Showing papers on "Optimal design published in 1983"
TL;DR: In this article, a rigorous mathematical formulation for the problem of optimal design under uncertainty is presented, which involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region.
Abstract: A rigorous mathematical formulation is presented for the problem of optimal design under uncertainty. This formulation involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region. To circumvent the problem of infinite dimensionality in the constraints, an equivalence for the feasibility condition is established which leads to a max-min-max constraint. It is shown that if the inequalities are convex, only the vertices in the polyhedron need to be considered to satisfy this constraint. Based on this feature, an algorithm is proposed which uses only a small subset of the vertices in an iterative multiperiod design formulation. Examples are presented to illustrate the application to flexible design problems.
439 citations
TL;DR: In this article, the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation are discussed. And empirical evidence for improving single-point methods are given.
Abstract: Some problems unique to the construction of N-point D-optimal designs on convex design spaces are considered. Multiple-point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single-point procedures. Moreover, some recommendations for improving single-point methods are given. Finally, empirical evidence is found that supports the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation.
139 citations
TL;DR: In this paper, the orthogonality condition ensuring that both information matrices are equal is examined in the model for repeated measurements designs which was considered e.g. by Cheng and Wu (1980).
Abstract: The information matrices of one design in a finer and a simpler linear model are compared to each other. The orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e.g. by Cheng and Wu (1980). Examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum. Moreover, nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved, if the numbers of units and periods are sufficiently large.
115 citations
TL;DR: For a linear elastic structure, the first variation of an arbitrary stress, strain and displacement functionals corresponding to variation of material parameters within specified domain is derived by using the solution for primary and adjoint systems.
97 citations
TL;DR: In this paper, nonlinear programming techniques are applied to obtain optimal tuning and damping parameters for dynamic absorbers for damped as well as undamped primary systems, and it is found that optimal tuning parameters, obtained with the goal of minimizing the main mass maximum displacement, undergo small changes as damping is introduced into the main system.
Abstract: Nonlinear programming techniques are applied to obtain optimal tuning and damping parameters for dynamic absorbers The optimization has been carried out for damped as well as undamped primary systems It is found that optimal tuning parameters, obtained with the goal of minimizing the main mass maximum displacement, undergo small changes as damping is introduced into the main system The use of other objective functions, such as minimizing maximum velocity, or mean-squared motion to white noise excitation lead to more significant changes in optimal parameter values It is shown, on the basis of approximate solutions to the nonlinear absorber problem, that only small improvements in steady state response are obtained using hardening or softening coupling springs
90 citations
TL;DR: In this article, the problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied, and conditions for a design to be φ-optimal are found for a large class of functions.
Abstract: The problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied. B.I.B. designs are found to be $D$-optimal. $A$- and $E$-optimal designs are also obtained. For a large class of functions $\phi$, conditions for a design to be $\phi$-optimal are found. Most of the optimal designs are certain types of B.T.I.B. designs, introduced by Bechhofer and Tamhane (1981), which are binary in test treatments.
83 citations
46 citations
TL;DR: In this article, the optimal design of a clamped-hinged beam is determined with the objectives of minimizing the maximum deflection, maximum normal and shearing stresses and of maximizing the fundamental eigenfrequency.
41 citations
01 Feb 1983
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
36 citations
TL;DR: The optimal design for a 10.7 km long collection system at Indian Institute of Technology, Bombay with 52 lines, 245 links, 224 ordinary manholes and 21 junction manholes has been compared with conventional design to bring out that the algorithm requires small computer memory, small execution time and leads to optimal solution of a complete gravity wastewater collection system.
Abstract: A computer algorithm for the selection of optimal depth‐diameter combinations for all links of a complete gravity wastewater collection system has been developed using dynamic programming. The algorithm incorporates two subprocesses P1 and P2. The subprocesses P1 generates all feasible designs of inflowing lines at a junction manhole whereas P1 uses these feasible designs to provide the upstream invert level of the outflow line, simultaneously solving the matching problem encountered at each junction manhole. The problem of dimensionality has been minimized by exploiting the characteristic features of wastewater collection system. The optimal design for a 10.7 km long collection system at Indian Institute of Technology, Bombay with 52 lines, 245 links, 224 ordinary manholes and 21 junction manholes has been compared with conventional design to bring out that the algorithm requires small computer memory, small execution time and leads to optimal solution of a complete gravity wastewater collection system.
35 citations
TL;DR: In this article, the authors deal with techniques for finding optimal designs for weighing objects in weightings using a spring balance, and the optimality functions considered encompass a large class of functions.
Abstract: This paper deals with techniques for finding $\Phi$-optimal designs for weighing $v$ objects in $b$ weighings using a spring balance. The optimality functions considered encompass a large class of functions. Results are applied to find $A$-, $D$- and $E$-optimal designs and the optimal designs obtained are seen to be related to certain types of well known block designs.
TL;DR: In this article, a method is developed for the optimal design of multisource, looped, gravity-fed water distribution systems subjected to a single loading pattern based on linear programming (LP) techniques and produces a locally optimal solution.
Abstract: A method is developed for the optimal design of multisource, looped, gravity‐fed water distribution systems subjected to a single loading pattern. The method is based on linear programming (LP) techniques and produces a locally optimal solution. Initially, design feasibility constraints are derived to check whether network design and therefore network optimization is feasible. Based on classical transportation problem principles, a theory is developed to formulate an LP problem for obtaining design paths from the source nodes to the demand nodes and thereby for obtaining the design distribution graph for the entire distribution system. Separate LP optimization models are then formulated to deal with the either the D‐specified condition in which the nonprimary links are of some minimum or specified diameter, or the Q‐specified condition in which the nonprimary links carry some minimum or specified discharge. The proposed method is illustrated through a design example in an accompanying paper dealing with a...
TL;DR: In this paper, the existence of an optimal allocation is proved for each Bayesian optimality criterion, i.e. each criterion defined on the posterior covariance matrix for the treatments, under a special assumption on the treatment prior, the structure of the optimal design is specified.
Abstract: SUMMARY Bayes designs are considered for a two-way analysis of variance model with a normal prior for treatments and blocks, one of the treatments acting as a control. The existence of an optimal allocation is proved for each Bayesian optimality criterion, i.e. each criterion defined on the posterior covariance matrix for the treatments. Under a special assumption on the treatment prior, the structure of the optimal design is specified; for the case of only one test treatment such a design is universally optimal. Bayes D- and E-optimal designs are found as special cases and results are compared with classical ones. Two examples are included.
TL;DR: In this paper, the problem of optimal experimental design for estimating parameters in linear regression models is placed in a general convex analysis setting and duality results are obtained using two approaches, one based on subgradients and the other on Lagrangian theory.
Abstract: The problem of optimal experimental design for estimating parameters in linear regression models is placed in a general convex analysis setting. Duality results are obtained using two approaches, one based on subgradients and the other on Lagrangian theory. The subgradient concept is also used to derive a potentially useful equivalence theorm for establishing the optimality of a singular design and, finally, general versions of the original equivalence theorems of Kiefer and Wolfowitz (1960) are obtained.
TL;DR: In this article, the authors discuss the interrelations of these definitions using a recent characterization due to Friedland of convex functions of matrices, and show that any universally optimal design is (M, S)-optimal in the sense of K. Shah.
Abstract: Several definitions of universal optimality of experimental designs are found in the literature; we discuss the interrelations of these definitions using a recent characterization due to Friedland of convex functions of matrices. An easily checked criterion is given for a design to satisfy the main definition of universal optimality; this criterion says that a certain set of linear functions of the eigenvalues of the information matrix is maximized by the information matrix of a design if and only if that design is universally optimal. Examples are given; in particular we show that any universally optimal design is (M, S)-optimal in the sense of K. Shah.
TL;DR: In this paper, a design optimality criterion, tr (L)-optimality, is applied to the problem of designing two-level multifactor experiments to detect the presence of interactions among the controlled variables.
Abstract: A design optimality criterion, tr (L)-optimality, is applied to the problem of designing two-level multifactor experiments to detect the presence of interactions among the controlled variables. We give rules for constructing tr (L)-optimal foldover designs and tr (L)-optimal fractional factorial designs. Some results are given on the power of these designs for testing the hypothesis that there are no two-factor interactions. Augmentation of the tr (L)-optimal designs produces designs that achieve a compromise between the criteria of D-optimality (for parameter estimation in a first-order model) and tr (L)-optimality (for detecting lack of fit). We give an example to demonstrate an application to the sensitivity analysis of a computer model.
01 Jan 1983
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 parametric analysis of dynamics and control for Space-Shuttle-attached long 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 parametric analysis of dynamics and control for Space-Shuttle-attached long beams. An optimization scheme using a quadratic cost function is introduced yielding the optimal sizing of the tip vibration absorber. Analytical solutions 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 multiple mode case. An algorithm is developed to make an initial estimate of optimal tuning parameters which minimize the quadratic error cost function. Examples are given to illustrate the design concept.
TL;DR: In this article, it was shown that parameters corresponding to those used for partially balanced incomplete block designs can be defined for certain designs with m distinct concurrences, leading to a new upper bound for the efficiency factor which is attained if a PBIB (2) design exists.
Abstract: SUMMARY Incomplete block designs can be regarded as being in some sense approximately partially balanced. In this paper, we show that parameters Pjk corresponding to those used for partially balanced designs can be defined for certain designs with m distinct concurrences. These parameters have properties analogous to those for m associate-class partially balanced incomplete block (PBIB (m)) designs and have proved useful in searching for optimal designs. This leads to a new upper bound for the efficiency factor which, for given PJk values, is attained if a PBIB (2) design exists. Some results on complement and dual designs are also given.
TL;DR: In this article, a general formalism is presented for the optimal design of controllers of arbitrary prescribed order with the usual quadratic cost functionals, and the gradients of the cost functional are obtained in explicit form and involve Liapunov equations.
Abstract: Linear-Quadratic-Gaussian (LQG) theory generally requires the use of a full-order dynamic observer whose dimension is often prohibitive in applications so that reduced-order controller design techniques are needed. A general formalism is presented here for the optimal design of controllers of arbitrary prescribed order with the usual quadratic cost functionals. The gradients of the cost functional are obtained in explicit form and involves Liapunov equations. A fundamental aspect of this paper is a unifying formalism; direct output feedback and reduced-order controllers, stochastic and deterministic systems, infinite-time and finite-time problems and time-invariant and time-varying problems are considered. Optimization of sensor and actuator locations and parameter-variation-insensitive controller design are also considered within this framework. Examples are treated.
TL;DR: Algorithm based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems, and a general-purpose computer code GRP2 is developed based on this concept.
Abstract: In this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one-dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general-purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.
TL;DR: In this paper, a method for the optimal design of multisource, looped, gravity-fed water distribution systems subjected to a single loading pattern is illustrated through a design example, which uses linear programming (LP) techniques for two different purposes.
Abstract: A method for the optimal design of multisource, looped, gravityfed water distribution systems subjected to a single loading pattern is illustrated through a design example. The proposed methodology uses linear programming (LP) techniques for two different purposes. Initially, an LP problem similar to the classical transportation problem is formulated and solved to obtain the design distribution graph. This system is then optimized by successively formulating (if necessary) and solving an LP problem for obtaining the locally optimal solution. General comments on the suggested methodology and the limitations are also presented.
TL;DR: In this paper, the optimality properties of approximate block designs are studied under variations of the class of competing designs, optimality criterion, the parametric function of interest, and the statistical model.
TL;DR: In this article, a feedback system that optimizes the dynamic response of a synchronous machine connected to an infinite bus through a transmission line is designed. But the main purpose of this paper is not to design a feedback mechanism, but to design an optimal linear regulator.
Abstract: The main purpose of this paper is to design a feedback system that optimize the dynamic response of the system shown in Fig. (l). Such a system should be stable for any small disturbance. Pontryagin's maximum principle, which gives the solution for the optimal linear regulator problem through the eigenvector method , is applied. The system consists of a synchronous machine connected to an infinite bus through a transmission line. The effect of two control signals fed to the voltage requlator and the mechanical system is investigated. Also the effect of machine saturation on dynamic response is included.
TL;DR: The basic ideas of computer-aided design of manipulation robots based on adopted optimizational criteria and on set constraints of strengths, as well as on actuator capabilities are presented.
01 Jan 1983
TL;DR: In this article, the authors consider the problem of determining the optimal design of a transportation network using a vector valued criterion function when the flow pattern is assumed to correspond to a spatial price equilibrium.
Abstract: In this paper we consider the problem of determining the optimal design of a transportation network using a vector valued criterion function when the flow pattern is assumed to correspond to a spatial price equilibrium. Two alternative solution methods are tested for this problem. The first is based on iteration between the equilibrium model and the vector optimization model; the second employs the Hooke and Jeeves algorithm for nonlinear programming.
TL;DR: An application of the main ideas to data from assays of mouse jejunal crypt cell survival illustrates that use of a near-optimal design would have produced better results with 80 mice than were obtained with 140 mice.
Abstract: Certain fractionation protocols for multifraction in vivo colony assays permit the use of a statistical method to test the hypothesis that equal dose fractions produce equal decrements in cell survival and to obtain an estimate of the number of clonogens initially capable of structure regeneration. The essential requirement is that common doses per fraction be given in two or more regimens consisting of different fraction numbers. It is shown that the accuracy of the method is dependent upon the particular selection of common-dose regimens used in the assay. Calculations with theoretical data were used to determine guidelines for selecting the optimal experimental design. It was found that the fraction number pairs (n,m) which result in observable levels of survival tend to lie in a triangular region when plotted in the plane. Use of regimens corresponding to points along the lower edge of this triangle can substantially improve the results of the statistical method. It was also found to be optimal to use a minimal dose for each regimen, subject to the constraint that survival levels lie in the observable range. An application of the main ideas to data from assays of mouse jejunal crypt cell survival illustrates that use ofmore » a near-optimal design would have produced better results with 80 mice than were obtained with 140 mice.« less
TL;DR: In this article, minimum weight designs of statically indeterminate elastic beams subject to given loading are provided, and the resulting mathematical optimization problems are solved by using concepts from differential game theory and variational calculus.
Abstract: Minimum weight designs of statically indeterminate elastic beams subject to given loading are provided. Constraints are prescribed on flexural and shear stresses, and on the maximum deflection. The resulting mathematical optimization problems are solved by using concepts from differential game theory and variational calculus. The game problem under stress constraints is reduced to a minimax one. The solution procedure is illustrated by several examples of statically indeterminate beams. The optimal designs are compared with prismatic and linearly tapered beams. Suggestions are made as to the extension of the procedure to other indeterminate structures, such as beam columns (a).
01 Dec 1983
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 non-linear, deterministic and stochastic, multi-input 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.
TL;DR: In this paper, the optimal design of data collection for regionalized variables is studied in hydrology, the mining industry and other geostatistical applications, where an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.
TL;DR: In this paper, the optimal design of elastic beam-columns which are acted upon simultaneously by an axial compressive and transverse forces is considered, and the design has to be such that it uses least amount of material to achieve prescribed strength under given loading conditions.