Showing papers on "Optimal design published in 1988"
TL;DR: In this article, a formulation for finding the combined optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components; a structural objective and a control objective is presented.
Abstract: A formulation is presented for finding the combined optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components; a structural objective and a control objective. When the structural objective is a function of the structural design variables only, and when the control objective is represented by the quadratic functional of the response and control energy, it is possible to analytically express the optimal control in terms of any set of “admissible” structural design variables. Such expression for the optimal control is used recursively in an iterative Newton-Raphson search scheme, the goal of which is to determine the corresponding optimal set of structural design variables that minimize the combined objective function. A numerical example is given to illustrate the computational procedure. The results indicate that significant improvement of the combined optimal design can be achieved over the traditional separate optimization.
102 citations
TL;DR: In this article, existing knowledge on optimal designs for comparing test treatments with controls under 0-, 1-, and 2-way elimination of heterogeneity models is presented. But the results are motivated through numerical examples.
Abstract: This article outlines existing knowledge on optimal designs for comparing test treatments with controls under 0-, 1- and 2-way elimination of heterogeneity models. The results are motivated through numerical examples.
98 citations
TL;DR: In this paper, an efficient numerical method is applied to obtain optimal parameters for both linear and non-linear damped dynamic vibration absorbers, and the minimization of the vibration response has been carried out for damped as well as undamped force excited primary systems with linear and nonsmooth spring characteristics.
67 citations
TL;DR: A trigonometric regression model is assumed for a problem involving circadian rhythm exhibited by peak expiratory flow and optimal and nonoptimal designs are derived and their relative efficiencies are established.
Abstract: A trigonometric regression model is assumed for a problem involving circadian rhythm exhibited by peak expiratory flow. Experimental designs are sought with a view to estimating a particular nonlinear function of the parameters. Both optimal and nonoptimal, but more practicable, designs are derived and their relative efficiencies are established.
63 citations
TL;DR: A survey is given of recent statistical work on the design of experiments, based on the literature of the last six years, with the emphasis on nonstandard applications of optimum design theory.
Abstract: Summary A survey is given of recent statistical work on the design of experiments, based on the literature of the last six years. The emphasis is on nonstandard applications of optimum design theory. Reference is made to surveys on the theory of optimum experimental design, crossover designs and incomplete block designs.
63 citations
TL;DR: In this paper, three procedures for calculating design derivatives of the non-linear critical load are described, and a simple and effective procedure among the three derived, which uses most of the information already calculated during analysis and sensitivity analysis of other constraints is selected.
Abstract: This paper describes three procedures for calculating design derivatives of the non-linear critical load. Constraints on the critical load arise naturally in optimal design of structures having non-linear behavior. The incremental procedures used for non-linear analysis can fail before reaching the final load level due to buckling or collapse of the structure. Therefore, load carrying capability of the structure must be improved before optimal design process can proceed further. This requires design derivatives of the critical load factor. A very simple and effective procedure among the three derived, is selected. It uses most of the information already calculated during analysis and sensitivity analysis of other constraints. Design sensitivity analysis is verified using two known examples. Several other structures are optimized to show effectiveness of the procedure. The sensitivity analysis can be combined with another constraints to optimize structures with more general requirements.
63 citations
TL;DR: A review of recent developments in the design of crossover experiments is presented in this article, where the effect of previous treatments may still be present when the current treatment is applied; most attention is paid to a model that assumes that these carryover effects persist for one period.
Abstract: Summary A review of recent developments in the design of crossover experiments is presented. The characteristic feature of such designs is that the effects of previous treatments may still be present when the current treatment is applied; most attention is paid to a model that assumes that these carryover effects persist for one period. Emphasis is placed on the impact of optimal design theory. The paper concludes by considering recent attempts to accommodate dependency in the error term of the model. Designs in which experimental units receive more than one treatment application in the course of the experiment are called crossover designs, change-over designs or repeated measurements designs. The former terms, abbreviated COD, seem preferable for experi- ments in which some units receive more than one treatment; the latter term can then be reserved for the case when each unit receives only one treatment. The experiment is split up into different periods, each unit receiving one treatment in each period. For designs considered in this paper, each unit is intended to be treated in the same number of periods, generally denoted by p. Designs are composed of several treatment sequences, each subject being allocated to a sequence at the start of the experiment; unless stated to the contrary, it is assumed that equal numbers of units are allocated to each sequence. The class of all COD comparing t treatments over p periods, using a total of n units, is denoted by co (t, n, p). The response variable is assumed to be continuous. The analysis of COD when the response is binary has been discussed in the literature (Gart, 1969; Prescott, 1981; Farewell, 1985; Jones & Kenward, 1987; Kenward & Jones, 1987a) but little has been written concerning the design of such experiments There are several reasons why COD are attractive.
55 citations
TL;DR: A separation principle for D -optimal design which states that under certain conditions the sensor placement problem is decoupled from the input design problem significantly simplifies the overall optimal experiment design determination for large multi-input multi-output structural systems with many unknown modal parameters.
50 citations
TL;DR: In this paper, the generalized simulated annealing algorithm was applied to the construction of exact optimal designs, and evaluated its effectiveness on both finite and continuous design spaces, and applied to both continuous and finite design spaces.
Abstract: SYNOPTIC ABSTRACTExact optimal designs have generally been constructed using a finite design space and various exchange algorithms, which are subject to premature convergence Branch-and-bound methods guarantee optimal designs, but are only computationally feasible for small problems We apply the generalized simulated annealing algorithm to the construction of exact optimal designs, and evaluate its effectiveness on both finite and continuous design spaces
47 citations
TL;DR: In this paper, the authors considered polynomial regression for estimating higher degree terms on the $q$-cube and provided approximate solutions for product designs with some efficiency calculations, including exact solutions within the class of product designs.
Abstract: Polynomial regression in $q$ variables of degree $n$ on the $q$-cube is considered. Approximate $D$-optimal and approximate $D_s$-optimal designs for estimating higher degree terms are investigated. Numerical results are given for $n = 2$ with arbitrary $q$ and for $n = 3, 4, 5$ and $q = 2, 3$. Exact solutions are given within the class of product designs together with some efficiency calculations.
45 citations
TL;DR: In this paper, the problem of combining optimality criteria using constrained optimization techniques is considered, and a necessary and sufficient condition similar to Kiefer (Theorem 1, 1974a) is obtained using Frechet derivatives.
TL;DR: Computer simulations of ligand-receptor interactions to evaluate the robustness of D-optimal designs for receptor assays when these designs are based on unrealistic models for ligand binding suggest that an optimal design for estimation of the parameters of a simple hyperbolic dose-response curve is nowhere near to being optimal in practice.
Abstract: The present paper reports the use of computer simulations of ligand-receptor interactions to evaluate the robustness of D-optimal designs for receptor assays when these designs are based on unrealistic models for ligand binding. Particular attention is paid to the assumed distribution of the measurement errors together with complications caused by 'non-specific' binding of a radioligand to a tissue or cell preparation. It is the latter factor which suggests that an optimal design for estimation of the parameters of a simple hyperbolic dose-response curve is nowhere near to being optimal in practice.
TL;DR: In this paper, an experimental design for quadratic (or linear) blending in the presence of process variables is presented, where the number of design points needed when different orthogonal blocks are used is usually smaller than when a single block is repeated at the various process variables levels.
Abstract: Blending experiments with mixture in the presence of process variables are considered. We present an experimental design for quadratic (or linear) blending. The design in two orthogonal blocks is D-optimized in the case where there are no restrictions on the blending in two orthogonal blocks is presented when there are arbitrary restrictions on the blending components. The pair of orthogonal blocks can be used with and arbitrary number of process variables. The number of design points needed when different orthogonal blocks are used is usually smaller than when a single block is repeated at the various process variables levels.
TL;DR: In this article, the p- version of the finite element method (FEM) was used for shape optimal design and the results indicated that similar optimal shapes can be obtained with fewer degrees of freedom than when compared with the h- version FEM.
Abstract: This paper presents some research results obtained recently using the p- version of the finite element method (FEM) for shape optimal design. The use of Bezier and B-spline curves to define design elements has proven to be an excellent way to model the geometry of the design problem. The p- version 2D elastic element was extended to employ part of a Bezier or B-spline curve as its element side for this purpose. This new element has been tested successfully with the patch test. Moreover, it is compatible, has no preferred direction, and contains all the required rigid-body modes (three zero eigenvalues are found in the element stiffness matrix). There are several advantages in using the p- version FEM for shape optimal design. The analysis and design models are often identical. In the p- version FEM, the stresses along an element side are as accurate as those inside the element. This feature is important because usually the critical stress constraints are found along the design element boundary. The final design can very easily be reanalyzed with a different element order to check the accuracy of the result. Some classical shape optimal design problems have been solved using the Conlin optimizer. The results indicate that similar optimal shapes can be obtained with fewer degrees of freedom than when compared with the h- version FEM. As with the h- version , less than ten structural analyses are sufficient for convergence in most of the problems.
TL;DR: In this article, the determinant of the information matrix in terms of canonical moments is expressed as a polynomial regression model on the unit q-ball and the robust-type D-optimal designs in the sense of Stigler (1971) and Studden (1982) are given.
22 Aug 1988
TL;DR: Analyzes geometric parameters of polar exponential arrays, and their relation to 3-D sensing precision requirements which drive sensor design, and a software testbed for simulation of the sensor geometry and mappings is described.
Abstract: The polar exponential arrays whose geometric parameters are presently analyzed have proven superior to X-Y raster imaging sensors when wide FOV, high central resolution, and rotation- and zoom-invariance are required; attractive applications for such arrays are in spacecraft docking/tracking/stationkeeping and mobile robot navigation. Attention is given to optimal designs minimizing sensor configuration and computation requirements, and the relation of geometric parameters to the three-dimensional sensing precision requirements driving sensor design. A method for smooth patching of the 'blind-spot' singularity in the sensor with a uniformly high-resolution 'fovea' is also presented.
TL;DR: In this paper, a computationally simple method of improving D-optimum designs is described, which is used as the starting point for the adjustment algorithm of the second-order model.
Abstract: Existing algorithms for the construction of exact D-optimum designs customarily search a list of candidate points. This article describes a computationally simple method of improving such designs. Tables are given of designs for second-order models with as many as five factors found by search over candidate points. These are compared with designs already in the literature and used as the starting point for the adjustment algorithm.
TL;DR: In this article, the problem of determining the variation in structural response, due to variations of these parameters, is considered and the sensitivity result is employed in the solution procedure for an optimization problem for a simple truss-structure under elastoplastic deformation.
Abstract: Elastic-plastic analysis problems are formulated as quadratic programming problems that involve energy functionals and equilibrium and yield constraints that depend on the design, material, and loading. The paper considers the problem of determining the variation in structural response, due to variations of these parameters. A general result is obtained for discrete structures. As an example of a distributed structure, a statically determinate beam that is described by a model in two spatial variables is considered. Implications for optimal design are also discussed and the sensitivity result is employed in the solution procedure for an optimization problem for a simple truss-structure under elastoplastic deformation.
TL;DR: In this article, the Han-Powell method and boundary search along active constraints were used to compute the optimal design parameters of a 2 HP, 115 V single-phase induction motor, resulting in maximum efficiency and minimum cost.
