Showing papers on "Optimal design published in 1994"
TL;DR: In this article, optimal Latin-hypercube designs minimizing the integrated mean squared error (IMSE) and maximizing entropy are considered, and a 2-stage (exchange and Newton-type) computational algorithm for finding the proposed design is presented.
536 citations
TL;DR: In this paper, a two-stage decomposition model is proposed for the optimal design of a water distribution network, where the master problem is nonsmooth and nonconvex, while the inner problem is linear.
Abstract: Optimal design of a water distribution network is formulated as a two-stage decomposition model. The master (outer) problem is nonsmooth and nonconvex, while the inner problem is linear. A semi-infinite linear dual problem is presented, and an equivalent finite linear problem is developed. The overall design problem is solved globally by a branch and bound algorithm, using nonsmooth optimization and duality theory. The algorithm stops with a solution and a global bound, such that the difference between this bound and the true global optimum is within a prescribed tolerance. The algorithm has been programmed and applied to a number of examples from the literature. The results demonstrate its superiority over previous methods.
257 citations
TL;DR: This paper proposed a modification of the D-optimal approach that preserves the flexibility and ease of use of algorithmic designs while being more resistant to the biases caused by an incorrect model.
Abstract: D-optimal and other computer-generated experimental designs have been criticized for being too dependent on an assumed statistical model. To address this criticism, we introduce the notion of empirical models that have both primary and potential terms. Combining this idea with the Bayesian paradigm, this article proposes a modification of the D-optimal approach that preserves the flexibility and ease of use of algorithmic designs while being more resistant to the biases caused by an incorrect model. These designs provide a Bayesian justification for resolution IV designs. Several theoretical examples and a practical example from the literature demonstrate the advantages of the proposed method.
211 citations
01 Oct 1994
TL;DR: In this article, optimal robust control scalar LQG optimal control problem and solution scalar H infinity optimal control problems and solution multivariable H infinity control problem, and solution robust control design procedures H2 optimal filtering smoothing and prediction problems.
Abstract: Introduction to optimal robust control scalar LQG optimal control problem and solution scalar H infinity optimal control problem and solution multivariable LQG optimal control problems and solution multivariable H infinity optimal control problem and solution robust control design procedures H2 optimal filtering smoothing and prediction problems H infinity optimal filtering smoothing and prediction problems industrial applications of H infinity optimal control.
200 citations
TL;DR: Constrained and compound optimal designs represent two well-known methods for dealing with multiple objectives in optimal design as reflected by two functionals φ1 and φ2 on the space of information matrices as discussed by the authors.
Abstract: Constrained and compound optimal designs represent two well-known methods for dealing with multiple objectives in optimal design as reflected by two functionals φ1 and φ2 on the space of information matrices A constrained optimal design is constructed by optimizing φ2 subject to a constraint on φ1, and a compound design is found by optimizing a weighted average of the functionals φ = λφ1 + (1 - λ) φ2, 0 ≤ λ ≤ 1 We show that these two approaches to handling multiple objectives are equivalent
156 citations
TL;DR: In this paper, theoretical regularity and practical requirements of the design velocity field are discussed and the crucial step of using the velocity field to update the finite element mesh in the design optimization process is emphasized.
144 citations
TL;DR: In this paper, the structural optimization presented in this paper is based on an evolutionary procedure, developed recently, in which the low stressed part of a structure is removed from the structure step-by-step until an optimal design is obtained.
Abstract: The structural optimization presented in this paper is based on an evolutionary procedure, developed recently, in which the low stressed part of a structure is removed from the structure step‐by‐step until an optimal design is obtained. Various tests have shown the effectiveness of this evolutionary procedure. The purpose of this paper is to present applications of such an evolutionary procedure to the optimal design of structures with multiple load cases or with a traffic (moving) load.
139 citations
TL;DR: A new technique for the design optimization of electromagnetic devices that adopts the genetic algorithms (GAs) as the search method is presented, applied to the optimization of the shape of a pole face in an electric motor.
Abstract: A new technique for the design optimization of electromagnetic devices that adopts the genetic algorithms (GAs) as the search method is presented. The method is applied to the optimization of the shape of a pole face in an electric motor. The electromagnetic analysis of the devices implemented is performed using 2D finite elements. The results show an excellent promise and potential of using GAs as an efficient technique for the optimal design problem. >
97 citations
Book•
01 Jan 1994
TL;DR: A survey of experiments in the field of experimental design can be found in this article, where the authors discuss the nature and role of theory in science, and three principles of Experimental Design are discussed.
Abstract: 1. The Processes of Science. 1.1 Introduction. 1.2 Development of Theory. 1.3 The Nature and Role of Theory in Science. 1.4 Varieties of Theory. 1.5 The Problem of General Science. 1.6 Causality. 1.7 The Upshot. 1.8 What Is An Experiment?. 1.9 Statistical Inference. 2. Principles of Experimental Design. 2.1 Confirmatory and Exploratory Experiments. 2.2 Steps of Designed Investigations. 2.3 The Linear Model. 2.4 Illustrating Individual Steps: Study 1. 2.5 Three Principles of Experimental Design. 2.6 The Statistical Triangle and Study 2. 2.7 Planning the Experiment. 2.8 Cooperation between Scientist and Statistician. 2.9 General Principle of Inference. 2.10 Other Considerations for Experimental Designs. 3. Survey of Designs and Analyses. 3.1 Introduction. 3.2 Error-Control Designs. 3.3 Treatment Designs. 3.4 Combining Ideas. 3.5 Sampling Designs. 3.6 Analysis and Statistical Software. 3.7 Summary. 4. Linear Model Theory. 4.1 Introduction. 4.2 Representation of Linear Models. 4.3 Functional and Classificatory Linear Models. 4.4 The Fitting Of Y .= X-. 4.5 The Moore-Penrose Generalized Inverse. 4.6 The Conditioned Linear Model. 4.7 The Two-Part Linear Model. 4.8 A Special Case of a Partitioned Model. 4.9 Three-Part Models. 4.10 The Two-Way Classification Without Interaction. 4.11 The K-Part Linear Model. 4.12 Balanced Classificatory Structures. 4.13 Unbalanced Data Structures. 4.14 Analysis of Covariance Model. 4.15 From Data Analysis to Statistical Inference. 4.16 The Simple Normal Stochastic Linear Model. 4.17 Distribution Theory with GMNLM. 4.18 Mixed Models. 5. Randomization. 5.1 Introduction. 5.2 The Tea Tasting Lady. 5.3 A Triangular Experiment. 5.4 The Simple Arithmetical Experiment. 5.5 Randomization Ideas for Intervention Experiments. 5.6 The General Idea of the Experiment Randomization Test. 5.7 Introduction to Subsequent. 6. The Completely Randomized Design. 6.1 Introduction and Definition. 6.2 The Randomization Process. 6.3 The Derived Linear Model. 6.4 Analysis Of Variance. 6.5 Statistical Tests. 6.6 Approximating the Randomization Test. 6.7 CRD with Unequal Numbers of Replications. 6.8 Number of Replications. 6.9 Subsampling In A CRD. 6.10 Transformations. 6.11 Examples Using SASR. 7. Comparisons of Treatments. 7.1 Introduction. 7.2 Comparisons for Qualitative Treatments. 7.3 Orthogonality and Orthogonal Comparisons. 7.4 Comparisons for Quantitative Treatments. 7.5 Multiple Comparison Procedures. 7.6 Grouping Treatments. 7.7 Examples Using SAS. 8. Use of Supplementary Information. 8.1 Introduction. 8.2 Motivation of the Procedure. 8.3 Analysis of Covariance Procedure. 8.4 Treatment Comparisons. 8.5 Violation of Assumptions. 8.6 Analysis of Covariance with Subsampling. 8.7 The Case of Several Covariates. 8.8 Examples Using SASR. 9. Randomized Block Designs. 9.1 Introduction. 9.2 Randomized Complete Block Design. 9.3 Relative Efficiency of the RCBD. 9.4 Analysis of Covariance. 9.5 Missing Observations. 