Search NASASearch

SEARCH · Search NASA

Results for “Mathematical optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

User's manual for the Macintosh version of PASCO

A user's manual for Macintosh PASCO is presented. Macintosh PASCO is an Apple Macintosh version of PASCO, an existing computer code for structural analysis and optimization of longitudinally stiffened composite panels. PASCO combines a rigorous buckling analysis program with a nonlinear mathematical optimization routine to minimize panel mass. Macintosh PASCO accepts the same input as mainframe versions of PASCO. As output, Macintosh PASCO produces a text file and mode shape plots in the form of Apple Macintosh PICT files. Only the user interface for Macintosh is discussed here.

Lucas, S. H.

Sensitivity analysis and optimization issues in NASTRAN

The purpose is to develop procedures to extract sensitivity analysis information from COSMIC/NASTRAN and to couple it with a mathematical optimization package. At present, the analysis will be limited to stress, displacement, and frequency constraints with structures modeled with membrane elements, rods, and bar elements. Two types of sensitivity analysis are discussed: an adjoint variable approach which is most effective when the number of active constraints is significantly less than the number of physical variables, and an approach based on a first order approximation of a Taylor series. The latter approach is more effective when the number of independent design variables is significantly less than the number of active constraints.

Tischler, V. A.

Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Methods are presented for the reduction of helicopter rotor blade vibration through a formal mathematical optimization technique determination of optimum tuning mass sizes and locations; these are used as design variables that are systematically changed to achieve low values of shear without large mass penalty. Matrix expressions are obtained for the modal shaping parameter and modal shear amplitude that are required for FEM structural analysis of the blade as well as the optimization formulation. Sensitivity derivatives are also obtained. Three different optimization strategies are developed and tested.

Pritchard, Jocelyn I.

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail.

mission design

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail. GenETOC was developed in C# using the .NET framework with Windows Presentation Foundation (WPF) serving as the framework from which to create the graphical user interface (GUI). GenETOC user inputs can be categorized into three major data components: definition of the problem (areas of interest, satellite decision parameters, and sensor configurations), definition of performance objectives, and specification of the genetic algorithm (GA) parameters. In the problem definition component, the user is prompted to define the areas of interest against which the performance metrics will be computed, define the sensor parameters and attach them to specific spacecraft, select which satellite orbital parameters will be added to the decision space of the GA, and specify the range of desired values for each optimization parameter. For performance objectives, the user is presented with a list of available coverage and revisit performance based calculation options from which two metrics are chosen to serve as the objective functions that the GA will use to evaluate solutions during the optimization process. Finally, the definition of the GA parameters provides user control over the number of generations (number of optimization iterations), the population size (number of candidate constellations created in each generation), and the adaptive mutation and crossover threshold values (control parameters for how frequently each process occurs during the optimization). GenETOC has been extensively tested to verify the individual components of the optimization process. The GA has been tested against a suite of GA test problems to confirm convergence to the known two and three-dimensional Pareto fronts. The coverage and revisit performance metrics obtained in GenETOC are compared with STK desktop scenarios, confirming the constellations are being appropriately modeled within GenETOC simulations. A walkthrough of a simple, example problem is provided to illustrate the workings of GenETOC and to demonstrate the output available to the mission designer.

mission design

Integrated structure electromagnetic optimization of large space antenna reflectors

The requirements for extremely precise and powerful large space antenna reflectors have motivated the development of a procedure for shape control of the reflector surface. A mathematical optimization procedure has been developed which improves antenna performance while minimizing necessary shape correction effort. In contrast to previous work which proposed controlling the rms distortion error of the surface thereby indirectly improving antenna performance, the current work includes electromagnetic (EM) performance calculations as an integral of the control procedure. The application of the procedure to a radiometer design with a tetrahedral truss backup structure demonstrates the potential for significant improvement. The results indicate the benefit of including EM performance calculations in procedures for shape control of large space antenna reflectors.

Padula, Sharon L.

Integrated structural electromagnetic optimization of large space antenna reflectors

The requirements for extremely precise and powerful large space antenna reflectors have motivated the development of a procedure for shape control of the reflector surface. A mathematical optimization procedure has been developed which improves antenna performance while minimizing necessary shape correction effort. In contrast to previous work which proposed controlling the rms distortion error of the surface thereby indirectly improving antenna performance, the current work includes electromagnetic (EM) performance calculations as an integral part of the control procedure. The application of the procedure to a radiometer design with a tetrahedral truss backup structure demonstrates the potential for significant improvement. The results indicate the benefit of including EM performance calculations in procedures for shape control of large space antenna reflectors.

Padula, S. L.

Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Described are methods for reducing vibration in helicopter rotor blades by determining optimum sizes and locations of tuning masses through formal mathematical optimization techniques. An optimization procedure is developed which employs the tuning masses and corresponding locations as design variables which are systematically changed to achieve low values of shear without a large mass penalty. The finite-element structural analysis of the blade and the optimization formulation require development of discretized expressions for two performance parameters: modal shaping parameter and modal shear amplitude. Matrix expressions for both quantities and their sensitivity derivatives are developed. Three optimization strategies are developed and tested. The first is based on minimizing the modal shaping parameter which indirectly reduces the modal shear amplitudes corresponding to each harmonic of airload. The second strategy reduces these amplitudes directly, and the third strategy reduces the shear as a function of time during a revolution of the blade. The first strategy works well for reducing the shear for one mode responding to a single harmonic of the airload, but has been found in some cases to be ineffective for more than one mode. The second and third strategies give similar results and show excellent reduction of the shear with a low mass penalty.

Pritchard, Jocelyn I.

An integrated computer procedure for sizing composite airframe structures

A computerized algorithm to generate cross-sectional dimensions and fiber orientations for composite airframe structures is described, and its application in a wing structural synthesis is established. The algorithm unifies computations of aeroelastic loads, stresses, and deflections, as well as optimal structural sizing and fiber orientations in an open-ended system of integrated computer programs. A finite-element analysis and a mathematical-optimization technique are discussed.

Sobieszczanski-Sobieski, J.

A mixed optimization method for automated design of fuselage structures.

A procedure for automating the design of transport aircraft fuselage structures has been developed and implemented in the form of an operational program. The structure is designed in two stages. First, an overall distribution of structural material is obtained by means of optimality criteria to meet strength and displacement constraints. Subsequently, the detailed design of selected rings and panels consisting of skin and stringers is performed by mathematical optimization accounting for a set of realistic design constraints. The practicality and computer efficiency of the procedure is demonstrated on cylindrical and area-ruled large transport fuselages.

Sobieszczanski, J.

Implementing a unified solver for nonlinearly constrained optimization

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno’s software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.

97 MATHEMATICS AND COMPUTING

LLGOMAX: Enhancing Industry-Standard Tools for AC Optimal Unit Commitment (CRADA Final Report)

This was a collaborative effort between Lawrence Livermore National Security, LLC ("LLNS"), as manager and operator of Lawrence Livermore National Laboratory ("LLNL") and ECCO International Inc. ("Participant"). The team designed and implemented a new approach for the Security-Constrained Alternating-Current Unit Commitment (SCACUC) problem. The SCACUC problem is a mathematical optimization problem that decides which generating units should be online and how much power should be produced (and consumed) at each point of the power grid. The decisions are made so as to minimize the total cost of supplying electricity while respecting technical constraints of the power grid, both under normal and emergency conditions. The team developed a solution for SCACUC as specified in the ARPA-E Grid Optimization Competition (GOC) Challenge 3, which put forth a forward-looking version of the problem, which many features not present in today’s electricity market specifications for SCACUC.

24 POWER TRANSMISSION AND DISTRIBUTION

Risk Analysis for Resource Planning Optimization

The main purpose of this paper is to introduce a risk management approach that allows planners to quantify the risk and efficiency tradeoff in the presence of uncertainties, and to make forward-looking choices in the development and execution of the plan. Demonstrate a planning and risk analysis framework that tightly integrates mathematical optimization, empirical simulation, and theoretical analysis techniques to solve complex problems.

resource planning optimization

Integrated Thermal-structural-electromagnetic Design Optimization of Large Space Antenna Reflectors

The requirements for low mass and high electromagnetic (EM) performance in large, flexible space antenna structures is motivating the development of a systematic procedure for antenna design. In contrast to previous work which concentrated on reducing rms distortions of the reflector surface, thereby indirectly increasing antenna performance, the current work involves a direct approach to increasing electromagnetic performance using mathematical optimization. The thermal, structural, and EM analyses are fully integrated in the context of an optimization procedure, and consequently, the interaction of the various responses is accounted for directly and automatically. Preliminary results are presented for sizing cross-sectional areas of a tetrahedral truss reflector. The results indicate potential for this integrated procedure from the standpoint of mass reduction, performance increase, and efficiency of the design process.

Adelman, H. M.

Stability optimization of laminated composite plates

The optimum design of plates with orthotropic layers under axial compression and shear is discussed. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of + alpha sub i and - alpha sub i with respect to the plate axis. The fiber directions which give the highest axial buckling stress and the highest shear buckling stress are found by utilizing a mathematical optimization technique for various aspect ratios of the plates. Inhomogeneity in the direction of the plate thickness (stacking sequence) is taken into account in this analysis.

Hirano, Y.

Cell and module formation research area

Metallization is discussed. The influence of hydrogen on the firing of base-metal pastes in reducing atmospheres is reported. A method for optimization of metallization patterns is presented. A process sequence involving an AR coating and thick-film metallization system capable of penetrating the AR coating during firing is reported. Design and construction of the NMA implantation machine is reported. Implanted back-surface fields and NMA primary (front) junctions are discussed. The use of glass beads, a wave-soldering device, and ion milling is reported. Processing through the module fabrication and environmental testing of its design are reported. Metallization patterns by mathematical optimization are assessed.

Bickler, D. B.

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael