Showing papers on "Optimal design published in 1981"

Practical Experiment Designs: for Engineers and Scientists

Abstract: Preface. Acknowledgments. FUNDAMENTALS OF EXPERIMENT DESIGN. Introduction to Experiment Design: Fundamental Concepts. Introduction to Experiment Design: Elements of Decision Making. Simple Comparative Experiments: Decisions About Population Means. Simple Comparative Experiments: Decisions About Population Variances. Sequential Experiments. TWO-LEVEL MULTIVARIABLE EXPERIMENTS. Two-Level Multivariable Experiments: Eight-Trial Hadamard Matrix Designs. Two-Level Multivariable Experiments: Hadamard Matrices Greater Than Order 8. John's Three-Quarter Fractional Factorials. Unbalanced Resolution V Designs. Resolution V Designs with Efficiency = 1. Hadamard Matrix Designs for Binomial and Poisson Responses. Summary of Two-Level Matrix Designs. A Computer Program for Generating Hadamard Matrix Designs and Analyzing the Data from Such Designs. Analysis of Goodness. Alternative Methods of Analysis. MULTILEVEL MULTIVARIABLE EXPERIMENTS. Multilevel Experiments with Qualitative Variables. Multilevel Experiments with QuantitativeVariables. Experiment Designs for Chemical Composition Experiments. Random-Strategy Experiments. RELATED TOPICS. Blocking an Experiment. Validation of Test Methods. Concepts for a Complete Project Strategy. Project Engineer's Game. Estimation of Variance. Testing Distributions. GENERAL REFERENCES, SYMBOLS, TABLES, AND ANSWERS TO EXERCISES. General References. Symbols. Tables. Answers to Exercises. Index.

Incomplete Block Designs for Comparing Treatments Wth a Control: General Theory

Abstract: In this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control. This class of designs is appropriate for comparing simultaneously p ≥ 2 test treatments with a control treatment (the so-called multiple comparisons with a control (MCC) problem) when the observations are taken in incomplete blocks of common size k < p + 1. For this problem we propose a new general class of incomplete block designs that are balanced with respect to (wrt) test treatments. We shall use the abbreviation BTIB to refer to such designs. We study their structure and give some methods of construction. A procedure for making exact joint confidence statements for this multiple comparisons problem is described. By using a new concept of admissibility of designs, it is shown how “inferior” designs can be eliminated from consideration, and attention limited to a small class of BTIB designs that can be constructed from so-called generator designs in the minimal complete class of such d...

Optimized blood sampling protocols and sequential design of kinetic experiments

Abstract: Design of optimal blood sampling protocols for kinetic experiments is discussed and evaluated, with the aid of several examples--including an endocrine system case study. The criterion of optimality is maximum accuracy of kinetic model parameter estimates. A simple example illustrates why a sequential experiment approach is required; optimal designs depend on the true model parameter values, knowledge of which is usually a primary objective of the experiment, as well as the structure of the model and the measurement error (e.g., assay) variance. The methodology is evaluated from the results of a series of experiments designed to quantify the dynamics of distribution and metabolism of three iodothyronines, T3, T4, and reverse-T3. This analysis indicates that 1) the sequential optimal experiment approach can be effective and efficient in the laboratory, 2) it works in the presence of reasonably controlled biological variation, producing sufficiently robust sampling protocols, and 3) optimal designs can be highly efficient designs in practice, requiring for maximum accuracy a number of blood samples equal to the number of independently adjustable model parameters, no more or less.

Cost and performance of VLSI computing structures

Abstract: Using VLSI technology, it will soon be possible to implement entire computing systems on one monolithic silicon chip. Conducting paths are required for communicating information throughout any integrated system. The length and organization of these communication paths place a lower bound on the area and time required for system operations. Optimal designs can be achieved in only a few of the many alternative structures. Two illustrative systems are analyzed in detail: a RAM-based system and an associative system. It is shown that in each case an optimum design is possible using the area-time product as a cost function.

