Showing papers on "Optimal design published in 1984"
TL;DR: In this article, the shape optimal design of an elastic structure is formulated using a design element technique, where Bezier and B-spline curves, typical of the CAD philosophy, are well suited to the definition of design elements.
494 citations
TL;DR: Optimal Bayesian experimental designs for estimation and prediction in linear models are discussed in this article, where the authors show that the optimal design is optimal for estimating a linear combination of the regression parameters or prediction at a point where the expected response is under squared error loss.
Abstract: Optimal Bayesian experimental designs for estimation and prediction in linear models are discussed The designs are optimal for estimating a linear combination of the regression parameters $\mathbf{c}^T\theta$ or prediction at a point where the expected response is $\mathbf{c}^T\mathbf{\theta}$ under squared error loss A distribution on $\mathbf{c}$ is introduced to represent the interest in particular linear combinations of the parameters In the usual notation for linear models minimizing the preposterior expected loss leads to minimizing the quantity $\mathrm{tr}\psi(R + XX^T)^{-1}$ The matrix $\psi$ is defined to be $E(\mathbf{cc}^T)$ and the matrix $R$ is the prior precision matrix of $\theta$ A geometric interpretation of the optimal designs is given which leads to a parallel of Elfving's theorem for $\mathbf{c}$-optimality A bound is given for the minimum number of points at which it is necessary to take observations Some examples of optimal Bayesian designs are given and optimal designs for prediction in polynomial regression are derived The optimality of rounding non-integer designs to integer designs is discussed
131 citations
TL;DR: A description of time-varrying digital filters is developed that uses a transfer function of two frequency variables that proves to be particularly powerful for periodicallyTime-varying systems and results in the sources and effects of aliasing and folding being explicitly shown.
Abstract: A description of time-varrying digital filters is developed that uses a transfer function of two frequency variables. This proves to be particularly powerful for periodically time-varying systems and results in the sources and effects of aliasing and folding being explicitly shown. This method is used to allow the optimal frequency domain design of these systems using time-invariant methods. An application to a narrow-band filter design gives up to a factor of three improvement in efficiency.
80 citations
TL;DR: The authors generalizes Mitchell's DETMAX algorithm to an arbitrary design criterion and describes an efficient implementation for minimizing either the maximum variance or the average variance of the response estimator over the design region.
Abstract: In experiments for response estimation, algorithms developed for constructing D-optimal exact (integer replication) designs may be inappropriate when the number of observations is not large relative to the number of parameters. This article generalizes Mitchell's DETMAX algorithm to an arbitrary design criterion and describes an efficient implementation for minimizing either the maximum variance or the average variance of the response estimator over the design region. Some examples are given that demonstrate the possible improvements in response estimator variances.
79 citations
TL;DR: In this paper, the design of the design parameters of passive vibration absorbers attached to a long cantilevered beam is studied, motivated by the need for conducting p arametric analysis of dynamics and control for spaceshuttle-attached l ong beams.
Abstract: The selection of the design parameters of passive vibration absorbers attached to a long cantilevered beam is studied. This study was motivated by the need for conducting p arametric analysis of dynamics and control for spaceshuttle-attached l ong beams. An optimization scheme using a quadratic cost f unction is introduced yiedding the optimal sizing of the tip vibration absorber. Analytical s olutions for an optimal absorber are presented for the case of one beam vibrational mode coupled with the absorber dynamics, and results are extended to cover the m ultiple mode case. An algorithm is developed to make an initial estimate of optimal tuning parameters which m inimize the quadratic error cost function. Examples are given to illustrate the design concept.
67 citations
TL;DR: Three approaches to solving design optimization problems with multiple conflicting objectives are described and compared by considering their computational efficiencies and their abilities to produce an approximation of the Pareto optimal set.
Abstract: This paper describes and compares three approaches to solving design optimization problems with multiple conflicting objectives. The three techniques are described in detail and then applied lo an example which demonstrates how information is accumulated which leads to a logical and efficient multicriteria optimal design. The techniques employed (weighting, noninferior set estimation and constraint methods) ate compared to each other by considering their computational efficiencies and their abilities to produce an approximation of the Pareto optimal set.
58 citations
TL;DR: In this paper, an optimality criterion-based method was developed to locate the optimal design of WF steel frames with members having general cross-sectional relationships among the area, moment of inertia, and section modulus.
