Showing papers on "Optimal design published in 1987"

Response surfaces : designs and analyses

Abstract: Introduction to response surface methodology matrix algebra, least squares, the analysis of variance, and principles of experimental design first-order models and designs second-order models and designs determining optimum conditions methods of estimating response surfaces that rival least squares based on the integrated mean squared error criterion analysis of multiresponse experiments response surface models with block effects mixture designs and analyses nonlinear response surface models Taguchi's robust parameter design additional topics and some directions for future research. Appendix: solutions to selected exercises.

Sequential Analysis and Optimal Design

Abstract: Preliminaries on probability Generalities about the conventional theory of design of experiments Optimal sample size Preliminaries on regression Design for linear regression: Elfving's method Maximum-likelihood estimation Locally optimal designs for estimation More design in regression experiments Testing hypotheses Optimal sample size in testing Sequential probability-ratio test Optimality of sequential probability-ratio test Motivation for an approach to sequential design of experiments in testing hypotheses Asymptotic optimality of procedure A in sequential design Extensions and open questions in sequential design The problem of adjacent hypotheses Testing for the sign of a normal mean: no indifference zone Bandit problems Sequential estimation of a normal mean sequential estimation of the common mean of two normal populations.

Optimal groundwater quality management under parameter uncertainty

Abstract: To date optimization models for groundwater quality management give no assurance that water quality standards will be met. This is in part because they ignore errors in hydraulic heads, flows, and solute concentrations due to flow and transport model parameter uncertainty. Here we explicitly incorporate parameter estimation and estimate uncertainties into a model for the optimal design of an aquifer remediation scheme. Parameter uncertainty is incorporated into the decision-making process. The objective is to identify the best remediation strategies (well site selection and pumping-recharge rates) so that water quality standards are met at a specified reliability level. The procedure couples three methods: (1) a finite element flow and transport simulation model combined with nonlinear least squares multiple regression for simultaneous flow and transport parameter estimation; (2) first-order first- and second-moment analysis to transfer the information about the effects of parameter uncertainty to the management model; and (3) nonlinear chance-constrained stochastic optimization combined with flow and transport simulation for optimal decision making. This joint approach enables one to estimate unknown aquifer parameters, quantify the uncertainty of the parameter estimates, simulate flow and transport responses, and automatically account for parameter uncertainty in the decision-making process through the simulation management model. Results show that remediation requirements can increase dramatically due to parameter uncertainty. Risk-averse design solutions automatically provide insurance by “overdesigning” the strategy relative to the risk-neutral case. The approach is fairly general and is applicable to a variety of groundwater management problems. The influence on design solutions of the reliability level and verification of the underlying statistical assumptions of the first-order analysis are explored in a sensitivity study and 2000 Monte Carlo simulations, respectively.

An approach to structure/control simultaneous optimization for large flexible spacecraft

Abstract: This paper presents an approach to the simultaneous optimal design of a structure and control system for large flexible spacecrafts based on realistic objective function and constraints The weight or total cost of structure and control system is minimized subject to constraints on the magnitude of response to a given disturbance involving both rigid-body and elastic modes A nested optimization technique is developed to solve the combined problem As an example, simple beam-like spacecraft under a steady-state white-noise disturbance force is investigated and some results of optimization are presented In the numerical examples, the stiffness distribution, location of controller, and control gains are optimized Direct feedback control and linear quadratic optimal controls laws are used with both inertial and noninertial disturbing force It is shown that the total cost is sensitive to the overall structural stiffness, so that simultaneous optimization of the structure and control system is indeed useful

The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models

Abstract: This article reports the application of the annealing algorithm to the construction of exact D−, I−, and G-optimal designs for polynomial regression of degree 5 on the interval [—1, l] and for the second-order model in two factors on the design space [—1, l] × [—1, 1]. Details of the perturbation scheme and the annealing schedules used are given, and the method of implementation is illustrated by means of a simple example. The algorithm is assessed by comparing its performance, in terms of computer time and effkiency, with the modified Fedorov procedure, and it is shown to be particularly effective in finding G-optimal designs. The salient features of the exact designs constructed in this study are also summarized.