Design of Experiments for Estimating Enzyme and Pharmacokinetic Parameters

Abstract: Principles are described for optimally estimating precise model parameters. D-optimized designs, which minimize the volumes of joint confidence regions for the parameters, generally replicate p sampling points. (p is the number of parameters.) The observations are repeated at equal frequency when the estimation of all model parameters is essential, but often in unequal proportions if only some of the parameters are of interest. Usually, one of the design points yields the maximal experimentally attainable response. In the presence of constant relative errors another point measures the smallest possible response. The principles of optimization are applied to simple enzyme and pharmacokinetic models, and designs yielding the most precise parameters are described. These designs provide guidelines, and not rules, for experimentation. In practice, a few observations could test the validity of the model while others could be obtained close to the proposed design points. The usefulness of the strategy is demonstrated by the substantially reduced estimating efficiency (larger parameter variance) of frequently applied experimental designs, especially when the number of measurements is increased.

Role of Figures of Merit in Design Optimization and Technology Assessment

Abstract: An economical preliminary design procedure is discussed which transforms the complex relationships of a sophisticated design synthesis performance analysis into simpler second-order expressions through a regression analysis. These relationships can then be used to determine constrained optimal designs for a wide variety of figures of merit. A design study of military and commercial cargo transports is described in which optimum designs for seven different figures of merit are determined. Differences from previous studies due to technology representation are discussed and off-design penalties, trade boundaries, and design sensitivities are developed.

Optimal design of pid regulators

Abstract: Tuning of three-term controllers, a widely popular device for process control, has always been accomplished by semi-empirical rules. The aim of this paper is to establish a link between PID regulators and optimal feedback design for linear systems. After showing how the optimal control theory can be tailored to the design of optimal regulators, the results are extended to the discrete-time case and the feasibility of a microprocessor implementation is assessed with the aid of benchmark tests

An Algorithm for Optimum Structural Design without Line Search

Abstract: : In this paper, a new optimization algorithm for optimal design of engineering systems is presented. The main feature of the new algorithm is that it does not rely on one dimensional search to compute a step size at any design iteration. Implication of the feature is that algorithm requires evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of constraints for such systems is very expensive. The reason for the high cost is that many constraints for such design problems are implicit functions of design variables. Thus their evaluation requires solution for a high dimensional finite element model for the system. The new algorithm is based on finding upper and lower bounds on the optimum cost and is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general purpose computer code GRP2 is developed. The code is used to solve several small scale problems to gain experience and insight into the algorithm. Numerical experience with examples is discussed. It is shown that the algorithm has substantial potential for applications in optimal design of engineering systems. (Author)

Approximate Behavior Models for Optimum Structural Design

Abstract: : Efficient reanalysis models, which provide high quality explicit approximations for the structural behavior, are introduced. The presented algorithms are based on a series expansion which is shown to be equivalent to a simple iteration procedure. Only the decomposed stiffness matrix, known from exact analysis of the initial design, is required to obtain the approximate expressions. Two approaches of accelerated convergence are proposed to improve the quality of the approximations: (a) An approach where a scalar multiplier, used for scaling of the initial design, is chosen prior to the solution as the accelerating parameter; (b) An approach where information gathered during calculations of the series coefficient is used to improve the convergence rate. Numerical examples illustrate the efficiency and the quality of the proposed approximations. A special attention is focused on reanalyses along a line, a problem typical to many optimal design procedures. The computational effort in this case is considerably reduced, since only a single independent variable is involved.

A Comparison of Two Criteria for the Design of Experiments for Discriminating Between Models

Abstract: Box and Hill (1967) criticized a criterion for sequential experimental designs suggested by Hunter and Reiner (1965) for ignoring the effect of the variance of predicted responses Conditions are established under which the two criteria are asymptotically equivalent when there are only two rival models For moderate samples, both for cases in which the conditions for equivalence hold and for cases in which they do not, simulations fail to reveal any difference in behavior between the two criteria The extension of the results to criteria for more than two models is discussed

Sequentially Generated Second Order Quasi D-Optimal Designs for Experiments With Mixture and Process Variables

Abstract: Second order designs for experiments with mixture and process variables are proposed. They are constructed on the basis of continuous D-optimal designs by use of a three-stage procedure for sequentially generating optimal designs. The determinants of the information matrices of the designs obtained are very near to those of continuous D-optimal designs. Tables of discrete quasi D-optimal designs for q + r ≤ 7 are given, where q is the number of mixture components and r is the number of process variables. The experimenter can choose the number of trials N within the interval k ≤ N ≤ min(2k, k + 20), where k is the number of model coefficients. An application of the proposed designs in an investigation of truck tire properties is given.

