Showing papers on "Optimal design published in 1977"

Design of optimal water distribution systems

Abstract: A method called linear programing gradient (LPG) is presented, by which the optimal design of a water distribution system can be obtained. The system is a pipeline network, which delivers known demands from sources to consumers and may contain pumps, valves, and reservoirs. Operation of the system under each of a set of demand loadings is considered explicitly in the optimization. The decision variables thus include design parameters, i.e., pipe diameters, pump capacities and reservoir elevations, and operational parameters, i.e., the pumps to be operated and the valve settings for each of the loading conditions. The objective function, to be minimized, reflects the overall cost capital plus present value of operating costs. The constraints are that demands are to be met and pressures at selected nodes in the network are to be within specified limits. The solution is obtained via a hierarchial decomposition of the optimization problem. The primary variables are the flows in the network. For each flow distribution the other decision variables are optimized by linear programing. Postoptimality analysis of the linear program provides the information necessary to compute the gradient of the total cost with respect to changes in the flow distribution. The gradient is used to change the flows so that a (local) optimum is approached. The method was implemented in a computer program. Solved examples are presented.

Joint Economically Optimal Design of X and R Control Charts

Abstract: In this paper, we develop an expected cost model for a process whose mean is controlled by an XI„ chart and whose variance is controlled by an R chart. The expected cost comprises the fixed and variable costs of sampling, the cost of investigating and correcting the process when at least one control chart indicates that the process parameters have shifted, and the cost of producing defective units. We use a search procedure to determine the sample size, interval between samples and control limits for both charts that minimize the expected cost. Optimal solutions to numerical examples are presented. A sensitivity analysis of the model is performed. In addition, we find the optimal interval between samples and the expected cost for several examples with large shifts in the mean and variance where Shewhart's heuristic design is used in place of the optimal design. Comparison of the expected cost of the optimal design to the expected cost of Shewhart's design shows an increase in expected cost of only 0.4 to 8.2 percent for the latter design. But other situations are discussed and examples presented which indicate that the optimal design is preferred.

Optimal structural design under dynamic loads

Abstract: This paper presents an algorithm for optimal design of elastic structures, subjected to dynamic loads. Finite element, modal analysis and a generalized steepest descent method are employed in developing a computational algorithm. Structural weight is minimized subject to constraints on displacement, stress, structural frequency, and member size. Optimum results for several example problems are presented and compared with those available in the literature.

Some optimal designs for sampling in two dimensions

Abstract: SUMMARY Employing a superpopulation model, we derive conditions for which a sampling design of a two-dimensional finite population is optimal in the sense of minimum average variance, when the estimator of the population mean is the sample mean. We find that an overall optimal design does not exist, but that, if we consider three subclasses of two-dimensional sampling designs, then the optimal design within each subclass is a type of systematic sampling.

Comparison of Simplex Designs for Quadratic Mixture Models

Abstract: Designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x 1, x 2, …, x q + 1) of nonnegative components x i with Σ q + 1 1 x i = 1. The designs that are optimum with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except when q = 2, the A-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously known D-optimum design. Although the E-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.

Balanced 2m factorial designs of resolution v which allow search and estimation of one extra unknown effect, 4 ≤ m ≤ 8

Abstract: In this paper, we obtain balanced resolution V plans for 2m factorial experiments (4 ≤ m ≤ 8), which have an additional feature. Instead of assuming that the three factor and higher order effects are all zero, we assume that there is at most one nonnegligible effect among them; however, we do not know which particular effect is nonnegligible. The problem is to search which effect is non-negligible and to estimate it, along with estimating the main effects and two factor interactions etc., as in an ordinary resolution V design. For every value of N (the number of treatments) within a certain practical range, we present a design using which the search and estimation can be carried out. (Of course, as in all statistical problems, the probability of correct search will depend upon the size of “error” or “noise” present in the observations. However, the designs obtained are such that, at least in the noiseless case, this probability equals 1.) It is found that many of these designs are identical with optimal b...

Optimal search designs, or designs optimal under bias free optimality criteria*

Abstract: Publisher Summary This chapter discusses whether the usual optimal designs are really optimal, with the possibility of the underlying model may be biased. The theory of search models offers the possibility of searching the bias and correcting for the same. As the true model is rarely known and as it is far easier to postulate a family of models, one of which is the true model, the idea of search should be inherent in the statistical aspects of most scientific experimentation. Thus, the problem of optimal designs is more a problem of obtaining a design that would be good from the viewpoint of a whole family of models rather than of any single model inside this family. The chapter presents certain optimality criteria for designs, where optimality takes the above view point into account. It also presents search linear models needed for development. It highlights the concept of optimal search designs and the criteria of AD-optimality and DD-optimality.

