Showing papers on "Optimal design published in 1972"
TL;DR: In this paper, the problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that the variance of the least-square estimate of the slope at the fixed point is a minimum and the average variance of a least-squares estimator of the estimate is the minimum is discussed.
Abstract: The problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that (a) the variance of the least-square estimate of the slope at the fixed point is a minimum and (b) the average variance of the least-square estimate of the slope is a minimum is discussed in this paper. In general these designs can be obtained using Kiefer-Wolfowitz [5] characterization of c-optimal designs, Federov [2] characterization of L-optimal designs, and Studden's [10] generalization of the Elfving Theorem [1]. After presenting a brief review of these characterization theorems, specific illustrations for the quadratic and cubic regressions are presented in detail.
43 citations
TL;DR: In this paper, a technique for the optimal design of a large class of structures arising in civil and mechanical engineering is presented, where constraints on stress level, magnitudes of elastic deformation, natural frequency and buckling load are admitted.
Abstract: This paper presents a technique for the optimal design of a large class of structures arising in civil and mechanical engineering. Constraint conditions on stress level, magnitudes of elastic deformation, natural frequency and buckling load are admitted. A computational method is developed, which takes advantage of special features of the structural optimization problem. Numerical examples are solved to illustrate the applicability of the method. These problems are, in themselves, of engineering interest.
41 citations
TL;DR: In this paper, the problem of selecting an optimal mix of pipe diameters and slopes, given a set of economic and technological inputs as well as a network layout, is formulated as a separable convex programming problem.
Abstract: This paper addresses itself to the question of obtaining the minimum cost design for a wastewater collection network. The concept of optimization is explored with respect to overall collection networks. Present design methodologies and recent developments in both network layout and design are explored. The design problems of selecting an optimal mix of pipe diameters and slopes, given a set of economic and technological inputs as well as a network layout is then formulated as a separable convex programming problem. The formulation guarantees the generation of a global optimal solution, and a numerical solution can be obtained using existing commercially available computer software. The paper concludes with an evaluation of the developed procedure and its possible adoption in everyday sewer design.
36 citations
TL;DR: Although many papers have been published on obtaining optimal regression designs, the approach of this paper is different in that it uses Bayesian decision theory rather than orthodox (classical) methods.
Abstract: We will be considering what Lindley (1968) in his paper on the choice of variables in multiple regression termed 'a prediction problem'. By this we mean that data from a regression experiment is analyzed in such a way that we can predict a future value of the dependent variable and choose which independent variables to use for the prediction. In this paper, the regression experiment is designed, i.e. the levels of the independent variables are selected. Our object is to find the optimal design. Although many papers have been published on obtaining optimal regression designs, the approach of this paper is different in that it uses Bayesian decision theory rather than orthodox (classical) methods. Lindley (1968) considered the prediction problem given the results of the regression experiment, and we shall be using some of his results in this paper.
31 citations
Book•
01 Jun 1972TL;DR: An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration, and an optimal plate thickness distribution in analytical form is found.
Abstract: An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration An optimal plate thickness distribution in analytical form is found The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions The second equation requires dynamic equilibrium at the preassigned vibration frequency
27 citations
TL;DR: Dynamic programming has been found a useful technique for the synthesis of optimal layouts for braced frameworks, provided that the interconnection between different parts of the structure is relatively simple.
23 citations
TL;DR: In this paper, the effect of random error in interpolation or extrapolation was studied for first-degree polynomial models in k factors, although some results were given also for second-degree models.
Abstract: Designs are given for minimizing the effect of random error in interpolation or extrapolation. The case most intensively studied is that for first-degree polynomial models in k factors, although some results are given also for second-degree models. Emphasis is put on designs giving minimum variance at a particular point and satisfying additional requirements such as leading to good estimates of parameters.
20 citations
TL;DR: The geometric programming approach provides important design insights by yielding the proportions of the total cost to be assigned to the cost components, fill material, sheet piling and flooding in an optimal design.
Abstract: The design of circular type cellular cofferdams is formulated as a nonlinear optimization model that takes explicit account of relevant economic and technologic aspects. The objective is minimization of total expected cost. The constraints arise from stability critera to protect against failures due to slipping of the sheet piles on the river side and interlock stresses at the joint. A solution achieved with geometric programming techniques, yields optimal cell sizes and design heights. The geometric programming approach provides important design insights by yielding the proportions of the total cost to be assigned to the cost components, fill material, sheet piling and flooding in an optimal design.
16 citations
TL;DR: In this article, the optimal distribution of pressure drop over a network in which flow-rates are specified, but pipe diameters may vary, is considered, by using elements of the duality theory of nonlinear programming.