Optimal Designs for Binary Data

Abstract: This article is concerned with the problem of selecting the values of the explanatory variable in logistic regression to obtain likelihood-based confidence regions of minimum area. One way of finding analytic solutions is by replacing the log-likelihood by a quadratic surface around the maximum, approximating in this way the likelihood regions by ellipses. The optimal allocation for this local approximation is derived without unnecessary restrictions. Since the implementation of the optimal allocation requires accurate initial estimates, a two-stage procedure that uses the second stage to complement the first is recommended. An alternative approach is to deal directly with the likelihood regions. In this case, the identification of the globally optimal allocation calls for numerical integration and optimization. The results presented here attempt to strengthen those introduced by Abdelbasit and Plackett (1983), who derived optimal allocation for the local criterion under the restriction of symmet...

Designs for group sequential phase II clinical trials.

Abstract: The main goal of Phase II cancer clinical trials is to identify the therapeutic efficacy of new treatments. For ethical reasons, group sequential procedures, which allow for early stopping when a treatment is either extremely effective or extremely ineffective, have been widely employed in these trials. Although several useful design methods have been discussed in the literature (Fleming, 1982, Biometrics 38, 143-152; Lee, 1979, Cancer Treatment Reports 63, No. 11-12), we are unaware of any results addressing the problem of finding an optimal rule easily by computer. In this paper, using an idea based on the Neyman-Pearson lemma, we propose a method to search over a restricted set of designs and to select the optimal one in this set according to optimality criteria. In all the combinations we have investigated (more than 100) the optimal design produced by our method is the true global optimum. Other applications are discussed.

A Reliability-Based Optimal Design Using Advanced First Order Second Moment Method

Abstract: Reliability-based optimization that is found in most literature has been formulated using the first order second moment (FOSM) method, because of its simplicity. In this paper, an advanced FOSM method is adopted, in order to better approximate probabilities. The resulting formulation becomes a modified parametric optimal design problem and a parametric optimal design technique is utilized to solve it. The finite element method is incorporated with the formulation and a detailed sensitivity analysis is made. In order to illustrate application of the present methodology, several numerical calculations are carried out for a three-bar truss and a twenty five-bar truss structure under several load conditions. In these examples, loads and yield stress are taken as random parameters with normal distribution.

Optimization of Three-Phase Induction Motor Design Part I: Formulation of the Optimization Technique

Abstract: This two-part paper deals with the optimization of the induction motor designs with respect to cost and efficiency. Most studies on the design of an induction motor using optimization techniques are concerned with the minimization of the motor cost and describe the optimization technique that was employed, giving the results of a single (or several) optimal design(s). In the present paper, a more comprehensive study on the optimization of a three-phase induction motor design was performed. This includes the relationship between motor cost, efficiency, and power factor; the effect of the properties of the electrical steel; and other effects as they occur in an optimal design. In addition, the optimization procedure that was used in this paper includes a design program, where some of the secondary parameters (which are called here variable constants), are modified according to the optimal results, in contrast to other studies where these parameters remain constant for the entire optimization. In this part, a new mathematical formulation of the optimization problem of the induction motor is presented.

Gradient-based combined structural and control optimization

Abstract: This paper considers the combined structural and control optimization problem for flexible systems. The sum of structural mass and controlled system energy terms is minimized simultaneously in structural and control parameters using gradient searches. The purpose of control is to effectively suppress structural vibrations due to initial excitations. Starting with a baseline structural design, the objectives of the combined structural/control optimization are twofold: 1) to reduce the structure's mass, and 2) to reduce total system strain, kinetic and control energies observed when the structure is excited. The appropriate weighting of energy and structural mass for balanced design and the dependence of optimal designs on initial conditions are discussed. The ideas presented are illustrated through numerical simulations using a 10-bar cantilevered truss.

Optimal crossover designs for the comparison of two treatments in the presence of carryover effects and autocorrelated errors

Abstract: SUMMARY A model for responses in a crossover experiment that includes direct and first-order carryover treatment effects, together with an autocorrelated error term, is considered when there are two treatments. A method for generating designs that minimize the variance of the estimated treatment effects is proposed and explicit results are given for the three and four period cases. Efficiencies of some practical designs are calculated.

Optimal structural design with control gain norm constraint

Abstract: A structure/cont rol system optimization problem has been formulated with constraints on the closed-loop eigenvalue distribution, structural frequencies, and the minimum Frobenius norm of the required control gains. Suggested is simultaneous optimization where, at each iteration, the control objective function is minimized first with the closed-loop eigenvalue constraints and then structural optimization is performed to satisfy the constraints on the optimal control gain norm and structural frequencies. The feasibility of the approach is demonstrated on a two-bar truss structure. For each locally optimal design, response simulations have been made and control efforts observed. Qualitative aspects of the optimal designs are also included and general conclusions drawn.

Constrained optimal designs for regression models

Abstract: An attempt of combining several optimality criteria simulaneously by using the techniques of nonliear programming is demonstrated. Four constrained D- and G-optimality criteria are introduced, namely, D-restrcted, Ds-restricted, A-restricted and E-restricted D- and G-optimality. The emphasis is particularly on the polynomial regression. Examples for quadratic polynomial regression are investigated to illustrate the applicability of these constrained optimality criteria.

Design of 2-D digital filters with an arbitrary response and no overflow oscillations based on a new stability condition

Abstract: This paper presents a new optimal-design-oriented stability condition for 2-D state-space digital filters. A general formulation for optimal design of 2-D recursive digital filters is obtained by applying the new condition. The formulation can be reduced into an unconstrained minimization problem and be used to design 2-D state-space digital filters with an arbitrary response. Furthermore, the resulting filters are guaranteed to be not only stable but also able to suppress overflow oscillations due to adder overflows. Some practical design techniques for the spatialdomain specifications and the frequency-domain specifications are proposed on the basis of the general formulation. Several examples are given to show the effectiveness of the proposed techniques.

Optimal topologies of flexural systems

Abstract: The main objects of this paper are: a)To introduce some relationships between optimal topologies and the geometric parameters of flexural systems.b) To investigate the effect of compatibility conditions on the optimal topology. Assuming the force method analysis, a linear programming formulation can be obtained under certain circumstances. In such cases where the active constraints can be determined a priori, a direct solution in the space of redundant forces might be possible. It is shown that the optimal design might correspond to a singular point in the design space. Neglecting compatibility conditions, multiple optimal topologies might be obtained for certain geometries. In such cases some of the resulting solutions usually represent statically determinate structures, therefore compatibility conditions do not affect the optimum Numerical examples illustrate these phenomena and how the optimal topology and its corresponding load path change with the geometric parameters.

Optimal Placement of Critical Speeds in Rotor-Bearing Systems

Abstract: The design of a rotor-bearing system is an iterative process in which the parameters that influence the design are modified until the desired design objectives are achieved. Primary among the design objectives is the minimization of the response amplitude within the operating range of the rotor system. An automated design procedure for the optimal placement of the critical speeds of a rotor is presented. The desired design objective is cast as a nonlinear programming problem that minimizes an objective function subject to constraints. The optimization program interacts with an analysis program to search for the feasible optimal design.

Boundary elements in shape optimal design of structural components

Abstract: The shape optimal design of shafts and two-dimensional elastic structural components is formulated using boundary elements. The design objective is to maximize torsional rigidity of the shaft or to minimize compliance of the structure, subject to an area constrain Also a model based on minimum area and stress constraints is developed, where the real and adjoint structures are identical, but with different loading conditions. All degrees of freedom of the models are at the boundary and there is no need for calculating displacements and stresses in the domain. Formulations based on constant, linear and quadratic boundary elements are developed. A method for calculating accurately the stresses at the boundary is presented, which improves considerably the design sensitivity information. It is developed a technique for an automatic mesh refinement of boundary element models. The corresponding nonlinear programming problems are solved by Pshenichny’s linearization method. The models are applied to shape optimal design of several shafts and elastic structural components. The advantages and disadvantages of the boundary element method over the finite element technique for shape optimal design of structures are discussed with reference to applications. A literature survey of the development of the boundary element method for shape optimal design is presented.

Shape design sensitivity analysis and optimal design of structural systems

Abstract: The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to relate variations in structural shape to measures of structural performance. A domain method of shape design sensitivity analysis is used to best utilize the basic character of the finite element method that gives accurate information not on the boundary but in the domain. Implementation of shape design sensitivity analysis using finite element computer codes is discussed. Recent numerical results are used to demonstrate accuracy that can be obtained using the method. Result of design sensitivity analysis is used to carry out design optimization of a built-up structure.

