Showing papers on "Optimal design published in 1973"
276 citations
TL;DR: In this article, a cost-reliability curve is used to illustrate the feasibility of arriving at an optimal system design using the latter concept, which is more general and can be extended to any number of constraints.
Abstract: The reliability literature offers an abundance of methods for the optimal design of systems under some constraints. In most of the papers, the problem considered is: given reliabilities of each constituent component and their constraint-type data, optimize the system reliability. This amounts to the assignment of optimal redundancies to each stage of the system, with each component reliability specified. This is a partial optimization of the system reliability. At the design stage, a designer has many options, e.g., component reliability improvement and use of redundancy. A true optimal system design explores these alternatives explicitly. Our paper demonstrates the feasibility of arriving at an optimal system design using the latter concept. For simplicity, only a cost constraint is used, however, the approach is more general and can be extended to any number of constraints. A particular cost-reliability curve is used to illustrate the approach.
121 citations
TL;DR: In this paper, the General Equivalence Theorem of Kiefer and Wolfowitz is extended to nonlinear models and an analogue of the variance function is introduced, which is used for optimum designs when not all the parameters are of interest.
Abstract: SUMMARY The General Equivalence Theorem of Kiefer and Wolfowitz is extended to nonlinear models. For this an analogue of the variance function is introduced. The results are extended to optimum designs when not all the parameters are of interest.
110 citations
TL;DR: In this article, the authors used a deflected gradient procedure to generate a Fiacco-McCormi ck penalty function, which is then minimized with a reduced set of design variables.
Abstract: The automated synthesis of large structural systems using a reduced number of design variables is investigated. The synthesis is accomplished by generating a Fiacco-McCormi ck Penalty function which is minimized with a deflected gradient procedure. The optimization algorithm is modified using a reduced set of design variables which greatly reduces the computer effort usually required for large structural problems and provides an upper bound solution. A rational procedure based on the external loads and constraints on the system is developed for generating the reduced set of coordinates. Examples of truss systems subjected to stress constraints, displacement constraints, and constraints on the design variables are studied in detail. For the examples considered, the results show large reductions in computer effort and demonstrate the effectiveness and efficiency of the method. The method provides a powerful tool for preliminary design studies, and appears to be the most effective method for obtaining near optimal designs of large systems.
109 citations
TL;DR: In this article, a unified treatment of equivalence theorems for D-optimal and Ds-optimality is provided in the form of duality theorem established by means of Strong Lagrangian Theory.
Abstract: SUMMARY A geometric interpretation of optimal design problems is given. This provides a unified treatment of the equivalence theorems for D-optimal and Ds-optimal designs in the form of duality theorems established by means of Strong Lagrangian Theory. The appropriate theorem for Ds-optimality is proved. A monotonic procedure for construoting D-optimal designs is suggested by the duality. This is described and its convergenee established.
99 citations
TL;DR: In this paper, an iterative, finite element method for minimum weight design of structures with respect to buckling constraints is presented, which can handle problems characterized by the existence of two fundamental buckling modes at the optimal design.
45 citations
TL;DR: In this paper, a class of fractional factorial designs of the 27 series, which are of resolutionV, are presented, allowing the estimation of the general mean, the main effects and the two factors interactions (29 parameters in all for the 27 factorial) assuming that the higher order effects are negligible.
Abstract: In this paper, we present a class of fractional factorial designs of the 27 series, which are of resolutionV. Such designs allow the estimation of the general mean, the main effects and the two factors interactions (29 parameters in all for the 27 factorial) assuming that the higher order effects are negligible. For every value ofN (the number of runs) such that 29≦N≦42, we give a resolutionV design that is optimal (with respect to the trace criterion) within the subclass of balanced designs. Also, for convenience of analysis, we present for each design, the covariance matrix of the estimates of the various parameters. As a by product, we establish many interesting combinatorial theorems concerning balanced arrays of strength four (which are generalizations of orthogonal arrays of strength four, and also of balanced incomplete block designs with block sizes not necessarily equal).
40 citations
TL;DR: In this article, a general method of optimal synthesis of spatial mechanisms is developed by displacement matrix-derived objective functions and constraints, implemented by Powell's recently published algorithm providing rapidly converging residual functions from the objective function and constraints of mechanisms.
30 citations
TL;DR: In this paper, a class of fractional factorial designs of the 27 series, which are of resolutionV, are presented, allowing the estimation of the general mean, the main effects and the two factors interactions (29 parameters in all for the 27 factorial) assuming that the higher order effects are negligible.