13 citations
10 citations
TL;DR: In this article, a method to minimize the maximum decrease in the process performance caused by the hypothetical worst parameter variations is proposed, which is applied to the design of a tubular reactor associated with catalyst activity decay.
Abstract: Unpredictable variations in the values of plant parameters around their nominal values are often encountered in actual operation of process plants. In order to assure that process performance meets specifications, it is preferable to design and control the process, taking into account the uncertainty in the values of the plant parameters. In this paper, a method to minimize the maximum decrease in the process performance caused by the hypothetical worst parameter variations is proposed. Necessary condition for the worst parameter variations is derived for a class of distributed parameter systems by means of the maximum principle, and then the method for obtaining the optimal design and control subject to the worst parameter variations are discussed. The method is applied to the design of a tubular reactor associated with catalyst activity decay. The reactor obtained is fairly insensitive to the variations in the process parameters while maintaining fairly good performance even at the nominal values of parameters.
01 Oct 1972
TL;DR: In this article, it was shown that a design (f sub x) is equivalent to a real function of one variable delta sub ( f sub x), which is in turn very helpful not only in characterizing optimal designs, but also in constructing them.
Abstract: : Except for the proof of the convergence of the iterative method for the construction of (C sub 3)-constrained D-optimal designs this report gives a complete answer to the first step of what could be a theory of optimal designs for dynamic models: under realistic assumptions it is shown that a design (f sub x) is equivalent to a real function of one variable delta sub(f sub x), which is in turn very helpful not only in characterizing optimal designs, but also in constructing them.
TL;DR: In this paper, the authors presented an optimal design using the Selected Active Constraints Technique (SACT) and a systematic synthesis for the Vierendeel-type poles.
Abstract: Because presstressed concrete Vierendeel-type poles are cheaper than other types in India, millions are required to provide rural electrification. Using an optimal design for these repetitive-type components, considerable savings can be realized. The paper presents an optimal design using the Selected Active Constraints Technique (SACT), and a systematic synthesis. The direct design procedure is generated. Design behavior and loadings are treated as input and geometrical properties are systematically derived. The design procedure, based on SACT, requires extensive experience on the part of the design engineer, however, the calculations are simple. A design example is presented using physical data obtained from the Gujaret State Electricity Board (GEB), India, for a 8.53 m, 204 kg pole. Cost analysis is made, using prevailing prices in India, to show the economic gain obtained by the optimal design. The optimal design shows an economy of 18% in material cost per pole and 35% in high tensile wire weight, for the example considered.
Journal Article•
TL;DR: In this paper, KHER ET AL. presented a conceptual system-analysing program for the 50th ANNUAL MEETING of the Highway Research Board (HRLB) by KHER et al. The program is based on a COMPREHENSIVE ECONOMIC ANALYSIS of VARIOUS PHASES of RIGID PAVEMENT DESIGN and MANAGEMENT.
Abstract: IN 1971, A CONCEPTUAL SYSTEMS ANALYSIS WAS PRESENTED AT THE 50TH ANNUAL MEETING OF THE HIGHWAY RESEARCH BOARD BY KHER ET AL. THE PRESENT PAPER DESCRIBES THE EQUATIONS AND METHODS OF SOLUTION THAT ARE REQUIRED TO PERFORM THE SYSTEMS ANALYSIS OUTLINED IN THAT PAPER. A COMPUTER PROGRAM SOLVES THE MATHEMATICAL MODELS BY USING SYSTEMS ANALYSIS CONCEPTS PREVIOUSLY DESCRIBED BY THE AUTHORS. ANALYSIS TECHNIQUES, REQUIRED INPUTS, AND THE OUTPUT OBTAINED ARE ALSO DESCRIBED. A PRELIMINARY SYSTEM EVALUATION HAS BEEN ATTEMPTED THROUGH A SENSITIVITY ANALYSIS OF IMPORTANT VARIABLES AFFECTING RIGID PAVEMENT DESIGN. THE COMPUTER PROGRAM IS BASED ON A COMPREHENSIVE ECONOMIC ANALYSIS OF VARIOUS PHASES OF RIGID PAVEMENT DESIGN AND MANAGEMENT. IN GENERAL, PAVEMENT AND OVERLAY TYPE, REINFORCEMENT DESIGN, JOINT DETAILING, SUBBASE AND CONCRETE THICKNESS DESIGN, AND MAINTENANCE AND OVERLAYING ARE THE IMPORTANT PHASES THAT ARE ANALYZED TO OPTIMIZE FOR THE BEST POSSIBLE DESIGN CONFIGURATION. THE PROGRAM USES 117 DIFFERENT INPUT VARIABLES AND GIVES THE OPTIMAL DESIGN AND 23 NEARLY OPTIMAL DESIGNS IN INCREASING ORDER OF TOTAL OVERALL COST. THE ORDERED CHOICE PROVIDES THE DESIGNER OR THE ADMINISTRATOR WITH INFORMATION NEEDED IN MAKING A RATIONAL PAVEMENT DESIGN DECISION.
