Showing papers on "Optimal design published in 1971"

Optimal Experimental Design for Polynomial Regression

Abstract: The problem of choosing the optimal design to estimate a regression function which can be well-approximated by a polynomial is considered, and two new optimality criteria are presented and discussed. Use of these criteria is illustrated by a detailed discussion of the case that the regression function can be assumed approximately linear. These criteria, which can be considered as compromises between the incompatible goals of inference about the regression function under an assumed model and of checking the model's adequacy, are found to yield designs superior in certain respects to others which have been proposed to deal with this problem, including minimum bias designs.

Optimal designs and spline regression

Abstract: Publisher Summary This chapter discusses the optimal designs and spline regression. Spline polynomials have received considerable attention from mathematicians, working especially in approximation theory. These functions seem to be extremely suitable for interpolating or approximating data in real world situations as in many cases, the underlying functional from s(x) is different on different parts of X . The term spline usually refers to a piecewise polynomial. The spline polynomials are the least oscillatory functions for interpolating data. For the D-optimal designs, one has the equivalence theorem of Kiefer and Wolfowitz, which shows that the D-optimal and minimax designs are equivalent.

Analysis and optimal design of self- oscillating dc-to-dc converters

Abstract: A general and exact analysis is presented for a class of selfoscillating dc-to-dc converters which can be modeled by a single-loop nonlinear feedback system. The nonlinearity is assumed to be a hysteresis characteristic; however, it is not required to have odd symmetry. A set of equations is obtained which govern the switching frequency, duty cycle, dc error, and peak-to-peak ripple. Based on these equations, it is possible to predict the general performance and inherent limitations of various circuit configurations. An optimal design procedure for these circuits with respect to a quadratic performance index is suggested. Measured data from several voltage-regulator circuits verify the model chosen and its analysis.

Optimal Designs with a Polynomial Spline Regression with a Single Multiple Knot at the Center

Abstract: In this paper it is shown that the optimal design for estimating any specific parameter in a polynomial spline regression with a single multiple knot at the center is supported by one of two sets of points. Familiarity with the notation and terminology used in the paper by Studden (1968) is assumed.

Optimal Designs with a Tchebycheffian Spline Regression Function

Abstract: Studden (1968) showed that the optimal design for estimating any specific regression coefficient or parameter is supported by one of two sets of points for Tchebycheff systems with certain symmetry properties. In this paper we consider a Tchebycheffian Spline Regression Function, defined on an interval, and show that the optimal design for estimating any specified regression coefficient is supported on the same set of points. Familiarity with the notation and terminology used in the paper of Studden referred to above is assumed.

Simplified Experimental Design

Abstract: The amount of statistics, numerical analysis, mathematics and computer programming involved in the design of experiments for estimating parameters in non-linear models is such that most potential users are discouraged from considering nonlinear design techniques, and since too few statisticians are available to assist in and direct such work, an easy-to-use flexible computer program for experimental design has been developed. To use this program, it is only necessary to provide a routine to compute the model, since the program obtains the various terms needed to accumulate the design determinant by numerical differentiation. Using given values for the variances of the quantities actually measured, the program computes the effective variance of each experiment, and then makes use of this knowledge in determining the optimal design. The program can of course be used in a sequential mode, with small groups of experiments being designed, performed and analysed in turn. The change in the total number of experi...

Optimum synthesis of a class of multiple-loop feedback systems

Abstract: Realization of arbitrary transfer functions by a special class of multiple-loop feedback configuration is investigated. The n th-order system consists of n nominally identical single-pole active stages with arbitrary but constant interconnections. The constraints on the sensitivity functions with respect to the active stages of such a system are obtained. is shown that the effect of identical perturbations of the gains of active stages, such as those which may be expected due to environmental variations, is invariant for a given transfer function, and hence can be accurately predicted. Subject to these constraints, conditions are derived for the minimum of a suitably defined multiparameter sensitivity index, which may then be used to minimize the effect of mutually independent random perturbations of the gains, such as those expected due to manufacturing tolerances. For second-order systems, the optimal design is obtained analytically. For higher order systems, a general optimization scheme, employing steepest descent from an initial design, is outlined. The optimal design of a fourth-order stagger-tuned bandpass filter is presented as an illustration.

