Showing papers on "Optimal design published in 1993"

Optimal Design of Experiments

Abstract: Experimental Designs in Linear Models Optimal Designs for Scalar Parameter Systems Information Matrices Loewner Optimality Real Optimality Criteria Matrix Means The General Equivalence Theorem Optimal Moment Matrices and Optimal Designs D-, A-, E-, T-Optimality Admissibility of Moment and Information Matrices Bayes Designs and Discrimination Designs Efficient Designs for Finite Sample Sizes Invariant Design Problems Kiefer Optimality Rotatability and Response Surface Designs Comments and References Biographies Bibliography Index.

Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction

Abstract: This article is concerned with the problem of predicting a deterministic response function yo over a multidimensional domain T, given values of yo and all of its first derivatives at a set of design sites (points) in T. The intended application is to computer experiments in which yo is an output from a computer model of a physical system and each point in T represents a particular configuration of the input parameters. It is assumed that the first derivatives are already available (e.g., from a sensitivity analysis) or can be produced by the code that implements the model. A Bayesian approach in which the random function that represents prior uncertainty about yo is taken to be a stationary Gaussian stochastic process is used. The calculations needed to update the prior given observations of yo and its first derivatives at the design sites are given and are illustrated in a small example. The issue of experimental design is also discussed, in particular the criterion of maximizing the reduction in entropy...

An optimal design problem with perimeter penalization

Abstract: We study the optimal design problem of finding the minimal energy configuration for a mixture of two conducting materials when a perimeter penalization of the unknown domain is added. We show that in this situation an optimal domain exists and that, under suitable assumptions on the data, it is an open set.

Structural Optimization: Fundamentals and Applications

Abstract: 1 Problem Statement.- 1.1 Introduction.- 1.1.1 Automated Structural Optimization.- 1.1.2 Structural Optimization Methods.- 1.1.3 Historical Perspective.- 1.1.4 Scope of Text.- 1.2 Analysis Models.- 1.2.1 Elastic Analysis.- 1.2.2 Plastic Analysis.- 1.3 General Formulation.- 1.3.1 Design Variables.- 1.3.2 Constraints.- 1.3.3 Objective Function.- 1.3.4 Mathematical Formulation.- 1.4 Typical Problem Formulations.- 1.4.1 Displacement Method Formulations.- 1.4.2 Force Method Formulations.- Exercises.- 2 Optimization Methods.- 2.1 Optimization Concepts.- 2.1.1 Unconstrained Minimum.- 2.1.2 Constrained Minimum.- 2.2 Unconstrained Minimization.- 2.2.1 Minimization Along a Line.- 2.2.2 Minimization of Functions of Several Variables.- 2.3 Constrained Minimization: Linear Programming.- 2.3.1 Introduction.- 2.3.2 Problem Formulation.- 2.3.3 Method of Solution.- 2.3.4 Further Considerations.- 2.4 Constrained Minimization: Nonlinear Programming.- 2.4.1 Sequential Unconstrained Minimization.- 2.4.2 The Method of Feasible Directions.- 2.4.3 Other Methods.- Exercises.- 3 Approximation Concepts.- 3.1 General Approximations.- 3.1.1 Design Sensitivity Analysis.- 3.1.2 Intermediate Variables.- 3.1.3 Sequential Approximations.- 3.2 Approximate Behavior Models.- 3.2.1 Basic Displacement Approximations.- 3.2.2 Combined Displacement Approximations.- 3.2.3 Homogeneous Functions.- 3.2.4 Displacement Approximations along a Line.- 3.2.5 Approximate Force Models.- Exercises.- 4 Design Procedures.- 4.1 Linear Programming Formulations.- 4.1.1 Plastic Design.- 4.1.2 Elastic Design.- 4.2 Feasible-Design Procedures.- 4.2.1 General Considerations.- 4.2.2 Optimization in Design Planes.- 4.3 Optimality Criteria Procedures.- 4.3.1 Stress Criteria.- 4.3.2 Displacement Criteria.- 4.3.3 Design Procedures.- 4.3.4 The Relationship Between OC and MP.- 4.4 Multilevel Optimal Design.- 4.4.1 General Formulation.- 4.4.2 Two-Level Design of Prestressed Concrete Systems.- 4.4.3 Multilevel Design of Indeterminate Systems.- 4.5 Optimal Design and Structural Control.- 4.5.1 Optimal Control of Structures.- 4.5.2 Improved Optimal Design by Structural Control.- 4.6 Geometrical Optimization.- 4.6.1 Simultaneous Optimization of Geometry and Cross Sections.- 4.6.2 Approximations and Multilevel Optimization.- 4.7 Topological Optimization.- 4.7.1 Problem Statement.- 4.7.2 Types of Optimal Topologies.- 4.7.3 Properties of Optimal Topologies.- 4.7.4 Approximations and Two-Stage Procedures.- 4.8 Interactive Layout Optimization.- 4.8.1 Optimization Programs.- 4.8.2 Graphical Interaction Programs.- 4.8.3 Design Procedure.- Exercises.- References.

Optimum Experimental Designs for Properties of a Compartmental Model

Abstract: SUMMARY Three properties of interest in bioavailability studies using compartmental models are the area under the concentration curve, the maximum concentration, and the time to maximum concentration Methods are described for finding designs that minimize the variance of the estimates of these quantities in such a model These methods use prior information Both prior estimates and prior distributions are used The designs for an open one-compartment model are compared with the corresponding D,-optimum design for all parameters and also with designs that minimize the sum of the scaled variances of the individual properties

Optimal designs for binary response experiments: Fieller, D, and A criteria

Abstract: For binary response experiments, we consider the use of a confidence interval based on Fieller's theorem as a design criterion (F-optimality). For symmetric distributions and under mild conditions, we show that F-optimal, D-optimal, and A-optimal designs have two or three support points. A complete characterization of these designs is given. The possibility of having 4-point symmetric designs is discussed.

E-Optimal Designs for Polynomial Regression

Abstract: E-optmal designs for the full mean parameter vector, and for many subsets in univariate polynomial regression models are determined. The derivation is based on the interplay between E-optimality and scalar optimality. The scalar parameter systems are obtained as transformations of the coefficient vector c of the Chebyshev polynomial.

D-Optimal Designs in QSAR

Abstract: Statistical design in principal properties based on D-optimality criteria are particularly appropriate for selecting the most informative molecules to be synthesized and tested in the framework of QSAR studies. Selection by D-optimal designs are better than those based on fractional factorial designs since they allow one to reduce the number of required structures, to reduce polysubstitution, to exclude molecules too difficult to synthesize and to include molecules already available and/or tested.

Aerodynamic configuration design using response surface methodology analysis

Abstract: An investigation has been conducted to determine a set of optimal design parameters for a single-stage-to-orbit reentry vehicle. Several configuration geometry parameters which had a large impact on the entry vehicle flying characteristics were selected as design variables: the fuselage fineness ratio, the nose to body length ratio, the nose camber value, the wing planform area scale factor, and the wing location. The optimal geometry parameter values were chosen using a response surface methodology (RSM) technique which allowed for a minimum dry weight configuration design that met a set of aerodynamic performance constraints on the landing speed, and on the subsonic, supersonic, and hypersonic trim and stability levels. The RSM technique utilized, specifically the central composite design method, is presented, along with the general vehicle conceptual design process. Results are presented for an optimized configuration along with several design trade cases.

Experimental Designs for Model Discrimination

Abstract: We present designs that perform well for several objectives simultaneously. Three different approaches are discussed: to augment a given design in an optimal way, to evaluate a mixture of the various criteria, and to optimize one objective subject to achieving a prescribed efficiency level for the others. Our sample designs are for the situation of discriminating between a second- and third-degree polynomial fit, under the D-criterion and geometric mixtures of D-criteria.

