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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Bifurcations and sensitivity in parametric nonlinear programming

The parametric nonlinear programming problem is that of determining the behavior of solution(s) as a parameter or vector of parameters alpha belonging to R(sup r) varies over a region of interest for the problem: Minimize over x the set f(x, alpha):h(x, alpha) = 0, g(x, alpha) is greater than or equal to 0, where f:R(sup (n+r)) approaches R, h:R(sup (n+r)) approaches R(sup q) and g:R(sup (n+r)) approaches R(sup p) are assumed to be at least twice continuously differentiable. Some of these parameters may be fixed but not known precisely and others may be varied to enhance the performance of the system. In both cases a fundamentally important problem in the investigation of global sensitivity of the system is to determine the stability boundaries of the regions in parameter space which define regions of qualitatively similar solutions. The objective is to explain how numerical continuation and bifurcation techniques can be used to investigate the parametric nonlinear programming problem in a global sense. Thus, first the problem is converted to a closed system of parameterized nonlinear equations whose solution set contains all local minimizers of the original problem. This system, which will be represented as F(z,alpha) = O, will include all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points of the problem. The local existence and uniqueness of a solution path (z(alpha), alpha) of this system as well as the solution type persist as long as a singularity in the Jacobian D(sub z)F(z,alpha) is not encountered. Thus the nonsingularity of this Jacobian is characterized in terms of conditions on the problem itself. Then, a class of efficient predictor-corrector continuation procedures for tracing solution paths of the system F(z,alpha) = O which are tailored specifically to the parametric programming problem are described. Finally, these procedures and the obtained information are illustrated within the context of design optimization.

Lundberg, Bruce N.↗
NASA NTRS1981

The Lewis Chemical Equilibrium Program with parametric study capability

The program was developed to determine chemical equilibrium in complex systems. Using a free energy minimization technique, the program permits calculations such as: chemical equilibrium for assigned thermodynamic states; theoretical rocket performance for both equilibrium and frozen compositions during expansion; incident and reflected shock properties; and Chapman-Jouget detonation properties. It is shown that the same program can handle solid coal in an entrained flow coal gasification problem.

Sevigny, R.↗
NASA NTRS1984

Dilution jet mixing program

Parametric tests were conducted to quantify the mixing of opposed rows of jets (two-sided injection) in a confined cross flow. Results show that jet penetrations for two sided injections are less than that for single-sided injections, but the jet spreading rates are faster for a given momentum ratio and orifice plate. Flow area convergence generally enhances mixing. Mixing characteristics with asymmetric and symmetric convergence are similar. For constant momentum ratio, the optimum S/H(0) with in-line injections is one half the optimum value for single sided injections. For staggered injections, the optimum S/H(0) is twice the optimum value for single-sided injection. The correlations developed predicted the temperature distributions within first order accuracy and provide a useful tool for predicting jet trajectory and temperature profiles in the dilution zone with two-sided injections.

Srinivasan, R.↗
NASA NTRS1981

Systems design and analysis of the microwave radiometer spacecraft

Systems design and analysis data were generated for microwave radiometer spacecraft concept using the Large Advanced Space Systems (LASS) computer aided design and analysis program. Parametric analyses were conducted for perturbations off the nominal-orbital-altitude/antenna-reflector-size and for control/propulsion system options. Optimized spacecraft mass, structural element design, and on-orbit loading data are presented. Propulsion and rigid-body control systems sensitivities to current and advanced technology are established. Spacecraft-induced and environmental effects on antenna performance (surface accuracy, defocus, and boresight off-set) are quantified and structured material frequencies and modal shapes are defined.

Garrett, L. B.↗
NASA NTRS1989

Generalized mathematical models in design optimization

The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

Papalambros, Panos Y.↗
NASA NTRS2006

Program Predicts Performance of Optical Parametric Oscillators

A computer program predicts the performances of solid-state lasers that operate at wavelengths from ultraviolet through mid-infrared and that comprise various combinations of stable and unstable resonators, optical parametric oscillators (OPOs), and sum-frequency generators (SFGs), including second-harmonic generators (SHGs). The input to the program describes the signal, idler, and pump beams; the SFG and OPO crystals; and the laser geometry. The program calculates the electric fields of the idler, pump, and output beams at three locations (inside the laser resonator, just outside the input mirror, and just outside the output mirror) as functions of time for the duration of the pump beam. For each beam, the electric field is used to calculate the fluence at the output mirror, plus summary parameters that include the centroid location, the radius of curvature of the wavefront leaving through the output mirror, the location and size of the beam waist, and a quantity known, variously, as a propagation constant or beam-quality factor. The program provides a typical Windows interface for entering data and selecting files. The program can include as many as six plot windows, each containing four graphs.

Cross, Patricia L.↗
NASA NTRS1989

Automatic Parametric Testing Of Integrated Circuits

Computer program for parametric testing saves time and effort in research and development of integrated circuits. Software system automatically assembles various types of test structures and lays them out on silicon chip, generates sequency of test instructions, and interprets test data. Employs self-programming software; needs minimum of human intervention. Adapted to needs of different laboratories and readily accommodates new test structures. Program codes designed to be adaptable to most computers and test equipment now in use. Written in high-level languages to enhance transportability.