Abstract: In this paper, we present a class of fractional factorial designs of the 27 series, which are of resolutionV. Such designs allow the estimation of the general mean, the main effects and the two factors interactions (29 parameters in all for the 27 factorial) assuming that the higher order effects are negligible. For every value ofN (the number of runs) such that 29≦N≦42, we give a resolutionV design that is optimal (with respect to the trace criterion) within the subclass of balanced designs. Also, for convenience of analysis, we present for each design, the covariance matrix of the estimates of the various parameters. As a by product, we establish many interesting combinatorial theorems concerning balanced arrays of strength four (which are generalizations of orthogonal arrays of strength four, and also of balanced incomplete block designs with block sizes not necessarily equal).
27 citations
TL;DR: In this paper, the necessary condition for the optimal process system structure which includes both the optimal interconnection and optimal design of processing units is derived in terms of the structural parameters, essentially splitting factors of process streams connecting processing units.
24 citations
TL;DR: In this article, the optimal design of chemical processes involving parameter uncertainty is studied from the viewpoint of statistical decision theory, and a strategy which is more complicated but more suitable than those so far recommended by a few authors is proposed.
TL;DR: In this paper, numerical and analytical solutions to the problem of estimating the rate of a Poisson process were provided for various loss functions and the method of analysis is valid for any other loss function.
Abstract: SUMMARY This paper provides numerical and analytical solutions to the problem of estimating the rate of a Poisson process. Optimal designs are obtained for various loss functions and the method of analysis is valid for any other loss function. The cost of sampling plays a fundamental role and since there are many practical situations where there is a time cost and an event cost, a sampling cost per observed event and a cost per unit time are both included.
15 Jul 1973
TL;DR: In this paper, the authors apply steepest descent methods to optimal structural design problems in the context of finite-dimensional unconstrained optimization, using the calculus of variations and optimal process theory.
Abstract: : Contents: Elements of computer aided design; Finite dimensional unconstrained optimization; Linear programming; Nonlinear programming and finite dimensional optimal design; Finite dimensional optimal structural design; The calculus of variations and optimal process theory; Optimal structural design by the indirect method; Methods of steepest descent for optimal design problems; Application of steepest descent methods to optimal structural design.
TL;DR: In this article, the experimental situations in which block size is constant and exceeds the number of treatments; the cost of experimental units is high and this cost is principally associated with blocks as a whole; and a balanced design is requlired.
Abstract: In many biological and industrial experiments the number of experimental units and their groupings into blocks are such that the experimenter cannot influence them without sacrifice of experimental purpose or material. This paper is directed to those experimental situations in which block size is constant and exceeds the number of treatments; the cost of experimental units is high and this cost is principally associated with blocks as a whole; and a balanced design is requlired. Tests of pertinent hypotheses are developed, easily applied expressions for estimates of treatment effects, and their variances are found. The selection of the most effective designs for particular experimental situations is considered and tables of optimal designs for these are presented.
01 Jan 1973
TL;DR: In this paper, a new theoretical formulation of plane stress is given to obtain the optimal distribution of thickness under the condition that there is no collapse. But the number of constraints is not reduced, and static admissibility is not guaranteed.
Abstract: Two-dimensional problems in plane stress are considered, with a view toward obtaining the optimal distribution of thickness under the condition that there be no collapse. Geometrical constraints on the shape of the structure are included for the purpose of meeting practical limitations. The aim of the paper is to give a new theoretical formulation to the problem in order to effect greater savings in computer time. In particular, the number of constraints is shown to be significantly reduced, and static admissibility is guaranteed even when dealing with a reduced formulation of the problem. This is done by linearizing the yield surface and by expressing the stress vectors as linear nonnegative combinations of the vertices of the yield polyhedron, and by enforcing plastic conformity in a simple compact way. Known static and kinematic formulations are rederived by invoking the properties of linear programming. The effectiveness of the procedure is demonstrated through applications at the end of the ...
TL;DR: In this paper, a scheme is presented whereby a designer can achieve an optimal design by performing successive reanalyses (iterative design) using at each step the proper stiffness matrix.
TL;DR: In this article, the optimal design of an elastic truss subject to alternative loads and stress constraints is derived by the method of Lagrange multipliers, which provides practical means of determining whether a given fully stressed design is or is not optimal.
Abstract: This paper treats optimal design of an elastic truss subject to alternative loads and stress constraints. Necessary and sufficient conditions for local optimality of a fully stressed design are derived by the method of Lagrange multipliers. These criteria provide practical means of determining whether a given fully stressed design is or is not optimal.
TL;DR: In this article, upper and lower bounds for the optimal weight of a beam are derived, for single as well as for alternative loading conditions, and a superposition principle is established to establish the optimal design.
TL;DR: A new mathematical optimization technique, geometric programming, is used to optimize a number of journal bearing design problems and is found to be a powerful technique for optimizing journal Bearing design problems.
