Showing papers on "Optimal design published in 1991"

Research Design and Statistical Analysis

Abstract: Preliminary Considerations Samples and Populations Some Important Distributions Between-Subjects Designs - One Factor Between-Subjects Designs - Several Factors Contrasts Among Means Trend Analysis Repeated-Measures Designs Mixed Designs - Combining Between-Subject and Within-Subjects Factors Hierarchical Designs Latin Squares and Related Designs Bivariate Correlation and Regression Analysis of Covariance More About Correlation Multiple Regression Regression with Categorical Variables Appendices - Notation and Summation Operations, Expected Values and Their Applications, Matrix Algebra, Statistical Tables, Control Information for Computer Programmes for Statistical Analysis.

Genetic search strategies in multicriterion optimal design

Abstract: The present paper describes an implementation of genetic search methods in multicriterion optimal designs of structural systems with a mix of continuous, integer and discrete design variables. Two distinct strategies to simultaneously generate a family of Pareto optimal designs are presented in the paper. These strategies stem from a consideration of the natural analogue, wherein distinct species of life forms share the available resources of an environment for sustenance. The efficacy of these solution strategies are examined in the context of representative structural optimization problems with multiple objective criteria and with varying dimensionality as determined by the number of design variables and constraints.

Optimal weights for experimental designs on linearly independent support points

Abstract: An explicit formula is derived to compute the $A$-optimal design weights on linearly independent regression vectors, for the mean parameters in a linear model with homoscedastic variances. The formula emerges as a special case of a general result which holds for a wide class of optimality criteria. There are close links to iterative algorithms for computing optimal weights.

Optimum experimental design for discriminating between two rival models in the presence of prior information

Abstract: SUMMARY The design of experiments for discriminating between two rival models in the presence of prior information is analyzed. The method of Atkinson & Fedorov is extended. A theorem derived from the Kiefer-Wolfowitz General Equivalence Theorem is used to construct and check optimal designs. Some examples are provided. This paper is concerned with the design of experiments for discriminating between two regression models, one or both of which may be nonlinear in the parameters. Atkinson & Fedorov (1975a) describe T-optimum designs for this purpose which are optimum when it is known which one of the models is true. The designs, which satisfy an equivalence theorem of optimum design theory, are locally optimum, in the sense that they depend upon the values of the unknown parameters of the true model. In the present paper we extend the theory to situations in which there is a specified prior probability that each model is true and, conditionally on this probability, prior distributions for the parameters in the two models are specified. Our central result is that such designs again satisfy an equivalence theorem which can be used both for the construction of designs and for checking the optimality of a proposed design. In the next section we give the background to the problem and introduce our notation. The equivalence theorem for T-optimum designs with prior distributions is presented in ? 3. Examples are in ? 4. 2. BACKGROUND The aim of the experiment is to maximize the expected noncentrality parameter of the false model, the expectation being taken over models and over the prior distributions of the parameters. To be more precise we introduce our notation which is based on that of Silvey (1980, Ch. 3). Let , a compact set, be the design region; let X be the class of all probability

Compensator design for stability enhancement with collocated controllers

Abstract: A continuum model rather than a finite element model is used. The optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite-dimensional theory developed by the author despite the lack of exponential stabilizability. Infinite-dimensional steady-state Riccati equations characterizing the feedback control gain and the Kalman filter gain operators can be solved explicitly. The associated performance indexes including the mean-square control-effort are calculated in closed form. As a first approximation, the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies. Numerical calculations for the gain and bandwidths for a typical configuration are presented. The performance of the compensator is evaluated when in fact in the true model there is no actuator noise. The theoretical problem involved is to show that the infinite-dimensional stochastic process is asymptotically stationary. It is possible to calculate the steady-state covariance in closed form and thereby calculate performance indexes of interest explicitly, facilitating the choice of optimal design parameters. >

Optimal Design with Advanced Materials

Abstract: Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. Primarily the first order gradients of the total elastic energy are used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To get a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of only thickness design, only orientational design and combined thickness-orientational design will be presented.

Integrated topology and boundary shape optimization of 2-D solids

Abstract: This study is concerned with the development of an integrated procedure for the computation of the optimal topology as well as the optimal boundary shape of a two-dimensional, linear elastic body. The topology is computed by regarding the body as a domain of the plane with a high density of material and the objective is to maximize the overall stiffness, subject to a constraint on the material volume of the body. This optimal topology is then used as the basis for a shape optimal design method that regards the body as given by boundary curves. For this case the objective is to minimize the maximum value of the Von Mises equivalent stress in the body, subject to an isoperimetric constraint on the area as well as a constraint on the stiffness. The solution procedures for the shape design are based on variational formulations for the problems and the results of a variational analysis are implemented via finite element discretizations. The discretization grids are generated automatically by an elliptical method for general two-dimensional domains. Computational results are presented for the design of a fillet, a beam and a portal frame.

