance of these heuristics on several instances varying from small to large ones. Encouraging results have been obtained.     

Nonlinear discriminant clustering based on spectral regularization

Owing to sparseness, directly clustering high-dimensional data is still a challenge problem. Therefore, obtaining their low-dimensional compact representation by dimensional reduction is an effective method for clustering high-dimensional data. Most of existing dimensionality reduction methods, however, are developed originally for classification (such as Linear Discriminant Analysis) or recovering the geometric structure (known as manifold) of high-dimensional data (such as Locally Linear Embedding) rather than clustering purpose. Hence, a novel nonlinear discriminant clustering by dimensional reduction based on spectral regularization is proposed. The contributions of the proposed method are two folds: (1) it can obtain nonlinear low-dimensional representation that can recover the intrinsic manifold structure as well as enhance the cluster structure of the original high-dimensional data; (2) the clustering results can also be obtained in the dimensionality reduction procedure. Firstly, the desired low-dimensional coordinates are represented as linear combinations of predefined smooth vectors with respect to the data manifold, which are characterized by a weighted graph. Then, the optimal combination coefficients and the optimal cluster assignment matrix are computed by maximizing the ratio between the between-cluster scatter and the total scatter simultaneously as well as preserving the smoothness of the cluster assignment matrix with respect to the data manifold. Finally, the optimization problem is solved in an iterative procedure, which is proved to be convergent. Experiments on UCI data sets and real world data sets demonstrated the effectiveness of the proposed method for both clustering and visualization high-dimensional data set.