Showing papers on "Optimal design published in 1980"

A Comparison of Algorithms for Constructing Exact D-Optimal Designs

Abstract: An empirical comparison of existing algorithms for the computer generation of exact D-optimal experimental designs is carried out. Among algorithms considered were those due to Wyrnn, Mitchell, Fedorov, and Van Schalkwyk. A procedure for rounding off approximate designs as suggested by Kiefer is also evaluated. A modification of the Fedorov algorithm is given and shown to effect substantial decreases in the computer time required for design generation.

Optimal Design: An Introduction to the Theory for Parameter Estimation

Abstract: Prior to the 1970's a substantial literature had accumulated on the theory of optimal design, particularly of optimal linear regression design. To a certain extent the study of the subject had been piecemeal, different criteria of optimality having been studied separately. Also to a certain extent the topic was regarded as being largely of theoretical interest and as having little value for the practising statistician. However during this decade two significant developments occurred. It was observed that the various different optimality criteria had several mathematical properties in common; and general algorithms for constructing optimal design measures were developed. From the first of these there emerged a general theory of remarkable simplicity and the second at least raised the possibility that the theory would have more practical value. With respect to the second point there does remain a limiting factor as far as designs that are optimal for parameter estimation are concerned, and this is that the theory assumes that the model be collected is known a priori. This of course underlying data to is seldom the case in practice and it often happens that designs which are optimal for parameter estimation allow no possibility of model validation. For this reason the theory of design for parameter estimation may well have to be combined with a theory of model validation before its practical potential is fully realized. Nevertheless discussion in this monograph is limited to the theory of design optimal for parameter estimation.

A sequentially constructed design for estimating a nonlinear parametric function

Abstract: SUMMARY Properties of a design constructed sequentially for a simple nonlinear problem are investigated both theoretically and by simulation. It is proved that the design measure corresponding to the sequential design converges to an optimal measure, even when the latter has singular information matrix. The empirical study suggests that in repeatedsampling inference we can effectively ignore the fact that the design is sequential. Some key word8: Asymptotic efficiency; Fisher and sample information; Nonlinear design; Optimal design; Sequential design; Simulation; Singular design.

$D_s$-Optimal Designs for Polynomial Regression Using Continued Fractions

Abstract: Consider a polynomial regression of degree $n$ on an interval. Explicit optimal designs are given for minimizing the determinant of the covariance matrix of the least squares estimators of the highest $s$ coefficients. The designs are calculated using continued fractions.

Minimum Covering Ellipses

Abstract: With the aid of a duality relation originally obtained in the theory of statistical experimental design, an exact terminating algorithm is developed for finding the ellipse of smallest area covering a given plane point set. Some applications and related problems are discussed. Empirical timings show the algorithm to be highly efficient, particularly for large sets of points.

Circular balanced repeated measurements designs

Abstract: The concept of a circular design is defined and when proper balance for various effects is assumed, its universal optimality is proved over the class of all designs with the same set of parameters, Such designs are shown to minimize the variance of the best linear unbiased estimators of contrasts of residual and direct effects over the class of equireplicated designs. All models assume first order residual effects and are of a circular nature. The proofs are presented in a unified manner for several models at a time. They are based on certain matrix domination which occurs when parameters are eliminated from a linear modelj this latter fact is proved for a general linear model.

Exchange and Interchange Procedures to Search for Optimal Designs

Abstract: SUMMARY An algorithm to search for optimal block designs is described. This algorithm consists of an exchange procedure and an interchange procedure. During the exchange procedure the "correct" treatment replications are determined and during the interchange procedure an optimal set of treatment concurrences is searched for. The optimality criterion is the sum of the weighted variances of a set of treatment contrasts of interest. Examples which illustrate how the algorithm can be used to obtain designs which have a variance structure that reflects the interest expressed in a set of treatment contrasts are given and the performance of the algorithm is discussed.

Trend-Free Block Designs: Theory.

Abstract: : A common polynomial trend in one or more dimensions is assumed to exist over the plots in each block of a classical experimental design. An analysis of covariance model is assumed with trend components represented through use of orthogonal polynomials. The objective is to construct new designs through the assignment of treatments to plots within blocks in such a way that sums of squares for treatments and blocks are calculated as though there were no trend and sums of squares for trend components and error are calculated easily. Such designs are called trend-free and a necessary and sufficient condition for a trend-free design is developed. It is shown that these designs satisfy optimality criteria among the class of connected designs with the same incidence matrix. The analysis of variance for trend-free designs is developed. The paper concludes with two examples of trend-free designs. (Author)

Aspects of Optimal Design in Dynamic Systems

Abstract: The application of optimal experimental design theory to models for dynamic systems is surveyed. Preliminary sections briefly discuss the models used and the main points of statistical optimal design theory. Then the ways in which the latter carry over to dynamic models are described. These applications are split roughly into those involving choice of input functions and those in which sampling rates also are selected.