Designs in Three and Four Components For Mixtures Models With Inverse Terms

Abstract: Scheffe's mixture models are given and the D-optimality of various designs for these models is discussed. Approximate D-optimal (measure) and Dn -optimal (exact) designs are given for use with mixture models with inverse terms in three and four components.

Optimal designs for integrated variance in polynomial regression

Abstract: Publisher Summary This chapter discusses optimal designs for integrated variance in polynomial regression. It presents a general procedure for constructing an approximate Iσ -optimal design and highlights the procedure with an example. The chapter discusses a class of σ where the procedure is exact and presents a fairly accurate simple expression for the bound for the case of Lebesque measure. The general procedure presented in the chapter for finding an Iσ-optimal design is to start with the weight measure σ, pass to the measure σ maximizing the 2n th moment and then restrict the optimal designs to having mass on the support points of σ.

A Comparison of the Smith Predictor and Optimal Design Approaches for Systems with Delay in the Control

Abstract: The relatively recent application of optimal control theory to the design of control systems for processes with delay has made available an alternative design approach to the classical Smith Predictor approach. Although the designs resulting from the two approaches have many features in common, there are also important differences, and neither the similarities or differences have been examined in any detail in the literature. This paper surveys the work to date in this area, reviews the development of and examines the general characteristics of the control systems resulting from application of the two approaches to a general class of multivariable systems with delay in the control, and presents a detailed comparison of the designs for the case in which the process to be controlled is first order with delay. An important result which emerges is that the design resulting from the optimal approach as developed in the literature to date does not perform as well as the Smith Predictor design in controlling against output disturbances.

Iterative analysis of generalized lattice designs

Abstract: Summary Generalized lattice designs are defined. They include as special cases the square and rectangular lattice designs, and the α-designs defined by Patterson and Williams (1976). An iterative procedure is given for the combined estimation of variety effects in generalized lattice designs with optimal or near optimal efficiency factors. This procedure, together with an approximate variance matrix, enables the analysis of efficient generalized lattice designs to be carried out on mini computers.

An Optimal Design Procedure for Optimal Control Support

Abstract: Certain domain identification problems can be formulated in the following way : minimize the functional J(Ω) , Ω belonging to a given family of domains.

Experimental Design for Sensitivity Testing: The Weibull Model

Abstract: Attribute responses are often elicited by the simultaneous action of two or more variables. Experimental design and parameter estimation schemes, analogous to the familiar univariate plans, are developed here for the bivariate case. Using general exponential distributions of the form P(U = I) = exp (−γ). where γ is a suitably defined function, the elements of the information matrix are derived explicitly. Minimizing the determinant of this matrix. which is equivalent to minimizing the generalized variance. leads to optimal experimental designs. Explicit derivations are presented for univariate and bivariate exponential and Weibull distributions. The conditions are detined under which sequential optimal designs based on these results can be used.

Optimal Design of Structures Against Buckling: A Complementary Energy Approach

Abstract: The complementary energy approach is used to establish the basic principles in terms of generalized stress components for the optimum design of elastic structures against buckling. The necessary condition of optlmality is derived and its sufficiency is established for those structures whose compliance densities are convex and which are statically determinate. By way of illustration, the development is used to rederive the governing equations for the optimal design of a column against lateral buckling. The formulation is further applied to obtain optimum design of thin-walled beams against lateral-torsional buckling.

The Use of Decomposition in the Optimal Design of Reliable Systems

Abstract: The optimal design problem is to minimize the cost of a system of independent components subject to a lower bound constraint on the system reliability, and upper and lower bounds on the component reliabilities. This problem can be extremely difficult to solve for an arbitrary system, but for the rather general class of S-P systems, the optimal design problem can often be solved via a decomposition of the system structure. From this decomposition there arises a sequence of parallel and series optimal design subproblems that are parametric in the lower bound on the subsystem reliability. Given appropriate assumptions about the input data, these parallel and series subproblems can be easily solved. However, since the parametric solution of one subproblem is typically used as part of the data for a higher-level subproblem, the behavior of these parametric solutions must be investigated. We give conditions that ensure that the overall optimal design problem can be solved.