Optimal experimental design for another’s analysis

Abstract: We consider the optimal design of experiments in which estimation and design are performed by different parties. The parties are assumed to share similar goals, as reflected by a common loss function, but they may have different prior beliefs. After presenting a few motivating examples, we examine the problem of optimal sample size selection under a normal likelihood with constant cost per observation. We also consider the problem of optimal allocation for given overall sample sizes. We present results under both squared-error loss and a logarithmic utility, paying attention to the differences between one- and two-prior optimal designs. An asymmetric discrepancy measure features repeatedly in our development, and we question the extent of its role in optimal two-prior design.

Elfving's Theorem for $D$-Optimality

Abstract: We consider a model robust version of the $c$-optimality criterion minimizing a weighted product with factors corresponding to the variances of the least squares estimates for linear combinations of the parameters in different models. A generalization of Elfving's theorem is proved for the optimal designs with respect to this criterion by an application of an equivalence theorem for mixtures of optimality criteria. As a special case an Elfving theorem for the $D$-optimal design problem is obtained. In the case of identical models the connection between the $A$-optimality criterion and the model robust criterion is investigated. The geometric characterizations of the optimal designs are illustrated by a couple of examples.

Dimensional Tolerance Allocation of Stochastic Dynamic Mechanical Systems Through Performance and Sensitivity Analysis

Abstract: Uncertainties due to random dimensional tolerances within stochastic dynamic mechanical systems lead to mechanical errors and thus, performance degradation. Since design standards do not exist for these systems, analysis and design tools are needed to properly allocate tolerances. This paper presents probabilistic models and methods to allocate tolerances on the link lengths and radial clearances such that the system meets a probabilistic and time dependent performance criterion. The method includes a general procedure for sensitivity analysis, using the effective link length model and nominal equations of motion. Since the sensitivity analysis requires only the nominal equations of motion and statistical information as input, it is straight forward to implement. An optimal design problem is formulated to allocate random tolerances. Examples are presented to illustrate the approach and its generality. This paper provides a solution to the tolerance allocation problem for stochastic dynamically driven mechanical systems.

Optimal two-period repeated measurement designs with two or more treatments

Abstract: SUMMARY For two-period repeated measurement designs for comparing t ?> 2 treatments, we discuss universally optimal designs when the number of subjects N is a multiple of t2 and some cases when N is a multiple of t. We examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs. In addition, efficiencies of the universally optimal designs obtained by Hedayat & Zhao (1990) are examined under both fixed subject and random subject effect model assumptions.

A Graphical Approach for Evaluating Mixture Designs

Abstract: Single-valued criteria such as A-, D-, G- and V-optimality are used often in constructing and evaluating so-called «optimal» experimental designs. These criteria are especially popular with mixture experiments where the shape of the design region can become complicated by the imposition of additional constraints on the ingredient proportions. Although such criteria provide a valuable and reasonable basis for generating designs, the resulting designs are optimal only in the strict sense of the particular criterion used. Often, these criteria fail to convey the true nature of the design's support of the fitted model in terms of the variance of the prediction equation over the region of interest

Construction and parameterization of all static and dynamic H/sub 2/-optimal state feedback solutions, optimal fixed modes and fixed decoupling zeros

Abstract: A problem of H/sub 2/ optimization via state feedback is considered. The problems dealt with are of the general singular type, with a left invertible transfer matrix function from the control input to the controlled output. All the static and dynamic H/sub 2/ optimal state feedback solutions are constructed and parameterized, and all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed the optimal fixed modes, which must be assigned among the closed-loop eigenvalues. This set includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and location of pole-zero cancellations present in any H/sub 2/ optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary. >

Approximation techniques for broad-band acoustic radiated noise design optimization problems

Abstract: This study investigates the applicability of various approximation methods to broadband radiated noise design optimization problems. Low-order series approximations of dynamic response may be used to replace full numerical system solutions to effect significant computer cost savings during design iterations. Also, the ease of evaluating the approximate functions may be further exploited by using global optimization search methods, such as simulated annealing, at individual design iterations. The combination of approximating radiated noise spectra and evaluating the approximate spectra for all possible design alternatives greatly increases the possibility of finding a truly optimal design. The effectiveness of the approximation is measured by considering optimization accuracy, evaluated by the algorithm's ability to find a global or near-global minimum independent of the initial design; computational efficiency, based on the number of numerical design analyses required for convergence; and generality, where the method should be relatively independent of the problem type. Finite element models of three test cases with varying performance goals and design parameters were used to evaluate the optimization methods. Shell thicknesses, shell loss factors, and rib stiffener locations were varied to minimize structural weight and manufacturing costs while lowering broad-band radiated noise levels below a specified goal. First-order Taylor and half-quadratic series approximation optimization approaches were compared to traditional local minimization methods (Modified Method of Feasible Directions and Broydon-Fletcher-Goldfarb-Shanno). For all test cases, the approximation approaches found the global optimum design more frequently than the local minimization methods. Also, the half-quadratic method converged using fewer design evaluations than the first-order Taylor method for most test cases

Variational problems with free interfaces

Abstract: A large class of problems arise in the material sciences involving free interfaces. To establish the existence and regularity (including the regularity of free interfaces) of solutions has been an important and interesting issue. Here we were able to do so in a model case accounted in optimal designs.

Heteroscedastic G-optimal Designs

Abstract: This paper addresses the issue of constructing large sample G-optimal designs when the variability of the response varies across a compact design space. A useful characterization theorem is presented along with a computer algorithm for generating (heteroscedastic) G-optimal designs. To facilitate comparisons between D- and G-optimal designs, Atwood's inequality for comparing D- and G-efficiencies in homoscedastic models is generalized to heteroscedastic models. Some robustness properties of these designs are presented

Simulation designs and correlation induction for reducing second-order bias in first-order response surfaces

Abstract: Construction of simulation designs for the estimation of response surface metamodels is often based on optimal design theory. Underlying such designs is the assumption that the postulated model provides the correct representation of the simulated response. As a result, the location of design points and the assignment of pseudorandom number streams to these experiments are determined through the minimization of some function of the covariance matrix of the model coefficient estimators. In contrast, we assume that the postulated model may be incorrect. Attention is therefore directed to the development of simulation designs that offer protection against the bias due to possible model misspecification as well as error variance. The particular situation examined is the estimation of first-order response surface models in the presence of polynomials of order two. Traditional two-level factorial plans combined with one of three pseudorandom number assignment strategies define the simulation designs. Specificati...

Neural network approximations in a simulated annealing based optimal structural design

Abstract: The present paper examines the feasibility of using neural network based function approximations in conjunction with a simulated annealing (SA) strategy for optimization of structural systems. Such a stochastic search method is more “tolerant” of errors in objective and constraint function information than the more traditional mathematical programming techniques. The improved counterpropagation (CP) neural network is used to generate these approximations, and includes features such as dynamic adjustment of the network size, optimization based training of outstar weights, andfuzzification of output. The CP network is easy to train, and preliminary numerical results indicate that the modifications to the network significantly improve the quality of function approximations. The SA based search for optimal designs is illustrated by the sizing of planar and spatial truss structures for minimum weight and constraints on allowable stress levels.

Optimization of a Transonic Turbine Airfoil Using Artificial Intelligence, CFD and Cascade Testing

Abstract: A transonic turbine airfoil design is optimized using an artificial intelligence engineering design shell coupled with an inviscid, adaptive grid, CFD solver. The objective of the optimization is to minimize the downstream static pressure variation resulting from the trailing edge shock structure. Cascade test results verify the analytical predictions. Techniques are described which were used to couple the optimization shell to the 2-D turbine airfoil shape to allow the search for optimal designs and indicate the quality of those designs. The emphasis of the discussion is upon the application of these techniques rather than the physical details of the resulting blade design.Copyright © 1993 by ASME