9.6 Nonadditivity in the RCBD. 9.7 The Generalized Randomized Block Design. 9.8 Incomplete Block Designs. 9.9 Systematic Block Designs. 9.10 Examples Using SASR. 10. Latin Square Type Designs. 10.1 Introduction and Motivation. 10.2 Latin Square Design. 10.3 Replicated Latin Squares. 10.4 Latin Rectangles. 10.5 Incomplete Latin Squares. 10.6 Orthogonal Latin Squares. 10.7 Change-Over Designs. 10.8 Examples Using SAS. 11. Factorial Experiments: Basic Ideas. 11.1 Introduction. 11.2 Inferences from Factorial Experiments. 11.3 Experiments with Factors at Two Levels. 11.4 The Interpretation of Effects and Interactions. 11.5 Interactions: A Case Study. 11.6 2n Factorials in Incomplete Blocks. 11.7 Fractions of 2n Factorials. 11.8 Orthogonal Main Effect Plans for 2n Factorials. 11.9 Experiments with Factors at Three Levels. 11.10experimentswith Factors at Two and Three Levels. 11.11examples Using SAS. 12. Response Surface Designs. 12.1 Introduction. 12.2 Formulation of the Problem. 12.3 First-Order Models and Designs. 12.4 Second-Order Models and Designs. 12.5 Integrated Mean Squared Error Designs. 12.6 Searching For an Optimum. 12.7 Experiments with Mixtures. 12.8 Examples Using SAS. 13. Split-Plot Type Designs. 13.1 Introduction. 13.2 The Simple Split-Plot Design. 13.3 Relative Efficiency of Split-Plot Design. 13.4 Other Forms of Split-Plot Designs. 13.5 Split-Block Design. 13.6 The Split-Split-Plot Design. 13.7 Examples Using SAS. 14. Designs with Repeated Measures. 14.1 Introduction. 14.2 Methods for Analyzing Repeated Measures Data. 14.3 Examples Using SAS. 14.4 Exercises.
91 citations
TL;DR: This algorithm allows blocking, including the use of unequal block sizes, in the design of experiments on personal computers (PCs), and allows some of the candidate points, those in the experiment which has been carried out, to be forced into the design.
Abstract: Optimal design algorithms are particularly useful for creating designs in difficult situations, such as when experimental conditions enforce inconvenient block sizes. Several packages are now available for computer-aided design of experiments on personal computers (PCs) either in the form of Fortran source code or as easy-to-use commercial packages. Most of these packages could not find a good design for say a 23x 32 X 14 experiment in blocks of size 10. This kind of requirement is not unusual where there are say 14 species of timber or types of cheese, and the block size is dictated by the number of experimental runs which can be carried out in one day or from one batch of material. Our algorithm allows blocking, including the use of unequal block sizes. Another important application is in augmenting an experiment which has already been carried out. Our algorithm allows some of the candidate points, those in the experiment which has been carried out, to be forced into the design. Let X be an N x k matrix containing N possible or candidate design points. We want to find a subset of n out of the N points which maximizes the determinant D = IXnXn I
84 citations
TL;DR: In this paper, a probabilistic optimal design methodology for complex structures modelled with finite element methods is presented, where the main emphasis is on developing tools suitable for optimization and an advanced second-moment method is employed to evaluate the failure probability of the performance function.
TL;DR: In this paper, a concurrent design method of mechanical structure and control for two-link high speed robots is developed, in which comprehensive design parameters describing arm link geometry, actuator locations, and feedback gains are optimized with respect to the settling time of the system.