Combined control-structural optimization

Abstract: An approach to combined control-structural optimization aimed at enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and is capable of generating families of designs that can be used in early trade studies. Analytical results are obtained for classes of structure/control objectives with LQG and LQR costs. For these, it is demonstrated that global optima can be computed for small values of the homotopy parameter.

Decomposition technique for optimal design of water supply networks

Abstract: A decomposition technique is suggested for optimal design of water supply networks. The general mathematical model is decomposed into two submodels which are solved iteratively. The flow variables are solved in the first submodel for a fixed value of the head variables, using a minimum concave cost flow algorithm. The head variables are solved in the second submodel for a fixed value of the flow variable using LP. The solution is usually obtained after 2 iterations, and is proven to be a local optimum. A novel form of the pump equation, based on dimensional analysis, is also presented and used as part of the optimization model.

Cross-over designs for two treatments and correlated errors

Abstract: SUMMARY The paper aims to derive optimal two-treatment cross-over designs for experiments with many periods, when the observations are correlated and residual effects are present. The case of small numbers of periods was treated by Laska & Meisner (1985) and Matthews (1987). Their results are substantially affected by end effects arising because the first and last periods behave differently. We look at designs which maximize an upper bound of the information matrix and show that these designs are highly efficient, especially when the number of periods is large. Assume we have b experimental units, each of which is exposed to a series of treatments. The number of treatments is t and each unit receives k different or identical treatments in successive periods. The design d determines which treatment is applied to which unit at which period. We denote the set of all such cross-over designs by ft,b,k. The measurement on the jth period of the uth unit is denoted by Yd,u,j if design d E itb,k is applied. Williams (1949) introduced a model for this situation which assumes that

Sensitivity analysis and optimal design of thin laminated composite structures

Abstract: In this paper a numerical model for the optimal design of thin plate-shell laminated type structures made of composite materials is presented. The model is based on a plate-shell finite element with 18 degrees of freedom, using the discrete Kirchhoff theory. Sensitivity analysis with respect to fibre orientation and ply thickness is obtained through analytical formulation which is directly included in the finite element code. The model is applied to the optimal design of two test cases.

Optimal design of linear array of sensors

Abstract: The authors address the issue of design of linear arrays of sensors with application to high-resolution direction-of-arrival (DOA) algorithms, and present the D-optimality based design criterion (DOBC). The design technique employs certain prior information in the cases of low-angle tracking and where targets are close to each other, and provides an array which minimizes the joint estimation error in angles of arrival. Two examples are given, and both theoretical analysis and computer simulation are carried out, showing that significant improvement in performance can be achieved with this design over the conventional uniform arrays and a class of minimum redundancy (MR) arrays. >

Two-Dimensional Design for Correlated Errors

Abstract: Optimal and highly efficient two-dimensional designs are constructed for correlated errors on the torus and in the plane. The technique uses the method of differences to produce series of connectable planar squares. Efficiency calculations for planner versions of the torus designs show that the torus approximation is very satisfactory.

On the Efficiency of IRT Models When Applied to Different Sampling Designs

Abstract: The problem of obtaining designs that result in the greatest precision of the parameter estimates is encountered in at least two situations in which item response theory (IRT) models are used. In so-called two-stage testing procedures, certain designs may be specified that match difficulty levels of test items with abilities of examinees. The advantage of such designs is that the variance of the estimated parameters can be controlled. In situations in which IRT models are applied to different groups, efficient multiple-matrix sampling designs are applicable. The choice of matrix sampling designs will also influence the variance of the estimated parameters. Heuristic arguments are given here to formulate the efficiency of a design in terms of an asymptotic generalized variance criterion, and a comparison is made of the efficiencies of several designs. It is shown that some designs may be found to be most efficient for the one- and two- parameter model, but not necessarily for the three-parameter model. Index terms: efficiency, generalized variance, item response theory, optimal design.

Steady-state analysis and design optimization of an inductor-transformer resonant DC-DC converter

Abstract: The authors present a closed-form steady-state analysis of an inductor transformer resonant DC-DC power converter. This efficient method of analysis, which directly predicts the steady-state characteristics of the circuit, is used to develop an optimal design methodology. Normalized optimum design tables and curves are derived. The optimization procedure is summarized and is illustrated by a design example. State plane analysis is used to show the important role of the circuit leakage inductances on the steady-state performance of the system. Experimental results obtained from a prototype converter are used to verify the analytical results. >

Optimization and numerical models of silicon solar cells

Abstract: The coupling of a numerically intensive model of a silicon solar cell with an optimization algorithm is developed. It is demonstrated that the computational burden of evaluating the optimal design of a solar cell can be significantly decreased if the model is appropriately adapted for use in an optimization environment. It is shown that the resulting tool is extremely useful for performing a systematic analysis of optimal efficiencies and associated optimal designs under different levels of technology and fabrication processes. The paper also demonstrates that true sensitivity analyses can be carried out only in an optimization context.