Optimal design of sampled-data control systems by linear programming†

Abstract: This paper is devoted to the design of digital compensators for a special class of fnite-settling-time, linear, sampled-data control systems which are required to track both step and ramp inputs with no steady-state error. A general procedure is given to design the digital compensator so that the system is optimum on the basis of the ITAE (integral of time-weighted absolute value of error) criterion, subject to the constraint that the peak overshoot of the system for a step input is less than a certain percentage. Linear programming is used to find the optimum solution. Suitable upper bounds are imposed on the variables involved so that the peak overshoot of the system for a unit step input may not exceed a given value. A method of incorporating a specification on the acceleration constant (K a ) in the design is given, as also is a design example. For the case where finite settling time to a ramp input is not required, the design procedure is modified: a velocity constant (K a specification is incorporat...

An optimal system design process for a Mars roving vehicle

Abstract: The problem of determining the optimal design for a Mars roving vehicle is considered. A system model is generated by consideration of the physical constraints on the design parameters and the requirement that the system be deliverable to the Mars surface. An expression which evaluates system performance relative to mission goals as a function of the design parameters only is developed. The use of nonlinear programming techniques to optimize the design is proposed and an example considering only two of the vehicle subsystems is formulated and solved.

Quadratic performance index generation for optimal regular design

Abstract: Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.

Linear Combinations in Designing Experiments

Abstract: Parameters for experimental designs are selected so that their estimates are directly the answers to the investigator's questions Explicit consideration of the coefficients of the linear functions generating the estimates provides insight into the manner in which designs “work” Illustrations are given for the usually encountered treatment comparison designs

A sensitivity analysis of flexible pavement system fps2

Abstract: A SENSITIVITY ANALYSIS WAS PERFORMED TO ESTABLISH THE RELATIVE IMPORTANCE AND COST SENSITIVITIES OF THE DIFFERENT VARIABLES ON THE FLEXIBLE PAVEMENT SYSTEM, TO STUDY CHANGES IN THE STRUCTURAL DESIGNS GENERATED DUE TO CHANGES IN THE VARIABLE VALUES, AND TO COMPLETELY DEBUG THE PROGRAM TO FIND ANOMALIES AND PROBLEM AREAS. AN EXPERIMENT WAS DESIGNED TO OBTAIN THE REQUIRED INFORMATION. THREE BASIC SOLUTIONS WERE OBTAINED AT THREE BASIC LEVELS OF THE VARIABLES: LOW, AVERAGE, AND HIGH. THE SENSITIVITY OF EACH VARIABLE WAS STUDIED AT EACH OF THESE THREE BASIC LEVELS BY CHANGING THE VALUE OF THE PARTICULAR VARIABLE TO THE OTHER TWO LEVELS. A TOTAL OF OVER 400 PROBLEMS WERE SOLVED FOR THIS ANALYSIS. EACH PROBLEM THUS SOLVED WAS ANALYZED CAREFULLY FOR THE OVERALL COST OF THE OPTIMAL DESIGN AND ITS DIFFERENT COST CONSTITUENTS, DESIGN THICKNESS OBTAINED, AND NUMBER OF FEASIBLE DESIGNS GENERATED. BASED ON THE DESIGN AND COST SENSITIVITIES, THE VARIABLES PRODUCING SIMILAR EFFECTS WERE GROUPED TOGETHER. THE VARIABLES WERE RATED IN THE ORDER OF THEIR IMPORTANCE WITH RESPECT TO THE OVERALL COST OF THE OPTIMAL DESIGN. RECOMMENDATIONS ARE MADE IN TWO GENERAL AREAS, (1) THAT OF USING THE COMPUTER PROGRAM, AND (2) THAT OF ACHIEVING BETTER SENSITIVITY ANALYSIS INFORMATION FOR A SIMILAR EXPERIMENT IF PERFORMED IN THE FUTURE. /AUTHOR/

Optimal design procedures for two-level fractional factorial experiments given partial prior information about parameters

Abstract: Optimal design procedure as experimental design finite decision problem, using Bayes and minimax techniques