Abstract: A concurrent design method of mechanical structure and control is developed for two-link high speed robots. An integrated design approach to achieve high speed positioning is explored, in which comprehensive design parameters describing arm link geometry, actuator locations, and feedback gains are optimized with respect to the settling time of the system. First, a two-link, nonrigid arm is analyzed and a simple dynamic model representing rapid positioning processes is obtained. Optimal feedback gains minimizing the sealing time are obtained as functions of structural parameters involved in the dynamic model. The structural parameters are then optimized using a nonlinear programming technique in order to obtain an overall optimal performance. Based on the optimal design, a prototype high speed robot is built and tested
TL;DR: In this article, the shape sensitivity analysis for nonlinear parabolic systems is presented and coupled with nonlinear programming to optimize the design of a sand casting, where the sensitivity is derived via the domain parameterization method and computed with the finite element method.
TL;DR: The spatial domain is fixed during the optimization of nonlinear parabolic systems which govern a variety of processes including solidification and is exemplified for the optimal manufacture of crystals.
TL;DR: In this article, a new optimality criterion was proposed to minimize the variance of the least squares estimators for the coefficients of polynomial regression models of degree l = 1, 2, m - 1, m − 1 and l = m − 2, l = l. The canonical moments of the optimal measure satisfy a nonlinear equation and the support points are given by the zeros of an orthogonal polynomials.
Abstract: In the polynomial regression model of degree $m \in \mathbb{N}$ we consider the problem of determining a design for the identification of the correct degree of the underlying regression. We propose a new optimality criterion which minimizes a weighted $p$-mean of the variances of the least squares estimators for the coefficients of $x^l$ in the polynomial regression models of degree $l = 1,\cdots, m$. The theory of canonical moments is used to determine the optimal designs with respect to the proposed criterion. It is shown that the canonical moments of the optimal measure satisfy a (nonlinear) equation and that the support points are given by the zeros of an orthogonal polynomial. An explicit solution is given for the discrimination problem between polynomial regression models of degree $m - 2, m - 1$ and $m$ and the results are used to calculate the discrimination designs in the sense of Atkinson and Cox for polynomial regression models of degree $1,\cdots,m$.
TL;DR: In this article, the meter placement problem is formulated such that it results in a multi-objective optimization by seeking the best solution in terms of estimation accuracy and metering cost.
Abstract: With the help of meter measuring systems, state estimation of water distribution systems can show not only the hydraulic properties of all system components, but it can also provide an estimate of errors to enhance engineers' confidence in the results. The number of meters as well as their topological distribution in networks strongly influences the accuracy of the estimates. The meter placement problem is formulated such that it results in a multi-objective optimization by seeking the best solution in terms of estimation accuracy and metering cost. A method employing a dynamic analysis of the co variance matrix of state variables and the decision-trees technique has been developed for the design of an optimal meter placement for state estimation of water distribution systems. The conjugate gradient technique is used to solve the non-linear least-squares problem of state estimation. Two test examples are presented to assist in the explanation of the algorithm.
TL;DR: In this paper, a three-phase design process is used for structural optimization of two-dimensional solid structures, including a crane hook and a bicycle frame, where an initial topology is created by a homogenization method as a gray-scale image and then transformed to a realizable design using computer vision techniques.
Abstract: Structural optimization procedures usually start from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.
TL;DR: In this article, a new control design method for the control of flexible systems that not only guarantees closed-loop asymptotic stability but also effectively suppresses vibration is presented.
Abstract: This paper presents a new control design method for the control of flexible systems that not only guarantees closed-loop asymptotic stability but also effectively suppresses vibration. This method allows integrated determination of actuator/sensor locations and feedback gain via minimization of an energy criterion, which is chosen as the integrated total energy stored in the system. The energy criterion is determined via an efficient solution of the Lyapunov equation and minimized with a quasi-Newton or recursive quadratic programming algorithm. The prerequisite for this optimal design method is that the controlled system be asymptotically stable. This study shows that when the controller structure is a collocated direct velocity feedback design with positive definite feedback gain, the number and placement of actuators/sensors are the only factors needed to determine necessary and sufficient conditions for ensuring closed-loop asymptotic stability. The application of this method to a simple flexible structure confirms the direct relationship between our optimization criterion and effectiveness in vibration suppression.