Abstract: An optimality criterion-based method developed in this research is capable of locating the optimal design of WF steel frames with members having general cross-sectional relationships among the area, moment of inertia, and section modulus. The method uses the idea of one most critical constraint to avoid the calculation of large sets of Lagrange multipliers, and also avoids the scaling procedure normally used in other optimality criterion techniques. Several example structures, designed under stress, displacement, and minimum area constraints, demonstrate the efficiency, reliability, and simplicity of the method. Although the method of this research uses the idea of one most critical constraint, the optimal designs presented in this paper have several active constraints.
50 citations
TL;DR: In this paper, the robustness of nonlinear, deterministic and stochastic multi-input dynamical systems, under the assumption that all state variables can be measured, was studied.
Abstract: We study the robustness of optimal regulators for nonlinear, deterministic and stochastic multiinput dynamical systems, under the assumption that all state variables can be measured We show that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs These results are also valid for infinite horizon, average cost, stochastic optimal control problems
45 citations
TL;DR: In this article, a computer approach to the optimal design of structural concrete beams is presented, which allows the optimization for a variety of possible merit functions, considers all relevant limit state constraints by any standard code, and is valid for reinforced, prestressed and partially prestressed concrete members.
Abstract: A computer approach to the optimal design of structural concrete beams is presented The approach allows the optimization for a variety of possible merit functions, considers all relevant limit state constraints by any standard code (as well as other desirable engineering and construction requirements) and is valid for reinforced, prestressed and partially prestressed concrete members The problem formulation and a nonlinear programming technique for its solution are briefly described Four numerical examples illustrate some of the capabilities of the optimization program: (1) minimizing the amount of reinforcement for a given concrete section; (2) assessing the effect of steel cost ratios on optimal solutions; (3) optimizing the section shape of partially prestressed concrete beams; and (4) analysis of given designs with regard to all relevant criteria
43 citations
TL;DR: In this article, a block and row-column design for estimating the differences between two treatments with a single control control is presented, where the treatments are divided into two sets of u and w = v - u treatments.
35 citations
TL;DR: In this article, the variance of the difference between estimated responses at two points maximized over all pairs of points in the design space is taken as the criterion for selecting designs, and optimal designs under the criterion are derived for second-order polynomial models.
Abstract: SUMMARY Minimization of the variance of the difference between estimated responses at two points maximized over all pairs of points in the design space is taken as the criterion for selecting designs. Optimal designs under the criterion are derived for second-order polynomial models- when the design spaces are spherical.
01 Jan 1984
TL;DR: A state space design sensitivity analysis and optimization method is presented in which problems of optimal design of machines are formulated in a setting that allows treatment of general design objectives and constraints.
Abstract: A state space design sensitivity analysis and optimization method is presented in which problems of optimal design of machines are formulated in a setting that allows treatment of general design objectives and constraints. Synthesis of machines to perform both kinematic and kinetic functions is considered. A Cartesian coordinate formulation is employed for position, velocity, acceleration, and force analysis. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions that involve kinematic, force, and design variables. Linearization (or sequential quadratic programming) and gradient projection optimization algorithms are employed, using the design sensitivity analysis method developed, for design optimization. Four optimal design problems are solved to demonstrate use of the method.
TL;DR: In this paper, the authors demonstrate that Hill's statement is incorrect and present a suffkient condition under which it is valid and demonstrate that a D-optimal design for the estimation of a subset of the parameter vector in a partially nonlinear model depends on only those parameters that appear nonlinearly in the model.
Abstract: Hill (1980) states that a D-optimal design for the estimation of a subset of the parameter vector in a partially nonlinear model depends on only those parameters that appear nonlinearly in the model. In this note we demonstrate that Hill's statement is incorrect and present a suffkient condition under which it is valid.
TL;DR: In this paper, a computer simulation is performed to compare confidence regions arising from Fie1ler's theorem and approximate large sample intervals in estimating the point of extremum in quadratic regression.
Abstract: A computer simulation is performed to compare confidence regions arising from Fie1ler's theorem and approximate large sample intervals in estimating the point of extremum in quadratic regression. In addition, two designs, one of which is motivated by optimal design theory, are compared. These comparisons are made by examining the confidence level and accuracy of the regions, as well as the concentration of the standard point estimator, in a variety of settings. The results have implications for the more general problem of estimating a ratio of linear combinations in the general linear model.
TL;DR: In this article, the authors developed a minimax linear estimator robust against departures from an assumed model, and investigated concomitant questions of optimal design, including optimal design of the estimator.