Yield optimization for arbitrary statistical distributions: Part II-Implementation

Abstract: A suggested test problem for proposed algorithms in yield optimization is described in detail. The problem is a current switch emitter follower (CSEF) circuit originally described by Ho, which includes a transmission line. The ideas presented in Part I of this paper [1] are applied to this circuit in order to obtain an optimal statistical design. Production yield is maximized taking into consideration statistical distributions of circuit parameters and realistic correlations between transistor model parameters. Nonlinear programming employing the analytical formuias for yield and its sensitivities is used to provide optimal nominal values for the circuit parameters. Different design specifications are assumed and corresponding optimal designs are obtained.

Marginally restricted D-optimal designs

Abstract: In experimental design it often happens that values of some of the relevant carriers cannot be specified by the experimenter. We consider the problem of obtaining approximate D-optimal designs when the design space is a product space and the carriers associated with one margin are not subject to control. An equivalence theorem for D-optimal designs is presented. The essential ingredients of iterative schemes for generating designs are discussed and an example is presented.

Optimal Design of Large Structures for Damage Tolerance

Abstract: The basic idea presented herein is that a systematic method for optimal structural design can be developed that accounts for probable future damage to the structure. A general mathematical model for the damage-tolerant structure design problem is defined. Design sensitivity analysis and procedures for treatment of a large number of constraints for the problem are presented. As a practical design example, damage-tolerant design of an open truss helicopter tail-boom structure is considered. Optimal designs for several cases of the tail-boom are presented. It is shown that considerable design variation is necessary to achieve the damage-tolerant design objective. It is also shown that if the structure is optimized without consideration of damage, the structure will fail catastrophically when any damage occurs to the structure.

Optimal design by a homotopy method

Abstract: An optimal design problem is formulated as a system of nonlinear equations rather than the extremum of a functional. Based on a new homotopy method, an algorithm is developed for solving the nonlinear system which is globally convergent with probability one. Since no convexity is required, the nonlinear system may have more than one solution. The algorithm will produce an optimal design solution for a given starting point. For most engineering problems, the initial prototype design is already well conceived and close to the global optimal solution. Such a starting point usually leads to the optimal design by the homotopy method, even though Newton's method may diverge from that starting point. A simple example is given.

The Analysis and Design of Data Quantization Schemes for Stochastic-Signal Detection Systems

Abstract: The optimal design and performance analysis of nonuniform quantizers are considered in the context of data quantization in detection systems for stochastic signals. The case of detection with small signal-to-noise ratio is treated using two different statistical models for the presence of the signal in this situation. A general data-quantized detection system is proposed, and analytical expressions are presented for the asymptotic performance comparison of such systems within each of the two signal models. A design procedure for the optimal choice of quantizer parameters as also discussed, and optimal parameter values are presented for the particular case of four-level quantization for a class of noise propability densities exhibiting generalized exponential decay. Two suboptimal quantizer-detectors are also proposed, one based on minimum-distortion quantization and the other based on an approximation to the quadratic detector, and the performance of the optimal quantization scheme relative to these is analyzed with the result that the optimal quantizer-detector generally exhibits considerable performance improvement over the suboptimal schemes.

Incomplete Block Designs for Comparing Treatments with a Control (V): Optimal Designs for p = 6, k = 3.

Abstract: : The present paper continues the study of balanced treatment incomplete block (BTIB) designs initiated previously This class of designs was proposed for the problem of comparing simultaneously p or = 2 test treatments with a control treatment when the observations are taken in blocks of common size k p+1 The conjectured minimal complete class of generator designs, a catalog of admissible designs, and tables of optimal designs are given for p = 6, k = 3 The efficiency of the optimal BTIB design relative to that of replications of a BIB design is computed for situations in which both provide the same probability guarantee for the multiple comparisons with a control problem

Optimal Design Theory in Relation to Combinatorial Design

Abstract: Publisher Summary This chapter devotes to indicating how, in recent years, the relationship between combinatorial and optimal design developments has begun to exhibit a motivational reversal. Instead of constructing exotic designs on intuitive grounds and then proving that they are indeed optimum, one encounters settings in which optimality considerations motivate the construction of new combinatorial structures, or the selection of a particular subset of the known ones for special emphasis and study. An interesting example is the setting of “one-way heterogeneity,”—that is, of block designs. If the parameter values are such that a BIBD did not exist, the early design developments sought designs that were still quite symmetric, as in the construction of PBIBD's by Bose and Nair.

Optimal design of ring stiffened cylindrical shells using multiple stiffener sizes

Abstract: : This report describes the solution to the singly reinforced discrete stiffener problem by direct use of an optimization scheme employing mathematical programming. The optimization formulation and procedure used here admit a large number of simultaneous buckling modes thus allowing optimization under conditions of mode coalescence, which are usual in this type of problem. This is a preliminary study, the purposes of which are; to develop and evaluate methodology for the treatment of this problem, to develop preliminary insights into how multiple frame sizes may efficiently be employed in submersible structures, to examine the nature of design improvement resulting from use of multiple size frames, and to investigate the nature of such optimal designs. (Author)

Use of constrained optimization in the conceptual design of a medium-range subsonic transport

Abstract: Constrained parameter optimization was used to perform the optimal conceptual design of a medium range transport configuration. The impact of choosing a given performance index was studied, and the required income for a 15 percent return on investment was proposed as a figure of merit. A number of design constants and constraint functions were systematically varied to document the sensitivities of the optimal design to a variety of economic and technological assumptions. A comparison was made for each of the parameter variations between the baseline configuration and the optimally redesigned configuration.

Optimal Design of Arches Using the Complex Method

Abstract: Optimal designs of arches under multiple load cases using an automated design routine are presented. The design variables consist of geometric (arch shape) as well as member sizing variables (cross-sectional dimensions). The members are sized on the basis of working stress design procedure, and all the relevant provisions of the AISC specifications are met. The optimal arch shapes produced by the present method for a uniformly distributed load case show a good agreement with the theoretical results. The optimal designs under two and three load cases are also obtained. Under two load cases, the optimal shapes are not very different than a parabolic curve passing through the supports and crown of the arch.

Some features of the optimal design theory – a survey

Abstract: In this survey paper the regression model with uncorrelated observations and its infinitedimensional generalization are considered. The stress is on a functional approach to the experiment in both models. Results of several authors on the convex properties of the decision problem connected with the experimental design are collected, The iterative methods of computing optimal designs for convex criteria functions are considered from a geometrical aspect, Singular designs and designs for the nonlinear estimation. are considered as well.

Plastic Design under Combined Stresses

Abstract: Based on matrix algebra and linear programming techniques, a general mathematical model is developed for the rigid-plastic optimal design of planar and space frameworks under combined stresses. An iterative design procedure is introduced to account for the nonlinear growth in plastic capacity of the elements of the structure as they vary in size to meet the requirements of the design. The convergence properties of the iterative procedure are investigated for three different design approaches. Two simple examples are presented to illustrate the theory for plane and space frameworks.

Optimal design of structures subjected to follower forces

Abstract: The optimal design of columns, consisting of segments with arbitrary thickness and length, subjected to follower forces is considered in this paper. The solution is presented for the case of cross modal interaction of a vibrating system. Since the resulting boundary value problem is nonselfadjoint only approximate solutions are generally possible. Herein, for the solution the method of the generalised functional and the transfer matrix technique have been used. As typical examples, the solutions of Beck's, Reut's, Leipholz's and Hanger's column are investigated.

Optimal design of a class of high frequency power inductors

Abstract: A method for the design of inductors which exchange recurrently all of their energy in the order of Joules at frequencies of tens of kHz with the thereto associated network is presented. The constraint of the inductor's allowable surface temperature and the there with implied "hot spots" for an assumed type of specific geometrical configuration, governs a multiphase and concurrent search for the inductor's minimum physical weight, its minimum power loss, or a compromise thereof. The search is supported with the "mechanization" of magnetic component design by way of a computer program, which was developed for this purpose. The rate of heat removal from the component's surface is calculated in accordance with the prevailing conditions. The best suited permeability μ r results from the analysis of a specific inductor design for an assumed magnetic core material. A discrete or a "distributed" air gap can be prescribed. Test of fabricated inductors confirm the validity of the described method. The usefulness of the presented method is seen in the circumspection which is gained by a methodical and comprehensive analysis of a specific design requirement.