TL;DR: An analysis and optimal design of a capacitor-driven inductive coilgun and the proposed algorithm gives a better result in the energy efficiency of the system, namely it enables one to obtain a higher muzzle velocity of the projectile with the same amount of energy.
Abstract: The paper presents an analysis and optimal design of a capacitor-driven inductive coilgun. An equivalent circuit is used for a launch simulation of the coilgun. The circuit equations are solved together with the equation of motion of the projectile by using the Runge-Kutta method. The numerical results are compared with the experimental values to verify the usefulness of the developed simulation program. It is shown that the numerical and the experimental results are in a good agreement. In the design of the system optimization is achieved by employing the genetic algorithm. The resultant specifications of the coilgun optimally designed by the proposed algorithm are tested by experiment. Finally the obtained results are compared with those designed by approximate equations and by linear search methods as well. It is found that the proposed algorithm gives a better result in the energy efficiency of the system, namely it enables one to obtain a higher muzzle velocity of the projectile with the same amount of energy. >
TL;DR: Since at the synthesis level the reactor network represents an exhaustive superposition of the existing structural and operational alternatives, the approach fully exploits these alternatives and coordinates a weighted optimal search that improves the objective and accommodates a stable reactor network.
Abstract: A systematic methodology applicable to the optimal design of stable process systems is presented. It is based on the formulation of a parametric problem that provides bounds on the optimal stable solution and an iterative algorithmic approach that attains convergence of the bounds in a finite number of iterations. The bounds on the optimal stable solution are based on analytical expressions of bounds on the eigenvalues of the Jacobian matrix using the concept of the measure of the matrix. When extended to the synthesis problem of reactor networks, the approach is able to couple the optimization problem with stability issues even in cases where the number of reactors is large and the reaction mechanism is described by a general complex reaction scheme. Furthermore, since at the synthesis level the reactor network represents an exhaustive superposition of the existing structural and operational alternatives, the approach fully exploits these alternatives and coordinates a weighted optimal search that improves the objective and accommodates a stable reactor network. This approach is not restricted to the synthesis of reactor networks and can be applied to the design of total process flowsheets.
TL;DR: In this paper, three optimization levels are identified: (1) Level 1-component optimization; (2) Level 2-structural configuration optimization; and (3) Level 3-overall system optimization.
Abstract: Superstructure design of short‐ and medium‐span highway bridge systems may be conceived as a process of multilevel and multiobjective optimization. Three optimization levels are identified: (1) Level 1—component optimization; (2) level 2—structural configuration optimization; and (3) level 3—overall system optimization. Designs may be optimized by separately or simultaneously considering one, two, or more of the following objectives: cost, prestressing steel or concrete consumption, and superstructure depth. The optimal solution may be found by a sequence of nonlinear programming and sieve‐search techniques. Levels 1 and 2 optimizations identify the best solutions for specific components (precast I‐girders, voided and solid slabs, single‐ and two‐cell box girders) and layouts (for precast I‐girder: one, two, and three; simple or continuous spans). Level 3 optimization selects the overall best system for given bridge lengths, widths, and traffic loadings. The present study results in: (1) A systematic proc...
TL;DR: The suitability of this model for use in medical applications is reviewed in this paper, with particular emphasis on its implications for design theory, and the optimal designs for two treatments under an amended model are presented.
TL;DR: Based on the duality between a nonlinear approximation problem of Chebyshev type and a weighted polynomial regression problem, in many cases the optimal approximate designs on nonnegative and nonpositive experimental regions are found to be supported by the extrema of the only equioscillating weighted poynomial over this region with leading coefficient 1.
Abstract: Based on a duality between $E$-optimality for (sub-) parameters in weighted polynomial regression and a nonlinear approximation problem of Chebyshev type, in many cases the optimal approximate designs on nonnegative and nonpositive experimental regions $\lbrack a, b\rbrack$ are found to be supported by the extrema of the only equioscillating weighted polynomial over this region with leading coefficient 1. A similar result is stated for regression on symmetric regions $\lbrack -b, b\rbrack$ for certain subparameters, provided the region is "small enough," for example, $b \leq 1$. In particular, by specializing the weight function, we obtain results of Pukelsheim and Studden and of Dette.
TL;DR: In this paper, the authors examined the A, D, E and G-efficiencies of using the optimal design for the polynomial regression model of degree k when the hypothesized model is of degree j and 1 Q j < k Q 8.
TL;DR: In this article, an effective algorithm for constructing optimal or near-optimal incomplete block designs with up to 100 treatments is described, and the algorithm is found to perform well when evaluated against 874 optimal and near-optimally incomplete block design in the literature.
Abstract: This article describes an effective algorithm for constructing optimal or near-optimal incomplete block designs with up to 100 treatments. The algorithm is found to perform well when evaluated against 874 optimal or near-optimal incomplete block designs in the literature. Examples that motivated the development of the algorithm are given.
TL;DR: This work surveys some of the existing approaches to optimal design of multivariate sensors, according to the different types of systems they are applied to and discusses two examples of optimal sensor design.
Abstract: The design of sensing systems for the measurement of multiple physical quantities related to a dynamical system is considered. A multivariate sensor comprises several simple transducers, each measuring a scalar quantity that comes from the combination of the components of the quantity to be measured. From the collection of measurements of single transducers at different times, the desired information is extracted by analogue or digital processing. Besides the choice of technological characteristics of the transducers to be employed, the designer of multivariate sensors is usually allowed some freedom in choosing the number of transducers, their arrangement in the system, and the time scheduling of their measurements. These choices are the subject of optimal policies in the design phase, whose goal is to maximize some performance (or minimize some cost) criterion. We survey some of the existing approaches to optimal design of multivariate sensors, according to the different types of systems they are applied to. Two examples of optimal sensor design are discussed as an illustration of the methods.
01 Jan 1994
TL;DR: In this article, the GA technique is applied to the search for the optimal water distribution system design, which simulates mechanisms of natural population genetics in artificial evolutionary strategy, and the GA optimisation model coupled with a steady state hydraulic simulation model generates and evaluates trial pipe network designs in search of optimal designs.
Abstract: All communities need an adequate water supply. A water distribution pipe network, water storage tanks and pumping station facilities are the usual features of a water supply system. The selection of the layout, capacity and operation of these components of the distribution system significantly affects the hydraulic and economic efficiency of the design. The genetic algorithm (GA) technique is applied to the search for the optimal water distribution system design. The GA technique simulates mechanisms of natural population genetics in artificial evolutionary strategy. The genetic algorithm optimisation model coupled with a steady state hydraulic simulation model generates and evaluates trial pipe network designs in search of optimal designs just as nature may save, combine and manipulate genetic information in the process of evolution. The genetic algorithm search is applied to a case study which demonstrates its flexibility and the opportunity for significant cost savings offered by this method.
TL;DR: In this paper, a new method allowing the optimal design of baffled shell-and-tube heat exchangers is discussed, where simplified expressions describing interaction between heat transfer and pressure drop are presented as simplified expressions that can be used for optimal design from economic viewpoint.
TL;DR: In this article, a method for constructing E-optimal designs for a broad class of two-parameter models is presented, based on the two-dimensional geometry of the induced design space and of the first Elfving set.
Abstract: SUMMARY A method for constructing E-optimal designs for a broad class of two-parameter models is presented. The procedure is based on the two-dimensional geometry of the induced design space and of the first Elfving set and guarantees to find E-optimal designs which have exactly two points of support. For E-optimal designs based on three support points, the procedure is less clear-cut. Efficient designs based on 'essentially' two points can be constructed using the geometry of the first Elfving set, but globally E-optimal designs must, at least in general, be found by other strategies, such as those based on symmetry considerations, the geometry of the second Elfving set, systematic searches, or numerical methods. The methodology is illustrated by means of selected examples involving generalised linear models.