TL;DR: In this article, a class of optimal design problems is considered, where the state problem is governed by a variational inequality and the coefficients of which are chosen as the design (control) variables.
Abstract: A class of optimal design problems is considered, where the state problem is governed by a variational inequality. The latter includes an elliptic operator, the coefficients of which are chosen as the design (control) variables.
TL;DR: In this paper, two frequency response optimization methods for vibrating systems are developed by appending absorbers to the original structure, which are suitable for discrete models with a large number of degrees of freedom and are applied to obtain optimal broadband response.
TL;DR: The application of information theory in a recursive least-squares context is described and its suitability for the optimal design problem is discussed and the resulting algorithms are simple, fast and easy to implement.
TL;DR: In this paper, a -optimal design in K(n,n) is given for n < 6 and for n = 6 for n ≥ 1.0. But small n and n are more important for practical use.
Abstract: Let K(N,n) denote the set of all N × n matrices X = (Xij ) where and Xij = −1.0.1 and N≥ n. Such matrices arise in designs of experiments. Certain results on A-optimal designs are obtained. Small N and n are more important for practical use. A -optimal designs in K (N,.n) are known for N <6 and are given here for N = 6.
TL;DR: In this paper, the minimum weight design of a delta-wing with stress, displacement and natural frequency constraints is presented, which is a combination of a previously developed method for stress and displacement constraints alone and one for frequency limited structures.
14 May 1984
14 May 1984
TL;DR: In this paper, an optimization problem for rotational maneuvers of a flexible structure is considered, and both structural parameters and active control torques are determined so that a specific cost functional is minimized.
Abstract: An optimization problem for rotational maneuvers of a flexible structure is considered. Both structural parameters and active control torques are to be determined so that a specific cost functional is minimized. Obtaining a numerical solution to the problem is shown to be practical if reduced-order structural models are employed. The time and frequency nature of the problem is discussed, and numerical examples are presented for a single a xis slew maneuver of a symmetric four boom structure.
TL;DR: In this article, the effect of prestress on a simple truss design problem with two loading conditions is discussed and optimality criteria are formulated to imply that the optimal design is fully stressed and to develop an iterative design scheme.
Abstract: This paper reviews the effect of prestress on a simple truss design problem with two loading conditions. Optimality criteria are formulated on the “sum” and “difference” problems. These criteria are subsequently interpreted to imply that the optimal design is fully stressed and to develop an iterative design scheme. Examples are included.
TL;DR: In this article, the problem of characterizing exact U- or D-optimal designs for a linear model with one qualitative and two quantitative factors of influence is treated, and necessary conditions for optimal designs are derived if no useful characterizations could be found.
Abstract: The problem of characterizing exactU- orD-optimal designs for a linear model with one qualitative and two quantitative factors of influence is treated. For three parameter-functionals of special interest easily applicable characterizations of optimal designs are given within the class of designs with fixed total sample size as well as in the class of designs with fixed treatment marginals. Necessary conditions for optimal designs are derived if no useful characterizations could be found.
TL;DR: In this paper, the modeling and design of general experiments with qualitative and quantitative factors of influence is presented and discussed, and a complete and ready to apply characterization of concrete optimal designs and their operational characteristics are given for the two basic models of analysis of covariance and of intra class regression under different experiment constraints.
Abstract: The modeling and design of general experiments with qualitative and quantitative factors of influence is presented and discussed. A complete and ready to apply characterization of concrete optimal designs and their operational characteristics are given for the two basic models of analysis of covariance and of intra class regression under different experiment constraints.
TL;DR: A simple method to obtain an optimal design by solving two sets of p1-linear simultaneous equations and a polynomial equation of p2th order is proposed and two nontrivial examples are given to illustrate this methodology.
TL;DR: In this paper, four general classes of partially balanced designs for 2n factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented, and the typical design in each class, the simplified form of the non-centrality parameter λ2 of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H0 is derived under defined local alternatives.
Abstract: Four general classes of partially balanced designs for 2n factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented. For the typical design in each class, the simplified form of the non-centrality parameter λ2 of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H0 is derived under defined local alternatives. Optimal designs d1 maximizing λ2 in the i-th class and minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix, i =1,…,4, are determined.
TL;DR: Optimal designs of the RSSR crank-rocker mechanism for various combinations of axis angle, oscillation angle and time ratio (quick return ratio) are presented in this article, where the optimization is on the basis of maximizing the minimum transmission angle in the motion cycle.