The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques

Structural Optimization for Reliability Using Nonlinear Goal Programming

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem

Control system design using optimization techniques Final report

Optimization techniques for control of fuel valve systems for air breathing jet engines and 40-60 inlet control problem

Application of optimization algorithms in the design of a superconducting A.C. generator rotor

The superconducting a.c. generator is expected to be the optimum choice among a.c. generation systems in future because of its reduced size, high efficiency, high terminal voltage and its contribution to the stability of the power system. Such machines also exhibit unique design problems which remain unsolved. The optimal selection of the basic design parameters is a current problem of interest. This thesis is intended as a contribution in this direction, and a general design strategy has been developed for the superconducting a.c. generator. Elements of the design process include magnetic field analysis, losses, and mechanical performance all which of are discussed in the thesis. An analytical model has been developed to help determine the distribution of magnetic flux density inside the superconducting machine. This model takes into account the number, and the geometric structure, of the winding slots and allows the rotor of the superconducting machine to be designed with optimum magnetic field distribution. A general design strategy has been developed for the superconducting a.c. generator rotor for predicting the optimum design. The design optimization process incorporates "direct search" and random-shrinkage methods. Two direct search methods of minimization have been compared on mathematical functions and also on machine design problems. The best method is highlighted and discussed. A general computer program package is presented that will optimize and analyse machine design problems. The package is organised in such away that future addition or deletion of performance specifications, constraints, optimization methods and design process elements are readily implemented

Weight minimization of structural components for launch in space shuttle

Minimizing the weight of structural components of the space station launched into orbit in a space shuttle can save cost, reduce the number of space shuttle missions, and facilitate on-orbit fabrication. Traditional manual design of such components, although feasible, cannot represent a minimum weight condition. At NASA Lewis Research Center, a design capability called CometBoards (Comparative Evaluation Test Bed of Optimization and Analysis Routines for the Design of Structures) has been developed especially for the design optimization of such flight components. Two components of the space station - a spacer structure and a support system - illustrate the capability of CometBoards. These components are designed for loads and behavior constraints that arise from a variety of flight accelerations and maneuvers. The optimization process using CometBoards reduced the weights of the components by one third from those obtained with traditional manual design. This paper presents a brief overview of the design code CometBoards and a description of the space station components, their design environments, behavior limitations, and attributes of their optimum designs

Variable penalty methods for constrained minimization

AbstractThis paper describes a class of variable penalty methods for solving the general nonlinear programming problems. The algorithm poses a sequence of unconstrained optimization problems with mechanisms to control the quality of the approximation for the Hessian matrix. The Hessian matrix is proposed in terms of the constraint functions and their first derivatives. The unconstrained problems are solved using a modified Newton's algorithm. The convergence of the method is accelerated by choosing variable penalty function parameters which in a given constraint environment, during an unconstrained minimization process, best control the error in the approximation of the Hessian matrix. Several possibilities for obtaining such parameters are discussed. The numerical effectiveness of this algorithm is demonstrated on a relatively large set of test problems

Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints

The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the fully utilized design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the modified fully utilized design (MFUD) method, has been tested successfully on a number of designs that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favorably with the optimum results that can be generated by using nonlinear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favor traditional design methods rather than methods based on advanced calculus and nonlinear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are presented along with a number of illustrative examples

Optimal offline broadcast scheduling with an energy harvesting transmitter

We consider an energy harvesting transmitter broadcasting data to two receivers. Energy and data arrivals are assumed to occur at arbitrary but known instants. The goal is to minimize the total transmission time of the packets arriving within a certain time window, using the energy that becomes available during this time. An achievable rate region with structural properties satisfied by the two-user AWGN BC capacity region is assumed. Structural properties of power and rate allocation in an optimal policy are established, as well as the uniqueness of the optimal policy under the condition that all the data of the “weaker ” user are available at the beginning. An iterative algorithm, DuOpt, based on block coordinate descent that achieves the same structural properties as the optimal is described. Investigating the ways to have the optimal schedule of two consecutive epochs in terms of energy efficiency and minimum transmission duration, it has been shown that DuOpt achieves best performance under the same special condition of uniqueness. Index Terms Packet scheduling, energy harvesting, AWGN broadcast channel, energy-efficient scheduling

A comparative study of nonlinear programming routines on the microcomputer versus the large computer

Call number: LD2668 .T4 1984 H92Master of Scienc