Abstract: For pt.I see ibid., vol.3, no.2, p.349-56 (1988). Emphasis on energy conservation demands an improvement of the efficiency of single-phase induction motors. The optimization techniques formulated in part I are used to compute the optimal design parameters of a commercially available 2 HP, 115 V single-phase induction motor, resulting in maximum efficiency and minimum cost. Based on the optimization results due to four optimization components, the relationships between efficiency, power factor, cost, active materials, and the values of the capacitance of the run capacitor are studied and the limited validity of the model law is discussed. The method of boundary search along active constraints and the Han-Powell method are applied to the above single-phase induction motor and the optimization results are compared. A hybrid method incorporating the advantages of both above-mentioned methods yields the best numerical optimization results. >
TL;DR: In this paper, the problem of finding A-optimal designs for comparing v test treatments with a control in b blocks of size k each is considered, and a condition on the parameters (u, b, k) is identified for which optimal step-type designs can be obtained.
Abstract: The problem of obtaining A-optimal designs for comparing v test treatments with a control in b blocks of size k each is considered. A condition on the parameters (u, b, k) is identified for which optimal step-type designs can be obtained. Families of such designs are given. Methods of searching for highly efficient designs are proposed for situations in which it is difficult to determine an A-optimal design. Under the usual additive homoscedastic model, an A-optimal design minimizes the average variance of the least squares estimators of the control-test treatment comparisons. Majumdar and Notz (1983) gave a method for finding A-optimal designs. Their optimal designs can basically be of two types, using the terminology of Hedayat and Majumdar (1984): rectangular (R), in which every block has the same number of replications of the control, and step (5), in which some blocks contain the control t times and the others t + 1 times. Optimal R-type designs were studied by Hedayat and Majumdar (1985). F...
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24 Feb 1988
TL;DR: In this paper, the authors present a method for the automatic design of optical thin films and a simple model of the Mean Value-Level Set (M-L) method, which is used in this paper.
Abstract: I Preliminary.- x1 Introduction.- 1.1 Statement of the Problem.- 1.2 Examples.- 1.3 Outline.- x2 An Appropriate Concept of Measure.- 2.1 Q-Measure.- 2.2 Lemmata.- II Integral Characterizations of Global Optimality.- x1 Mean Value Conditions.- 1.1 Mean Value over Level Sets.- 1.2 A Limit-Based Definition.- 1.3 Mean Value Conditions.- x2 Variance and Higher Moment Conditions.- 2.1 Variance over Level Sets.- 2.2 A Limit-Based Definition.- 2.3 Variance Conditions.- 2.4 Higher Moments.- 2.5 Higher Moment Conditions.- x3 The Constrained Cases.- 3.1 Rejection Conditions.- 3.2 Reduction Conditions.- 3.3 Linear Equality Constraints.- x4 Penalty Global Optimality Conditions.- 4.1 Penalty Mean Value.- 4.2 Penalty Mean Value Conditions.- 4.3 Penalty Variance and Higher Moment Conditions.- x5 Convex Programming.- 5.1 Optimality Conditions for Differentiable Convex Functions.- 5.2 Optimality Lemmas.- 5.3 Optimality Conditions for Convex Minimization.- 5.4 Generalized Gradient.- x6 Optimality Conditions for Differentiable Functions.- 6.1 General Discussion: the Unconstrained Case.- 6.2 The Inequality Constrained Case in ?n.- 6.3 Equality and Inequality Constrained Cases in ?n.- x7 Integer and Mixed Programming.- 7.4 Integer Minimization Problems.- 7.5 Optimality Conditions.- 7.6 Mixed Minimization Problems.- x8 Optimality Conditions for a Class of Discontinuous Functions.- 8.3 Robust Sets.- 8.4 The Structure of a Robust Set on the Real Line ?.- 8.5 Robust Continuity.- 8.6 Optimality Conditions.- III Theoretical Algorithms and Techniques.- x1 The Mean Value-Level Set (M-L) Method.- 1.1 Algorithm.- 1.2 Convergence.- 1.3 The Actual Descent Property.- 1.4 The Influence of Errors.- x2 The Rejection and Reduction Methods.