Jennings, Glenn A.↗
NASA NTRS1974

Shuttle station, and satellite communications program

A parametric approach is developed to analyze and evaluate the performance of any link or links of a satellite relay system. The approach factors into the calculations the constraints of coherent radio frequency interference, multipath, and equipment design. The report is divided into three sections dealing with Spread Spectrum Techniques (Section 1), Power Budget Calculations (Section 2), and Required Capabilities and Design Factors for Tracking and Data Relay Systems TDRS (Section 3).

Lawsine, L.↗
NASA NTRS1987

Vapor Compression Distillation Subsystem (VCDS) component enhancement, testing and expert fault diagnostics development, volume 1

Vapor compression distillation technology for phase change recovery of potable water from wastewater has evolved as a technically mature approach for use aboard the Space Station. A program to parametrically test an advanced preprototype Vapor Compression Distillation Subsystem (VCDS) was completed during 1985 and 1986. In parallel with parametric testing, a hardware improvement program was initiated to test the feasibility of incorporating several key improvements into the advanced preprototype VCDS following initial parametric tests. Specific areas of improvement included long-life, self-lubricated bearings, a lightweight, highly-efficient compressor, and a long-life magnetic drive. With the exception of the self-lubricated bearings, these improvements are incorporated. The advanced preprototype VCDS was designed to reclaim 95 percent of the available wastewater at a nominal water recovery rate of 1.36 kg/h achieved at a solids concentration of 2.3 percent and 308 K condenser temperature. While this performance was maintained for the initial testing, a 300 percent improvement in water production rate with a corresponding lower specific energy was achieved following incorporation of the improvements. Testing involved the characterization of key VCDS performance factors as a function of recycle loop solids concentration, distillation unit temperature and fluids pump speed. The objective of this effort was to expand the VCDS data base to enable defining optimum performance characteristics for flight hardware development.

Kovach, L. S.↗
DOE OSTI2019

A Multi-Parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems

Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.

42 ENGINEERING↗
DOE OSTI2026

Determining Stability Margins in Adiabatic Superconducting Magnets with 3-D Finite Element Analysis

Superconducting magnets play a key role in the development of experiments at Fermilab; understanding the operating stability of these can allow us to utilize more potent magnets for future experiments (like the proposed Muon Collider), optimize the design of magnets in more immediate experiments (like Mu2e), and research the future use of more exotic materials (like high-temperature superconductors). This summer, I developed a 3-D parametric FEA program in ANSYS Mechanical APDL that simulates quench in superconducting magnets, and I also developed a parametric MATLAB program that predicts thermal behavior in magnet quench using the MIITS method. These programs can provide useful quenching parameters (like minimum quench energy and normal zone propagation velocity) for different cases of quench, leading to the previously mentioned objective of magnet design optimization. To test the programs, preliminary cases were run and the data produced was compared and analyzed. The results of these analyses, as well as the program operating methods, are discussed in this project.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1987

Computable optimal value bounds for generalized convex programs

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.

Fiacco, Anthony V.↗
NASA NTRS1973

Evaluation of an electrochemical N2/H2 gas separator

A program was successfully completed to evaluate an electrochemical nitrogen/hydrogen (N2/H2) separator for use in a spacecraft nitrogen (N2) generator. Based on the technical data obtained a N2/H2 separator subsystem consisting of an organic polymer gas permeator first stage and an electrochemical second and third stage was estimated to have the lowest total spared equivalent weight, 257 kg (566 lb), for a 15 lb/day N2 generation rate. A pre-design analysis of the electrochemical N2/H2 separator revealed that its use as a first stage resulted in too high a power requirement to be competitive with the organic polymer membrane and the palladium-silver membrane separation methods. As a result, program emphasis was placed on evaluating the electrochemical. A parametric test program characterized cell performance and established second- and third-stage electrochemical N2/H2 separator operating conditions. A design verification test was completed on the second and third stages. The second stage was then successfully endurance tested for 200 hours.

Marshall, R. D.↗
NASA NTRS1989

Design of a flexure mount for optics in dynamic and cryogenic environments

The design of a flexure mount for a mirror operating in a cryogenic environment is presented. This structure represents a design effort recently submitted to NASA Ames for the support of the primary mirror of the Space Infrared Telescope Facility (SIRTF). The support structure must passively accommodate the differential thermal contraction between the glass mirror and the aluminium structure of the telescope during cryogenic cooldown. Further, it must support the one meter diameter, 116 kilogram (258 pound) primary mirror during a severe launch to orbit without exceeding the micro-yield of the material anywhere in the flexure mount. Procedures used to establish the maximum allowable radial stiffness of the flexural mount, based on the finite element program NASTRAN and the optical program FRINGE, are discussed. Early design concepts were evaluated using a parametric design program, and the development of that program is presented. Dynamic loading analyses performed with NASTRAN are discussed. Methods of combining modal responses resulting from a displacement response spectrum analysis are discussed, and a combination scheme called MRSS, modified root of sum of squares, is presented. Model combination schemes using MRSS, SRSS, and ABS are compared to the results of the modal frequency response analysis performed with NASTRAN.

Pollard, Lloyd Wayne↗