Simultaneous analysis and design optimization of nonlinear response

Abstract: The optimal structural design requiring nonlinear analysis and design sensitivity analysis can be an enormous computational task. It is extremely important to explore ways to reduce the computational effort so that more realistic and larger-scale structures can be optimized. The optimal design process is iterative requiring response analysis of the structure for each design improvement. A recent study has shown that up to 90 percent of the total computational effort is spent in computing the nonlinear response of the structure during the optimal design process. Thus, efficiency of the optimization process for nonlinear structures can be substantially improved if numerical effort for analyzing the structure can be reduced. This paper explores the idea of using design sensitivity coefficients (computed at each iteration to improve design) to predict displacement response of the structure at a changed design. The iterative procedure for nonlinear analysis of the structure is then started from the predicted response. This optimization procedure is called “mixed” and the original procedure where sensitivity information is not used is called the “conventional” approach. The numerical procedures for the two approaches are developed and implemented. They are compared on some truss type structures by including both geometric and material nonlinearities. Stress, strain, displacement, and buckling load constraints are imposed. The study shows the mixed method to be numerically stable and efficient.

On the Design of Structure and Controls for Optimal Performance of Actively Controlled Flexible Structures

Abstract: The simultaneous design of scruccure and active controls is considered for structures equipped with force controllers. Both requirements for mission control (prescribed terminal conditions) and for the control of structural response (control damping) are reflected in developments for the design of distributed parameter and large scale structures. As an example of problems with simple modal control, the optimal design is predicted for a cantilevered beam and for the feedback gains and actuator positions of its discrete controllers. Also the additional criterion to limit control spillover is incorporated into the formulation for modal control with a prescribed number of controlled modes. Computational results indicate that in some cases the use of a fully coupled model for the design of structure and its control devices leads to a considerable improvement in performance.

The sequential generation of multiresponse D-optimal designs when the variance-covariance matrix is not known

Abstract: : The construction of D-optimal designs for multiresponse experiments was previously considered. This algorithm required that the variance covariance matrix, Sigma, of the responses be known. This is rarely the case in practice. The primary objective of this paper is to develop a sequential procedure for the construction of multirespone designs when Sigma is not known. Several numerical examples are given to illustrate this procedure. Keywords: Multiresponse design; D optimality; Sequential generation.

Some optimal designs for repeated measurements with autoregressive errors

Abstract: SUMMARY A number of individuals are observed at equally spaced time points; different individuals behave independently but the observations on the same individual have the autocorrelation structure of a first-order autoregressive process. We are concerned with the optimal allocation of treatments, assuming that at each time point a new selection must be made. Conditions for optimality are given for models without nuisance parameters, and also with covariates and with block effects.

Sensitivity analysis and optimization of elastic-plastic structures

Abstract: Elastic-plastic analysis problems formulated as quadratic programming problems involve energy functional and equilibrium and yield constraints that depend on the design, material and loading. In this paper we consider the problem of determining the variation of structural response with respect to variations of these parameters. A general result for discrete structures is presented and implications for optimal design are discussed.

Probabilistic Design of Moment‐Resistant Frames Under Seismic Loading

Abstract: This is the second part of a two‐part paper on the development and preliminary testing of a methodology for the optimal probabilistic limit states design of seismic‐resistant steel frames. Part two illustrates the design of a three‐story, single‐bay, moment‐resistant steel frame using a computer‐aided design system called DELIGHT.STRUCT. Linear and non‐linear time history analyses are built into the design procedure itself rather than serving as a check at the end of the design process. The frame's performance is assessed on the basis of its statistical response to gravity loads alone, gravity loads plus a family of moderate earthquakes, and, finally, gravity loads combined with an ensemble of rare severe earthquake ground motions. Design objectives include the frame volume, minimum story drifts and maximum hysteretically dissipated energy. The Phase I–II–III Method of Feasible Directions is used to solve the constrained optimization problem for an optimal design that balances the attributes of minimum vo...

Optimal repeated measurements designs for comparing test treatments with a control

Abstract: A-optimal and mv optimal repeated measurments designs for comparing serveral test treatments with a control are considered. the models considered are basically of two types: without preperides and the cirular model. It is shown known that some known strongly balanced uniform repeated measurements designs can be modified to obtain optimal designs for this problem. Some other methods of finding optimal designs are also given.