- 2.1 The Rejection Method.- 2.2 The Reduction Method.- 2.3 The Reduction Method for Linear Equality Constrained Cases in ?n.- x3 Global SUMT and Discontinuous Penalty Functions.- 3.1 SUMT and the Set of Global Minima.- 3.2 Discontinuous Penalty Functions.- x4 The Nonsequential Penalty Method.- 4.1 Construction.- 4.2 Convergence.- x5 The Technique of Adaptive Change of Search Domain.- 5.1 A Simple Model.- 5.2 Convergence.- 5.3 Optimality Conditions of the Simple Model.- 5.4 The General Model.- x6 Stability of Global Minimization.- 6.1 Continuity of Mean Value.- 6.2 Stability of Global Minima.- x7 Lower Dimensional Approximation.- 7.1 Approximation of Global Minimum.- 7.2 Estimation of Degree of Approximation.- IV Monte Carlo Implementation.- x1 A Simple Model of Implemention.- 1.1 The Model.- 1.2 Monte Carlo Implementation.- 1.3 The Flow Chart.- x2 Statistical Analysis of the Simple Model.- 2.1 Estimators of the Search Domains.- 2.2 The Probability of Escape and the Sample Size.- 2.3 Asymtotic Estimation of the Amount of Computation.- x3 Strategies of Adaptive Change of Search Domains.- 3.1 Strategies.- 3.2 The Change of Domain Theorem.- 3.3 Reduction of the Skew Rate.- x4 Remarks on Other Models.- 4.1 Rejection and Reduction Models.- 4.2 Integer and Mixed Programming.- 4.3 The Multi-Solution Model.- x5 Numerical Tests.- V Applications.- x1 Unconstrained Problems.- 1.1 Automatic Design of Optical Thin Films.- 1.2 Optimal Design of an Equalizer Network.- x2 Applications of the Rejection Method.- 2.1 Optimal Design of Optical Phase Filters.- 2.2 Optimal Design of an Automatic Transmission Line Attenuation Compensation Network.- x3 Applications of the Reduction Method.- 3.1 Optimal Design of a Turbine Wheel.- 3.2 Nonlinear Observation and Identification.- x4 An Application of the Penalty Method.- 4.1 Weight Minimization of a Speed Reducer.- x5 An Application of Integer and Mixed Programming.- 5.1 Optimal Design of an Optical Thin Film System.
TL;DR: For fine quantization, an iterative algorithm for the design of an optimal analysis/synthesis system is presented, together with its convergence properties, and if no quantization is applied, the results obtained with the presented method coincide with previously reported results.
Abstract: A statistical model is used for the optimal design of analysis/synthesis systems that include quantization of the signals in separate bands. Two types of quantization approaches are analyzed: fine quantization modelled by additive noise, and matrix quantization. With proper modification, the model applies to other types of quantization approaches. Assuming that the system operates as a waveform coder, two error measures are used: a generalization of the usual statistical mean-square error (MSE) to time-varying systems, and the MSE between the outputs of the analysis of the original and reconstructed signals. The measures are shown to be equivalent. A method that is applicable to the design of optimal synthesis filters, given the analysis filters, is presented. For fine quantization, an iterative algorithm for the design of an optimal analysis/synthesis system is presented, together with its convergence properties. If no quantization is applied, the results obtained with the presented method coincide with previously reported results. >
TL;DR: The efficiency of balanced treatment allocation methods in clinical trials for comparing treatments with respect to survival is assessed and they are found to be very efficient.
Abstract: We assess the efficiency of balanced treatment allocation methods in clinical trials for comparing treatments with respect to survival. We compare optimal designs for each of three standard survival analysis techniques (maximum partial likelihood estimation, log-rank test, exponential regression) with balanced designs, over a range of hypothetical trials. Although balanced designs are not optimal, we find them to be very efficient. In view of the high efficiency demonstrated in this and in a previous paper (Begg and Kalish, 1984, Biometrics 40, 409-420), and practical difficulties in implementing an optimal design, we recommend the use of balanced allocation methods in practice.
