Showing papers on "Optimal design published in 1976"

Optimization of measurement schedules and sensor designs for linear dynamic systems

Abstract: This paper presents new results on the problem of measurement scheduling, sensor location, and design for linear dynamic systems. Both time-invariant and time-varying systems are considered and different norms of the observability and information matrices are maximized with respect to the structural parameters of the system. A close connection is established between these problems and the Kiefer-Wolfowitz theory of experimental design for regression problems. Both randomized and nonrandomized designs are considered. It is shown that the optimal designs obey certain minmax properties that lead to rapidly convergent algorithms. The results are illustrated by an analytical and a numerical example.

Respondent Jeopardy and Optimal Designs in Randomized Response Models

Abstract: Randomized response methods allow different kinds and degrees of privacy depending upon models and parameters. A theoretical approach to efficiency is suggested based on minimizing variance for given privacy requirements. Privacy requirements are defined in units of jeopardy from different points of view and indexed by measures suggested by information theory. Variances of competing models are compared only when the procedures meet the privacy requirements in terms of not exceeding the maximal jeopardizing information allowable for the particular application. The approach is illustrated through developing minimum variance under given jeopardizing information restrictions for a general dichotomous-population-dichotomous-response model.

Optimal multipurpose designs for regression models

Abstract: In this paper multipurpose designs are considered. Therefore the criterion is used to choose a design, where Mm(ξ) are the information matrices of a design ξ for several models. With suitable chosen matrices Amj, a S-optimal design is good for the estimation of parameters in several models at the same time or for the discrimination between two models together with the estimation in the accepted model. Results of A. C. ATKINSON and S. M. STIGLER generalized in this way. For S-optimal designs among others an Equivalence Theorem of the KIEFER-WOLFOWITZ typ is proved and computing methods are given. It should be noticed that the regularity of the information matrices is not used.

Efficient optimal design of structures by generalized steepest descent programming

Abstract: The purpose of this paper is to present refinements in a steepest descent algorithm for optimal design of structures and numerical experience that demonstrates its numerical efficiency. The algorithm is based on a state space optimization technique that was initially developed and applied to optimal control problems. Design constraints are divided into four distinct subsets, the special characteristics of which are exploited to improve computational efficiency of the algorithm. Some further improvements in structural analysis, design sensitivity analysis, and constrained steepest descent programming calculations are presented. Optimum designs for three test problems are obtained and convergence rates are compared with results presented in the literature.

Closed-loop structural stability for linear-quadratic optimal systems

Abstract: This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

Fail-Safe Optimal Design of Structures.

Abstract: : A general fail-safe optimal design problem for structures with fixed geometry is formulated in this report. Structural weight or some other performance index can be used as a cost function. Member stress, buckling load, nodal displacement, and natural frequency constraints on the complete and damaged structures are considered. The design variables are size, moment of inertia, or other mechanical properties of structural members. The structure is descretized and a finite element method is used for structural analysis. An iterative algorithm, based on a generalized steepest descent method, is developed to search for optimum designs. In this optimization process, the cost function, state equations, and inequality constraints are linearized and the dependence of these equations on the state variables is eliminated by solving adjoint equations. A fail-safe optimal design problem for a three member truss is solved analytically, to study the properties of fail-safe optimal design problems. A FORTRAN computer program is implemented to solve the fail-safe, minimum weight truss design problem. Structures with three, four, twenty-five, and seventy-two members are treated.

An Algorithm for Deriving Optimal Block Designs

Abstract: An algorithm is proposed for deriving optimal connected block designs. The method employed is to improve a given design by interchanging treatments between blocks, the treatment replications being kept fixed. Examples illustrating the use of the algorithm are given and its performance is discussed.

Optimum design in the presence of parametric uncertainty

Abstract: A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator design problem with a band of excitation frequencies.

Optimal Balanced Fractional $2^m$ Factorial Designs of Resolution VII, $6 \leqq m \leqq 8$

Abstract: Consider the class of balanced fractional $2^m$ factorial designs of resolution VII. Within this class, optimal designs with respect to the trace criterion are given for any fixed $N$ assemblies, which satisfy (i) $m = 6, 42 \leqq N \leqq 64$, (ii) $m = 7, 64 \leqq N \leqq 90$ and (iii) $m = 8, 93 \leqq N \leqq 128$. The covariance matrices of the estimates of the effects are also given for such designs.

Optimality of Two and Three Factor Designs

Abstract: In a two-factor design, a design which is optimal for one factor is shown to be optimal jointly for both the factors with respect to each of $A$-, $D$-, and $E$-optimalities. As an interesting consequence we have that a linked block design is optimal for the estimation of treatment differences. Similar results are also obtained for a class of three factor designs.