TL;DR: Optical experimental designs for the inverse estitator in the Linear Calibration problem using the crieterion of minimum intetrated or average mean squared error were developed for a linear approximation when the true model is linear and when it is quadratic as mentioned in this paper.
Abstract: Optical experimental designs are developed for the inverse estitator in the Linear Calibration problem using the crieterion of minimum intetrated or average mean squared error. Designs are developed for a linear approximation when the true model is Linear and when it is quadratic. In both cases, the optimal designs depend on unknown model parameters and are not realistically usable. Eowever, designs are shown to exist which are near optimal and do not depend on unknown model parameters
TL;DR: A probabilistic approach is presented that not only analyzes the probability of system failure but also uses this analysis to synthesize the optimal design of convective fins.
Abstract: In the design of convective fins, stochastic variations in fin dimensions have traditionally been handled by the use of safety factors. Often this process results in a multiplication of safety factors and thus an overly expensive design. This paper presents a probabilistic approach that not only analyzes the probability of system failure but also uses this analysis to synthesize the optimal design. Four methods of varying accuracy and difficulty are described and compared. The method based on the RMS approximation for the variances appears to be most useful for design purposes.
01 Jul 1973
TL;DR: In this article, the design of low-sensitivity optimal linear control systems with transportation lag, which are relatively insensitive to parameter variations, is presented, and the optimal control is with respect to a quadratic performance criterion which includes the state variable, control variable, state sensitivity function and control sensitivity functions as its arguments.
Abstract: The design of low-sensitivity optimal linear control systems with transportation lag, which are relatively insensitive to parameter variations, is presented. The optimal control is with respect to a quadratic performance criterion which includes the state variable, control variable, state sensitivity function and control sensitivity functions as its arguments. A detailed example shows that the low-sensitivity design is superior to the conventional optimal design with respect to sensitivity.
Journal Article•
TL;DR: In this paper, numerical optimisation based on mathematical programming is used to obtain both deterministic and stochastic lower-bound optimal designs for fiber-reinforced axisymmetric plates.
01 Sep 1973
TL;DR: The problem of determining the limiting performance characteristics of mechanical systems subject to random input is studied in this paper, where a review of the classical work in the optimal design of stochastic systems is presented.
Abstract: The problem of determining the limiting performance characteristics of mechanical systems subject to random input is studied. A review is presented of the classical work in the optimal design of stochastic systems. Some recent results of stochastic optimal control theory are employed. The solution to the limiting performance problem is formulated in both the frequency and time domains. Both formulations require substantial, burdensome computations when applied to large scale systems.
TL;DR: The proposed method yields a transient response, not only with faster settling time, but also insensitive to small parameter variations, which can be extended to the optimal design of multi-parameter systems.
Abstract: A method for the optimal design of linear time-invariant systems with low sensitivity is proposed. The criterion of optimality is to choose system parameters and the corresponding optimal control so as to obtain zero or near-zero sensitivity of the optimal cost function. The proposed method yields a transient response, not only with faster settling time, but also insensitive to small parameter variations. The procedure is simple and can be extended to the optimal design of multi-parameter systems. It can be easily programmed on a digital computer without excessive increase in computer memory.
TL;DR: The set of original variables has been transformed by linear and invertible mapping into a set of auxiliary variables for which a simple constraint space exists and a gradient technique has been used for the minimization of a nonlinear function subject to nonlinear constraints.
Abstract: In communication systems for digital signals, such as data transmission systems, electrical networks (filters) are used to: 1. 1. Concentrate the signal energy in a given frequency band in order to avoid disturbance outside this band. 2. 2. Produce a suitable signal form to allow high transmission rates together with low error rates. To design such networks, a performance index has been defined and an optimization problem has been formulated. This problem can be classified as the minimization of a nonlinear function subject to nonlinear constraints. Instead of using penalty function methods to solve this nonlinear programming problem, the set of original variables has been transformed by linear and invertible mapping into a set of auxiliary variables for which a simple constraint space exists. For the minimization with the new set of variables, a gradient technique has been used which takes into account that linearization is only valid for small step changes in the variables. The last part of the paper describes a typical example of a pulse-forming network with bandpass characteristics.
01 Jan 1973
TL;DR: In this paper, a simple matrix inequality that allows one to prove in a few lines the E -optimality of many max-min designs having a high degree of symmetry is presented.
Abstract: Publisher Summary This chapter focuses on max–min designs in the analysis of variance. In a restricted context, M -optimality and E -optimality of analysis of variance designs are closely related. This chapter presents a simple matrix inequality that allows one to prove in a few lines the E -optimality of many designs having a high degree of symmetry. Definitions of optimality may be found in the work of Kiefer; from it, one may obtain references to earlier work by A. Wald and S. Ehrenfeld. It is assumed that once a design C is decided and the random variable X is observed, the experimenter will use an analysis of variance test.