Uniqueness and Eventual Uniqueness of Optimal Designs in Some Time Series Models

Abstract: : Earlier results on the uniqueness and eventual uniqueness of optimal designs for certain time series models are extended to a wider class of processes which includes those with covariance structures such as that of multiple integrals of Brownian motion and Brownian bridge processes. The relationship between the problems of regression design for time series and piecewise polynomial approximation with free breakpoints is discussed and, consequently, asymptotic results obtained by Sacks and Ylvisaker (1970) are seen to hold under weaker assumptions for these processes.

Interactive optimal design of truss structures

Abstract: A CAD system based on combining structural optimization methods and graphical interaction is presented. The optimization methods implement the automated decisions and algorithms while the interaction provides the means to implement the designer's decisions. A new interactive optimization procedure for optimal truss design is proposed. The structural topology, geometry and member sizes are treated as design variables. Results show that the system provides a powerful tool to obtain a practical optimum design.

Optimal design of reinforced concrete frames based on inelastic analysis

Abstract: The paper presents a formulation for the nonlinear optimization of reinforced concrete frames based on inelastic analysis. A computer program is developed for this formulation and is described with the aid of flow-charts. Important computational steps of the optimization procedure are also given. Four selected frames are optimized using the program and the results are presented. It is concluded that the formulation leads to minimum cost designs of reinforced concrete frames through realistic analysis.

Shape Optimal Design of Elastic Structures

Abstract: : This paper investigates a relatively new class of structural optimization problems that are expected to be important in future applications. Instead of selecting explicit design parameters or functions defining dimensions of a distributed parameter structure over one or two space dimensions, as is normally done in structural optimization, the shape of the elastic solid under consideration plays the role of the design variable. The shape design formulation, for two and three dimensional elastic structures, is essential when load and support conditions lead to fully planar or three dimensional displacement fields that can not adequately be modeled by assumptions arising in beam, plate, or shell theory.

The interplay of optimality and combinatorics in experimental design

Abstract: The design of statistical experiments, as developed by R. A. Fisher and his followers, often used combinatorial structures that yielded simple calculation of estimates and/or symmetric variances and covariances. Examples are block designs with balance, regression experiments with equally spaced observations, etc. More recently, considerations of optimality (choosing a design that achieves most accurate inference in some sense) have sometimes justified the traditional designs, but have sometimes led to new combinatorial investigations. Illustrations are given.

Some classes of optimality criteria and optimal designs for complete two-way layouts

Abstract: For a given class of linear models in standard form an optimal experimental design is to be chosen for estimating some linear functions of the unknown parameters. An optimality criterion is defined to be a real function of the covariance matrices of the Gauss-Markov estimators. Conditions which are imposed on the criteria are monotonicity, quasiconvexity or quasiconcavity, and invariance or order-invariance. A characterization of the $D$-criterion by order-invariance is included which strengthens a result of P. Whittle. In the main part of the paper optimal designs for the usual two-way layouts in ANOVA are computed for large classes of optimality criteria. Some related optimization problems are solved with the technique of majorization of vectors in the sense of Schur.

Optimizing Distributed Structures for Maximum Flutter Load

Abstract: Introduction I in design optimization of distributed structures is increasing. A survey of optimization under nonconservative loading reveals, however, that virtually all work done in the area has been restricted to very simple structural domains and very simplified design spaces. Besides methods from optimal control theory, typical approaches have consisted in assuming a design function of simple form for the whole domain and optimizing its coefficients through a search in few dimensions or in using a finite-element model and optimizing the location of its nodes through discrete sensitivity methods. Such approaches allow only relative optimization to take place within a restricted design space which cannot be enlarged without problems: completeness of the general design function and convergence for the former, and size of the supporting analysis for the latter. This Note describes a method, based on ideas similar to some in Ref. 5, to find essentially true optimal designs for a wide class of distributed structures undergoing flutter in the presence of damping. Design has the form of a general function described by its values at points, whose number can be increased at will with little effort and without affecting the size of analysis. We solve a hitherto unsolved problem, and indicate how this method may be combined with the finiteelement method to solve large-scale problems in complex structural domains.

Unexpected Results in Structural Optimization

Abstract: Examples are presented to show that optimal designs may have unexpected properties that require particularly careful formulation of problems of structural optimization.