TL;DR: The optimal design of a panel flutter problem is investigated in this article, where the thickness distribution of the panel is allowed to vary while the total weight is held fixed, and the distribution which maximizes the critical flutter parameter for stability is chosen as the optimal design.
Abstract: The optimal design of a panel flutter problem is investigated in this paper. A semi-infinite flat panel with either a homogeneous or sandwich cross section is considered. The thickness distribution of the panel is allowed to vary while the total weight is held fixed, and the distribution which maximizes the critical flutter parameter for stability is chosen as the optimal design. This design is calculated here by means of a generalized Ritz procedure, with the panel thickness assumed to have a certain form.
01 Nov 1972
TL;DR: The numerical methods developed in relation with the notion of D-optimality allow for a greater flexibility in judging the overall quality of a design, suggesting the need for a more general theory.
Abstract: : In a preceding report (D-Optimal Designs For Dynamic Models, Part 1) some results on the theory of C-constrained D-optimal designs were presented. The present report is intended to be an illustration of the methods proposed: the consideration of different examples raises some interesting questions and remarks concerning both the theoretical situation considered in the previous report and the possible applications. The numerical methods developed in relation with the notion of D-optimality allow for a greater flexibility in judging the overall quality of a design, suggesting the need for a more general theory. (Author Modified Abstract)
01 Nov 1972
TL;DR: In this article, two low-order polynomial models are considered as approximations to unknown functionships, and an optimal means of designing experimental tests are presented which, for a modest number of measurements, yield prediction equations that minimize the error of an estimated response anywhere inside a selected region of experimentation.
Abstract: Some of the basic concepts are unified that were developed for the problem of finding optimal approximating functions which relate a set of controlled variables to a measurable response. The techniques have the potential for reducing the amount of testing required in experimental investigations. Specifically, two low-order polynomial models are considered as approximations to unknown functionships. For each model, optimal means of designing experimental tests are presented which, for a modest number of measurements, yield prediction equations that minimize the error of an estimated response anywhere inside a selected region of experimentation. Moreover, examples are provided for both models to illustrate their use. Finally, an analysis of a second-order prediction equation is given to illustrate ways of determining maximum or minimum responses inside the experimentation region.
TL;DR: In this paper, a non-linear programming (NLP) method is used to find an optimal solution to the design of a survey system to meet specified accuracy, in which the combination of various types of observations will yield the required accuracy of control points for a minimum cost.
Abstract: This paper discusses theory and results of an attempt to use non-linear programming methods to arrive at an optimal, in the sense of least cost, solution to the design of a survey system to meet specified accuracy. In other words, the method determines the combination of various types of observations which will yield the required accuracy of control points for a minimum cost. The theoretical background of the procedure is discussed, and methods of extension to photo-grammetry and other sciences are presented. Much of the paper is concerned with discussing results of numerical solutions for the optimal design of several small, but typical, mapping problems.
TL;DR: In this article, a problem of optimal design of a prestressed elastic structure is formulated and its relations to the problems of optimal limit design and optimal shakedown design of elastic, perfectly plastic structures are investigated.
TL;DR: In this article, the optimal plastic design of doubly symmetric closed ring and frame structures of idealized sandwich section is formulated utilizing the Marcal-Prager optimization method, and detailed results are presented for elliptical rings and rectangular frames under uniform internal pressure.
01 Jan 1972
TL;DR: In this article, the problem of systematically determining the optimal design for an unmanned Mars-roving vehicle is considered, and a system model, identifying all feasible designs, is generated by consideration of the physical constraints on the design parameters, and the requirement that the system be deliverable to the Mars surface.
Abstract: The problem of systematically determining the optimal design for an unmanned Mars-roving vehicle is considered. A system model, identifying all feasible designs, 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 is developed. The model and objective function together allow simulation of the effects of design trade-offs upon system performance for all feasible designs. Nonlinear programming techniques are utilized to identify the optimal design.
TL;DR: In this article, the optimal design for SO"3 in the oxidation of SO"2 over a commercial vanadium pentoxide catalyst is considered, where the control variables are the wall heat flux and the reactor radius, both as functions of axial distance.