Some universally optimal row-column designs with empty nodes

Abstract: SUMMARY General forms of the reduced coefficient matrix for estimation of treatment effects and the intrablock analysis of variance of row-column designs with n experimental units and v treatments are obtained from earlier work by the authors. These results are used to identify desirable properties for row-column designs with empty nodes. A need for such designs is apparent when the blocking criteria are implemented in sequence and empty nodes do not represent wasted experimental units. The construction and properties of three special classes of row-column designs with some empty nodes are discussed and examples given. In particular, it is shown that, if a row-column design belongs to one of these classes, then it is universally optimal for specified design parameters, where universally optimal designs are designs that maximize a generalized optimality criterion as defined by Kiefer.

Bayesian Optimal Designs for Linear Regression Models

Abstract: A Bayesian version of Elfving's theorem is given for the $\mathbf{c}$-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian $\mathbf{c}$-optimum are described. The class of prior precision matrices $R$ for which the Bayesian $\mathbf{c}$-optimal designs are supported by the points of the classical $\mathbf{c}$-optimal design is characterized. It is proved that the Bayesian $\mathbf{c}$-optimal design, for large $n,$ is always supported by the same support points as the classical one if the number of support points and the number of regression functions are equal. Examples and a matrix analog are discussed.

Optimality and Robustness to the Unavailability of Blocks in Block Designs

Abstract: SUMMARY This paper investigates the optimality of designs derived from binary, variance-balanced incomplete block designs (BIBDs) by removing t equal-sized blocks which are not necessarily disjoint. It is shown that the optimal design is derived by removing blocks which have disjoint sets of treatments, and the worst design is derived by removing identical blocks. For BIBDs and t = 2 all resulting designs are ordered. The implication for competing BIBDs which have the same parameters v, b and k but different support sizes (numbers of distinct blocks) is addressed. Optimality and robustness are measured through the non-zero eigenvalues of the C-matrix of the design missing observations using the universal optimality criteria of Bondar.

Optimization of synthesis-design-operation of a cogeneration system by the intelligent functional approach

Abstract: This paper reports that the Intelligent Functional Approach (IFA) is a method for optimal synthesis-design-operation of complex systems The formulation of the method has been presented in a preceding paper The method is applied here for the optimization of a cogeneration system, which supplies a process plant with electricity, steam and hot water, all known functions of time The synthesis of the system is not predetermined, but it is derived by the solution of the optimization problem, which also gives the optimal design specifications of the equipment and the optimal operation mode at each load condition Also, the optimal quantity of electricity generated by the system is obtained, which leads to a decision on whether there is a need for a grid connection A study of the internal economy of the system makes it possible to develop an optimization procedure much simpler than the general one, which reduces the computing time significantly A sensitivity analysis reveals the effect of important parameters on the optimal solution

Optimal designs for a grouped sequential binomial trial

Abstract: Several designs have been proposed for testing a one-sample study in a grouped sequential fashion, all of which create an approximately optimal design We give a geometric characterization of the actual optimal (or admissible) designs for the special case of a Bernoulli outcome, and from this derive an enumeration algorithm which may be used to explicitly construct all of the admissible designs for a user-specified range of size and power A computer implementation of the method is fast and efficient

Two requisite tools in the optimal design of electromagnetic devices

Abstract: The requisite methodology for performing optimal design-the synthesis of devices from specified performance standards-is now in place. Software that is reliable and transparent to the user is required. If this could be accomplished, then these sophisticated design methods would be quickly accepted in industry. Two of the requisite tools for such automatic implementation are presented: a parametrized mesh generator that allows the design iterations to proceed without interruption, and an optimization algorithm that takes care of different object function shapes, using different optimization algorithms, including the principle of tunneling. >

Structural Optimization: Case‐Based Approach

Abstract: A new approach to structural parametric optimization is proposed. A two-stage case-based optimization process, including learning and production stages, is presented. A brief description of a case-base reasoning system and its mathematical foundations are also provided. This system was used in four experiments in the area of design and optimization of steel frames under wind, live, and dead loading. Each experiment was a five-stage learning process. At each stage, a case-based reasoning system was used in a number of tests to make predictions regarding the optimal cross sections of individual members and the total weight of a rigid steel frame, based on a number of examples of optimal designs. The results of these predictions were compared with known optimal designs. The experiments were performed to determine the feasibility of the proposed optimization and to identify the relationship between the accuracy of case-based predictions and the number of training examples. The experiments confirmed the expected feasibility of the proposed optimization. Initial conclusions and suggestions for further research are included.