A Method for the Optimization of a Production Line of Electromagnetic Devices

Abstract: A method for finding the global minimum of a general nonlinear programming problem is introduced. The method is based on the sequential decomposition of the problem into two-dimensional subproblems. The method is discussed in the context of the optimal design of an electromagnetic device from an economical point of view. The suggested method is extended to include the optimal design of a production line of such devices, in which some design parameters are "common" to all the devices, while others are "uncommon" and belong to individual devices.

Comparison of nonlinear programming techniques for the optimal design of transformers

Abstract: In many papers on the application of nonlinear programming techniques to the solution of engineering problems, such as an induction-motor design, the sequential unconstrained minimisation technique is adopted. It is shown in the paper that a nonsequential approach will lead to the same end results with much less computational time. In addition it is shown that a considerable saving in computational time could be achieved in transformer design optimisation by considering the whole problem to consist of a single constraint such as the cost function, with the sum of all suitably weighted constraints on the design performances being brought under the objective function evaluation.

Optimization of Distributed Parameter Structures Under Dynamic Loads

Abstract: : In this report, optimal design of continuous structural systems under dynamic loads is considered. An optimization technique is developed based on the generalized steepest descent method and optimal control techniques Bryson and Ho. The method is then applied to some beam and plate problems. (Author)

A comprehensive method for the automated optimization of ship structures

Abstract: A comprehensive rationally-based method is presented for the automated optimum structural design of ships. The method contains three principal features:--a rapid, design-oriented finite element program developed especially for structural optimization;--a comprehensive set of subroutines for the accurate estimation of the various modes of collapse and unserviceability;--an optimization method based on a new form of sequential linearization capable of solving the resulting large-scale, non-linear, highly constrained optimization problem. The objective may be any continuous non-linear function of the design variables, such as weight or cost. The method is illustrated by applying it to the optimal design of a typical general cargo ship. The overall dimensions and the design loads are the same as for SD14. Also, since this vessel has proven to be a successful and cost-effective design, it was used as the basis for determining the load factors and cost ratios for the sample problem. The program contains 74 design variables and 542 constraints, of which 220 are non-linear. Order from BSRA as No. 53,346.

Optimal design and evaluation criteria for acoustic emission pulse signature analysis

Abstract: Design of pulse‐recording systems and evaluation criteria (method of analyzing the pulse signature) are investigated with the objective of defining optimal approaches to pulse signal analysis. A representative situation which this paper addresses is the modeling of acoustic emission (AE) pulse analysis as a nondestructive means of failure detection in which pulse density counting is presently the most common evaluative criterion. The instrumentation is modeled and selected analytical pulses are passed through the system. Two alternatives are considered here: frequency spectrum analysis, and time domain reconstruction of the pulse or pulse train (deconvolution). The pulse recording/analysis problem is modeled, and the various analysis techniques are considered. Within practical constraint optimal system designs are defined. It is shown that deconvolution of a pulse is a superior approach for transient pulse analysis. Reshaping of a transducer output back of the original input pulse is possible and gives an accurate representation of the generating pulse in the time domain. Frequency spectrum analysis methods and AE measurement systems have potential for segregation of different pulse shapes. Using deconvolution, in principle any definable transducer and filter system can be used to reconstruct pulse characteristics, i.e., to generate time domain signature. A number of major conclusions about the selection of design variables are made for general usage. In addition there are families of optimal selections for transducer and filter system parameters which give superior deconvoluted output signals. These may be significant when working with actual hardware and unknown characteristics. The optimal design results are new and possibly different from the expectations of engineers accustomed to working in the field of signal conditioning. In obtaining these results modern rational design techniques on a rather complex design problem are demonstrated.

A Convergence Theorem in $L$-Optimal Design Theory

Abstract: It is shown that the Fedorov procedure for finding $L$-optimal designs always converges to an $L$-optimal design, even when the limiting design is singular. Two lemmas are given first. An example illustrates the case of singular limiting design.

Designs in Five and Six Components for Mixtures Models with Inverse Terms.

Abstract: : Briefly reviewed are the polynomial plus inverse terms mixture models, and the approximately D-optimal (measure) and D sub n-optimal (exact) designs for these models in three and four components. The use of Atwood's (1973) improvement to Fedorov's D-optimality algorithm is reviewed and further improvements are suggested. In addition, design region and model symmetry, and a simplified procedure for re-distributing design measure, are used to obtain measure designs in five and six components. Finally, exact designs are obtained from these measure designs.