TL;DR: In this paper, an optimal design approach for a highly homogeneous coil system used in magnetic resonance imaging is described based on combination of a numerical boundary element method for analysis of the magnetic field distribution and a mathematical programming method for solving the corresponding optimization problem using a nonlinear least-squares technique.
Abstract: An optimal design approach is described for a highly homogeneous coil system used in magnetic resonance imaging. The technique is based on combination of a numerical boundary-element method for analysis of the magnetic-field distribution and a mathematical programming method for solving the corresponding optimization problem using a nonlinear least-squares technique. The details of the algorithm and examples of its application to the design of a 1-T whole-body superconducting coil system are given. In the example the coil cross-sectional shape and the coil position are optimized. >
TL;DR: By using the criterion of D-optimality of the Fisher information matrix, general optimal vectors are characterized which could be used for constructing Bayesian or locally D-optimal designs.
TL;DR: This algorithm is tested with a large number of examples to verify its usefulness for large problems with multiple loading conditions, the choice of a proper move limit factor, developing some approximate methods and possible extension to problems with frequency constraints.
Abstract: Optimal design of trusses requires the use of available discrete sections. The improved move limit method of sequential linear programming is a well established procedure for the optimal design of trusses. The branch and bound discrete linear programming method is effectively merged with sequential linear programming for the discrete optimal design of trusses. This algorithm is tested with a large number of examples to verify its usefulness for large problems with multiple loading conditions, the choice of a proper move limit factor, developing some approximate methods and possible extension to problems with frequency constraints. Two approximate methods are developed for the solution of the problem which gives results permitting the discrete solutions to be compared.
TL;DR: In this article, the authors considered comparative clinical trials with R (R ≥ 2) treatments and allocation designs that aim to balance the assignment of treatments while controlling selection bias, and presented a recursion procedure for computing the exact conditional randomization distribution of a wide class of test statistics under these restricted designs.
Abstract: This article considers comparative clinical trials with R (R ≥ 2) treatments and allocation designs that aim to balance the assignment of treatments while controlling selection bias. A general form of these restricted designs was presented by Smith (1984a). His class of designs encompasses most of the other designs, including Efron's (1971) biased coin design (BCD). Widespread use of these designs is impeded by the lack of knowledge concerning the proper statistical analyses of the resulting data. In particular, little is known about the small-sample randomization distributions of test statistics. Thus current approaches rely on large-sample approximations, simulation techniques, and distributional results derived under classical schemes such as the complete randomization design. Clearly, none of these approaches is exact. A recursion procedure is presented for computing the exact conditional randomization distribution of a wide class of test statistics under these restricted designs. This proced...
01 Aug 1988
TL;DR: In this paper, various approaches and mathematical models that have been used to simulate, design, and synthesize flotation circuits are examined, and the merits and demerits of these two approaches are discussed.
Abstract: In this review article, various approaches and mathematical models that have been used to simulate, design, and synthesize flotation circuits are examined. First, a brief review of flotation kinetics is presented which is followed by a discussion on simulation of flotation circuits. The existing literature on optimal design of flotation circuits has been divided into two broad categories. In the first category, a generalized integral approach is used wherein the optimal circuit design involves determination of both optimal interconnection of various flotation cells/ banks of cells in terms of structural parameters and optimal values of various operating parameters. In the second category, a conventional circuit configuration is assumed to be the best configuration; the optimal design here only means the optimization of operating parameters. The merits and demerits of these two approaches are discussed.
TL;DR: In this paper, a numerical design procedure is presented to optimise the structural and controller parameters simultaneously, and two examples illustrating the nature of the optimization problem and the numerical procedure involved are presented.
Abstract: The problem of optimal design of active structures has been shown to be one of simultaneous structural and control design optimization. The basic equations represent, in general, a large system of coupled nonlinear differential equations. The purpose of this paper is to present a numerical design procedure which optimizes the structural and controller parameters simultaneously. Two examples illustrating the nature of the optimization problem and the numerical procedure involved are presented.