Optimal Design of Wastewater Collection Systems

Abstract: The most sought-after requirements of an optimization algorithm are with respect to computer time and memory. For the six-link system the time required for execution of a program is 70 sec on an IBM-360 (Model No.44) computer indicating that the algorithms are fast converging. Further, it takes only 75 sec to compile and load the program on a disk. The requirement of storage space is also very small. The total memory requirement on this computer is 9E8 bytes. A nonlinear algorithm based on Powell’s method has been developed to optimize the design of wastewater collection systems. The algorithm is fast converging, requires small computer memory, employs the discrete set of commercially available diameters, and leads to a global optimum. The economics of optimal and conventional designs has been compared for a six-link wastewater collection system at Roorkee, India. A parametric study has also been presented.

Optimization of Continuous One-Dimensional Structures under Steady Harmonic Excitation

Abstract: The paper examines some questions relating to the optimal design of continuous one-dimensional structures driven by harmonically oscillating loads. Optimal-control methods are applied to a cantilever bar driven sinusoidally by an axial force at its tip to illustrate the minimum-weight design of one-dimensional structures under dynamic excitation. Realistic constraints are imposed during the optimizations, including a maximum allowable stress amplitude at any point along the bar and a minimum cross-sectional area. It is shown that in the absence of damping, the design space may contain many disjoint feasible regions, and multiple optima can exist. Detailed solutions are obtained for continuous bars with an excitation frequency less than, and then greater than, the fundamental free-vibration frequency. It is found that above a certain excitation frequency, two or more arcs with different constraints characterize the optimal designs. It is concluded that when more than two different constrained arcs characterize the optimal solution, the continuum approach may be impractical, and finite-element approximations may offer the only alternative.

Integrated Approach to Microwave Design

Abstract: A new, integrated approach to microwave design is presented involving concepts such as optimal design centering, optimal design tolerancing, optimal design tuning, parasitic effects, uncertainties in models and reference planes, and mismatched terminations. The approach is of the worst case type, and previously published design schemes fall out as particular cases of the ideas presented. The mathematical and computational complexity as well as the benefits realized by our approach is illustrated by transformer examples, including a realistic stripline circuit.

Asymptotically Optimal Randomized Response Procedures

Abstract: An abstract general model of multiway randomized response procedures is investigated, with the aim of minimizing the variance matrix while bounding the risk to which respondents are subjected. A general result on the structure of possible optimal designs is obtained, an improved result is derived for the three-way case, and a complete answer is found for the dichotomous case.

Parametric optimal design

Abstract: Two algorithms for the solution of a parametric optimal design problem are developed and applied to example problems from diverse fields, such as finite allocation problems, optimal design of dynamical systems, and Chebyshev approximation. Sensitivity analysis gives rise to a first-order feedback law, which contains a compensating term for any error in the nominal solution, as well as sensitivity of the solution with respect to design parameters. The compensating term, when used alone, leads to a new second-order method of maximization for a linearly-constrained nonlinear programming problem.

Efficient optimal design of suspension systems for rotating shafts

Abstract: A new technique is proposed for the optimum design of suspension systems for rotating shafts In this approach the conventional method of trial and error search for optimum parameter values for a prescribed design configuration has been replaced by an efficient two-stage procedure In the first stage a generic force is substituted for the suspension system to be designed and the absolute optimum (or limiting) performance characteristics of the shaft are computed In the second stage, using a chosen suspension system configuration, parameter identification techniques are are applied to find the design parameters so that the suspension system will respond as close as possible to the absolute optimal performance In this approach the repetitive shaft analyses required in the conventional search techniques are avoided Hence, the new technique is relatively efficient computationally and is suitable for large systems Both linear and nonlinear suspension systems can be designed A simple Jeffcott rotor is used to demonstrate the new technique

Optimal static and sequential design : a critical review

Abstract: The aim of this thesis is to review and augment the theory and methods of optimal experimental design In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem A necessary and sufficient condition for optimality of a design measure is given Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed A new algorithm is presented with illustrations of how it should be used in practice It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design In situations where this is not satisfactory algorithms for improvement of this design are reviewed Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures Alternative suggestions are made along with conjectures as to how these might improve performance Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5 The results of this study provide empirical support for these conjectures In Chapter 7 examples are analysed These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially Further examples are considered which stress the importance of the use of prior information in situations of this type Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold

Application of statistical methods to the design of pavement systems

Abstract: This paper describes some of the applications of statistical or probabilistic methods to the design and analysis of pavement structures and discusses the theory on which they are founded. The major purpose for applying probabilistic methods to design of pavement systems is to help the engineer optimize design. The technology of statistical or probabilistic methods enables the engineer to directly consider the effect of many of the variabilities and uncertainties associated with the design, construction, and in-service life of pavements in the design process. Design adequacy or reliability or, conversely, the probability of distress can therefore be assessd to a much greater degree than without these concepts, and hence more optimal designs can be provided. Basic variabilities and uncertainties involved in the design, construction, and in-servie life of pavements are described and shown to have significant effects on performance. Theory to estimate the probable fracture distress and the loss of serviceability of portland cement and concrete pavement due to repeated traffic loadings is presented and illustrated. A relationship between estimated probability of traffic-associated fracture distress and measured slab cracking is developed. The application of these techniques to design is illustrated by several examples. Some of the methods described have been implemented and have been shown to be practical and useful. /Author/

Optimal design of pressure relieving piping networks by discrete merging

Abstract: Refinery relief-header network design can be optimized by a new discrete optimization technique which requires no rounding of decision variables, no initial guesses for the solution, and no artificial termination criteria; it produces parametric solutions when the optimum is attained. The method is also faster and more compact than the alternative continuous optimization methods.

Computer Simulation of Ion Beam Extraction from a Free Plasma Surface

Abstract: A method of computer simulation of an ion beam emitted from a free boundary plasma surface is described for the case of a three-electrode ion extractor. The geometry of the beam and extractor here treated is two dimensional. The case of an asymmetric extractor is simulated and it is shown that the beam is deflected when the saturated ion current density, which can be extracted from the plasma, is nonuniform over the plasma surface and/or the electrodes of the extractor are mutually displaced. Results of the simulation are available for the optimal design of the beam extractor.

Computer‐aided optimal melt screw design

Abstract: The paper describes a computer software package applying a steady-state hill-climbing optimization routine to the plastics melt-extruder screw constrained-design problem. The purpose primarily is to introduce the optimal screw-design technique, to show how it is applied to this particular type of problem, to indicate its potential and to encourage its wider use. Screw performance criteria are defined by a theoretical model consisting of the non-Newtonian isothermal polymer flow equations in terms of the screw-geometric variables for particular process conditions. The design method is quite general however and a non-isothermal model may be substituted. Use of the method offers considerable scope and potential for the design engineer to make design processes faster, more positive and logical while reducing the effort required. Interactive use is possible and empirical adjustments can be incorporated with experience. In using the method, the design engineer first specifies the required process conditions of pressure and flow rate at the die and the computer then searches for the set of screw design variables which optimizes the screw power utilization efficiency or any other specified criterion of performance. Such optimal designs are obtained within the set limits of practical constraints on machine dimensions, screw strength and product quality requirements. Some experimental evidence is given relating to the accuracy of the isothermal non-Newtonian polymer flow model and to its use in the design of small diameter extruder screws. The optimal search technique offers considerable potential as a computer-based design tool.

Optimal design of structures with unspecified loading distribution

Abstract: The problem of the optimal distribution of loading on a structure that corresponds to the minimum of the elastic compliance or the maximum of the safety factor for plastic collapse is considered. Optimality criteria are derived, and their applicability is illustrated in the case of beams. Besides the optimally varying cross section, also the support positions and the load distribution are determined from the optimal solution.

Optimal design of helical springs by geometrical programming

Abstract: The optimal design of helical springs has often been of interest in optimization and in engineering design. The spring problem is developed for music wire compression springs and considers material properties as a function of diameter and finite life. A straightforward strategy based on geometric programming is developed. Hand calculations can easily determine the optimal design and can also identify problems with infeasible solutions. The reliability is optimized by using the safety factors in fatigue and yielding as the objective functions.

Geometric Discussion of the Optimal Design of a Simple Truss

Abstract: This paper is concerned with the optimal design of a truss of given layout that consists of bars connecting the loaded joint to fixed joints on a horizontal ceiling. Simple graphical procedures are developed for optimal plastic or elastic design for a single load and optimal plastic design for two alternative loads.

An alternative formulation of a distributed-parameter optimal cotrol problem applied to nuclear shielding

Abstract: An alternative formalism for optimal control of distributed parameter systems is proposed. Necessary conditions for optimality and transversality conditions are developed for a class of distributed-parameter systems. It is shown that when the distributed system becomes a lumped-parameter one, the results obtained become identical to known results of optimal control of lumped systems. The formalism developed is applied to solve a problem of optimal design of a shielding installation around a neutron source.

An optimal structural design algorithm using optimality criteria

Abstract: An algorithm for optimal design is given which incorporates several of the desirable features of both mathematical programming and optimality criteria, while avoiding some of the undesirable features. The algorithm proceeds by approaching the optimal solution through the solutions of an associated set of constrained optimal design problems. The solutions of the constrained problems are recognized at each stage through the application of optimality criteria based on energy concepts. Two examples are described in which the optimal member size and layout of a truss is predicted, given the joint locations and loads.