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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multiparametric Programming in Process Systems Engineering: Recent Developments and Path Forward

The inevitable presence of uncertain parameters in critical applications of process optimization can lead to undesirable or infeasible solutions. For this reason, optimization under parametric uncertainty was, and continues to be a core area of research within Process Systems Engineering. Multiparametric programming is a strategy that offers a holistic perspective for the solution of this class of mathematical programming problems. Specifically, multiparametric programming theory enables the derivation of the optimal solution as a function of the uncertain parameters, explicitly revealing the impact of uncertainty in optimal decision-making. By taking advantage of such a relationship, new breakthroughs in the solution of challenging formulations with uncertainty have been created. Apart from that, researchers have utilized multiparametric programming techniques to solve deterministic classes of problems, by treating specific elements of the optimization program as uncertain parameters. In the past years, there has been a significant number of publications in the literature involving multiparametric programming. The present review article covers recent theoretical, algorithmic, and application developments in multiparametric programming. Additionally, several areas for potential contributions in this field are discussed, highlighting the benefits of multiparametric programming in future research efforts.

Pappas, Iosif↗
NASA NTRS1973

Automated sizing of large structures by mixed optimization methods

A procedure for automating the sizing of wing-fuselage airframes was developed and implemented in the form of an operational program. The program combines fully stressed design to determine an overall material distribution with mass-strength and mathematical programming methods to design structural details accounting for realistic design constraints. The practicality and efficiency of the procedure is demonstrated for transport aircraft configurations. The methodology is sufficiently general to be applicable to other large and complex structures.

Sobieszczanski, J.↗
NASA NTRS1995

Expanding your horizons in science and mathematics

The purpose of the 'Expanding Your Horizons in Science and Mathematics' program is to interest young women in grades six through twelve in a variety of careers where mathematics and science are important. Progress in encouraging young women to take courses in mathematics, science, and technological subjects is discussed. Also included are adult, student, and organizational information packets used for 'Expanding Your Horizons' conferences.

Palmer, Cynthia E. A.↗
NASA NTRS1983

Structural optimization - Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.↗
NASA NTRS1984

Structural optimization: Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.↗
NASA NTRS1994

Automation of reverse engineering process in aircraft modeling and related optimization problems

During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for quadratic programming problems.

Li, W.↗
NASA NTRS1976

ACCESS 1: Approximation Concepts Code for Efficient Structural Synthesis program documentation and user's guide

The program documentation and user's guide for the ACCESS-1 computer program is presented. ACCESS-1 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure. Implementation of the computer program, preparation of input data and basic program structure are described, and three illustrative examples are given.

Miura, H.↗
NASA NTRS1978

ACCESS-2: Approximation Concepts Code for Efficient Structural Synthesis, user's guide

A user's guide is presented for the ACCESS-2 computer program. ACCESS-2 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure.

Miura, H.↗
DOE OSTI2018

Fast Approximate Union Volume in High Dimensions with Line Samples

The classical problem of calculating the volume of the union of d-dimensional balls is known as "Union Volume." We present line-sampling approximation algorithms for Union Volume. Our methods may be extended to other Boolean operations, such as setminus; or to other shapes, such as hyper-rectangles. The deterministic, exact approaches for Union Volume do not scale well to high dimensions. However, we adapt several of these exact approaches to approximation algorithms based on sampling. We perform local sampling within each ball using lines. We have several variations, depending on how the overlapping volume is partitioned, and depending on whether radial, axis-aligned, or other line patterns are used. Our variations fall within the family of Monte Carlo sampling, and hence have about the same theoretical convergence rate, 1 /$\sqrt{M}$, where M is the number of samples. In our limited experiments, line-sampling proved more accurate per unit work than point samples, because a line sample provides more information, and the analytic equation for a sphere makes the calculation almost as fast. We performed a limited empirical study of the efficiency of these variations. We suggest a more extensive study for future work. We speculate that different ball arrangements, differentiated by the distribution of overlaps in terms of volume and degree, will benefit the most from patterns of line samples that preferentially capture those overlaps. Acknowledgement We thank Karl Bringman for explaining his BF-ApproxUnion (ApproxUnion) algorithm [3] to us. We thank Josiah Manson for pointing out that spoke darts oversample the center and we might get a better answer by uniform sampling. We thank Vijay Natarajan for suggesting random chord sampling. The authors are grateful to Brian Adams, Keith Dalbey, and Vicente Romero for useful technical discussions. This work was sponsored by the Laboratory Directed Research and Development (LDRD) Program at Sandia National Laboratories. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fleury, C.↗
NASA NTRS2010

Using MathCad to Evaluate Exact Integral Formulations of Spacecraft Orbital Heats for Primitive Surfaces at Any Orientation

With the advent of high speed computing Monte Carlo ray tracing techniques has become the preferred method for evaluating spacecraft orbital heats. Monte Carlo has its greatest advantage where there are many interacting surfaces. However Monte Carlo programs are specialized programs that suffer from some inaccuracy, long calculation times and high purchase cost. A general orbital heating integral is presented here that is accurate, fast and runs on MathCad, a generally available engineering mathematics program. The integral is easy to read, understand and alter. The integral can be applied to unshaded primitive surfaces at any orientation. The method is limited to direct heating calculations. This integral formulation can be used for quick orbit evaluations and spot checking Monte Carlo results.

Pinckney, John↗
DOE OSTI2023

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Open-source Tools for Solving Grid Optimization Problems: ARPA-e Benchmark Algorithm Overview [Slides]

This document contains the official formulation that will be used for evaluation in Challenge 2 of the Grid Optimization (GO) Competition. Minor changes may occur within the formulation. Entrants will be notified when a new version is released. Changes are not expected to be of a significance that would cause a change in approach for the Entrants. This formulation builds upon the Challenge 1 formulation published in ARPA-E DE-FOA-0001952. Entrants will be judged based on the current official Challenge 2 formulation posted on the GO Competition website (this document, which is subject to change), not the formulation posted in DE-FOA-0001952. Entrants are permitted and encouraged to use any alternative problem formulation and modeling convention within their own software (such as convex relaxation, decoupled power flow formulations, current-voltage formulations, etc.) in an attempt to produce an exact or approximate solution to this particular mathematical program. However, the judging of all submitted approaches must conform to the official formulation presented here.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1981

Optimum structural design with plate bending elements - A survey

A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.

Haftka, R. T.↗
NASA NTRS1973

Automated procedure for design of wing structures to satisfy strength and flutter requirements

A pilot computer program was developed for the design of minimum mass wing structures under flutter, strength, and minimum gage constraints. The wing structure is idealized by finite elements, and second-order piston theory aerodynamics is used in the flutter calculation. Mathematical programing methods are used for the optimization. Computation times during the design process are reduced by three techniques. First, iterative analysis methods used to reduce significantly reanalysis times. Second, the number of design variables is kept small by not using a one-to-one correspondence between finite elements and design variables. Third, a technique for using approximate second derivatives with Newton's method for the optimization is incorporated. The program output is compared witH previous published results. It is found that some flutter characteristics, such as the flutter speed, can display discontinous dependence on the design variables (which are the thicknesses of the structural elements). It is concluded that it is undesirable to use such quantities in the formulation of the flutter constraint.

Haftka, R. T.↗
NASA NTRS1974

WINDOWAC (Wing Design Optimization With Aeroelastic Constraints): Program manual

User and programer documentation for the WIDOWAC programs is given. WIDOWAC may be used for the design of minimum mass wing structures subjected to flutter, strength, and minimum gage constraints. The wing structure is modeled by finite elements, flutter conditions may be both subsonic and supersonic, and mathematical programing methods are used for the optimization procedure. The user documentation gives general directions on how the programs may be used and describes their limitations; in addition, program input and output are described, and example problems are presented. A discussion of computational algorithms and flow charts of the WIDOWAC programs and major subroutines is also given.

Haftka, R. T.↗
DOE OSTI2020

ASCR@40: Highlights and Impacts of ASCR’s Programs

A report compiled by the ASCAC Subcommittee on the 40-year history of ASCR for the U.S. Department of Energy’s Office of Advanced Scientific Computing Research. The Office of Advanced Scientific Computing Research (ASCR) sits within the Office of Science in the Department of Energy (DOE). Per their web pages, “the mission of the ASCR program is to discover, develop, and deploy computational and networking capabilities to analyze, model, simulate, and predict complex phenomena important to the DOE.” This succinct statement encompasses a wide range of responsibilities for computing and networking facilities; for procuring, deploying, and operating high performance computing, networking, and storage resources; for basic research in mathematics and computer science; for developing and sustaining a large body of software; and for partnering with organizations across the Office of Science and beyond. While its mission statement may seem very contemporary, the roots of ASCR are quite deep—long predating the creation of DOE. Applied mathematics and advanced computing were both elements of the Theoretical Division of the Manhattan Project. In the early 1950s, the Manhattan Project scientist and mathematician John von Neumann, then a commissioner for the AEC (Atomic Energy Commission), advocated for the creation of a Mathematics program to support the continued development and applications of digital computing. Los Alamos National Laboratory (LANL) scientist John Pasta created such a program to fund researchers at universities and AEC laboratories. Under several organizational name changes, this program has persisted ever since, and would eventually grow to become ASCR.

97 MATHEMATICS AND COMPUTING↗