Search NASASearch

SEARCH · Search NASA

Results for “Discrete 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 235 records · Page 13

Closed loop models for analyzing the effects of simulator characteristics

The optimal control model of the human operator is used to develop closed loop models for analyzing the effects of (digital) simulator characteristics on predicted performance and/or workload. Two approaches are considered: the first utilizes a continuous approximation to the discrete simulation in conjunction with the standard optimal control model; the second involves a more exact discrete description of the simulator in a closed loop multirate simulation in which the optimal control model simulates the pilot. Both models predict that simulator characteristics can have significant effects on performance and workload.

Baron, S.

Viscous aerodynamic design using the adjoint variable approach

The use of classical optimal control methods, in particular variational methods, to solve the airfoil optimization problem, by deriving a set of adjoint (costate) equations and boundary conditions has already been done for inviscid (potential and Euler flows) and two dimensional, steady state, incompressible flow governed by the Navier-Stokes equations. The interior and boundary terms of the volume integral have been derived (in this work) for the steady Navier-Stokes equations in three dimensions for a viscous, compressible heat conducting fluid. This can be used to derive the adjoint equations and numerical boundary conditions for general classes of problems and hence paves the way for a solution to the aerodynamic optimization problem for compressible viscous flows. The next steps to the realization of that goal are projected as below. The usual square integral pressure functional as an objective function is being replaced by a more realistic drag functional subject to a lift constraint. The feasibility of attempting the more difficult time dependent problem is being investigated. It remains to get the full system of adjoint equations and boundary conditions with the new functional. The state and adjoint equations must be discretized and coded. An appropriate optimization program must be used (steepest descents seems inadequate) and various known airfoil shapes should be recovered in test cases of the computer program.

DeRise, George

A variational framework for residual-based adaptivity in neural PDE solvers and operator learning

Residual-based adaptive strategies are widely used in scientific machine learning yet remain largely heuristic. We introduce a variational framework that formalizes these methods through convex transformations of the residual, where different transformations correspond to distinct objective functionals. For instance, exponential weights target uniform error minimization, while linear weights recover quadratic error minimization. This perspective reveals adaptive weighting as a means of selecting sampling distributions that optimize a primal objective, directly linking discretization choices to error metrics. This principled approach yields three key benefits: it enables systematic design of adaptive schemes, reduces discretization error by lowering estimator variance, and enhances learning dynamics by improving gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across diverse optimizers and architectures. Our results provide a theoretical perspective for residual-based adaptivity and establish a foundation for principled discretization and training.

97 MATHEMATICS AND COMPUTING

Optimal design of compact spur gear reductions

The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Savage, M.

Shape optimization of single- and two-element airfoils on multiblock grids

A multiblock, discrete sensitivity analysis method is used to couple a direct optimization method and a flow analysis method. The domain is divided into smaller subdomains for which the sensitivities are obtained separately. Then, an effective sensitivity equation is solved to complete the coupling of all the sensitivity information. The flow analysis is based on the thin-layer Navier-Stokes equations solved by an implicit, upwind-biased, finite-volume method. The method of feasible directions is used for the present gradient-based optimization approach. First, a transonic airfoil is optimized to investigate the behavior of the method in highly nonlinear flows as well as the effect of different blocking strategies on the procedure. A supercritical airfoil is produced from an initially symmetric airfoil with multiblocking affecting the path but not the final shape. Secondly, a two-element airfoil is shape optimized in subsonic flow to demonstrate the present method's capability of shaping aerodynamically interfering elements simultaneously. For a very low and a very high Reynolds number cases, the shape of the main airfoil and the flap are optimized to yield improved lift-to-drag ratios.

Lacasse, James M.

Closed loop models for analyzing the effects of simulator characteristics

The optimal control model (OCM) of the human operator is used to develop closed-loop models for analyzing the effects of (digital) simulator characteristics on predicted performance and/or workload. Two approaches are considered: the first utilizes a continuous approximation to the discrete simulation in conjunction with the standard optimal control model; the second involves a more exact discrete description of the simulator in a closed-loop multi-rate simulation in which the optimal control model 'simulates' the pilot. Both models predict that simulator characteristics can have significant effects on performance and workload.

Baron, S.

Preconditioned domain decomposition scheme for three-dimensional aerodynamic sensitivity analysis

A discrete sensitivity analysis algorithm had previously been developed and applied to two-dimensional aerodynamic optimization problems, where the computational domains were discretized by using single grids. The sparse, unsymmetric systems of linear equations resulting from this algorithm were solved by a direct matrix inversion matrix. However, for large two-dimensional problems and, practically, all three-dimensional problems, direct inversion methods become inapplicable, primarily due to the prohibitive computer storage needed. In an attempt to alleviate such hindrances, the sensitivity analysis with domain decomposition (SADD) scheme was developed. This scheme divides the computational domain into smaller and nonoverlapping subdomains (multiblock grids) that are solved separately. Then, the final solution is constructed from the subdomain solutions. As the number of grid points in the interface boundaries of the subdomains becomes large, the computer memory required to store the effective coefficient matrix of these interface points starts to increase. Presented in this Technical Note is a preconditioned iterative procedure to overcome this particular problem.

Eleshaky, Mohamed E.

Aeroelastic Tailoring Study of N+2 Low Boom Supersonic Commerical Transport Aircraft

The Lockheed Martin N+2 Low - boom Supersonic Commercial Transport (LSCT) aircraft was optimized in this study through the use of a multidisciplinary design optimization tool developed at the National Aeronautics and S pace Administration Armstrong Flight Research Center. A total of 111 design variables we re used in the first optimization run. Total structural weight was the objective function in this optimization run. Design requirements for strength, buckling, and flutter we re selected as constraint functions during the first optimization run. The MSC Nastran code was used to obtain the modal, strength, and buckling characteristics. Flutter and trim analyses we re based on ZAERO code, and landing and ground control loads were computed using an in - house code. The w eight penalty to satisfy all the design requirement s during the first optimization run was 31,367 lb, a 9.4% increase from the baseline configuration. The second optimization run was prepared and based on the big-bang big-crunch algorithm. Six composite ply angles for the second and fourth composite layers were selected as discrete design variables for the second optimization run. Composite ply angle changes can't improve the weight configuration of the N+2 LSCT aircraft. However, this second optimization run can create more tolerance for the active and near active strength constraint values for future weight optimization runs.

low boom supersonic civil transport

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Conforming versus non-conforming boundary elements in three-dimensional elastostatics

A critical comparison of two basic formulations in three-dimensional elastostatics, using conforming and nonconforming boundary elements, is presented. The basic structure of the boundary element method is developed. The peculiarities that both types of boundary elements present in relation to the numerical implementation are discussed. Through selected examples, key issues such as the computational advantages and disadvantages of both formulations, mesh discretization and accuracy questions, and optimal location of the collocation nodes in the case of nonconforming elements are addressed. It is shown that conforming elements are able to produce more accurate results than nonconforming ones, with substantial economy in the final size of the system equations.

Manolis, G. D.

Two-Stage Path Planning Approach for Designing Multiple Spacecraft Reconfiguration Maneuvers

The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft. These maneuvers involve well-coordinated and highly-coupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is particularly difficult because of the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling between the positions and attitudes of all spacecraft. As a result, the trajectory design must be solved as a single 6N DOF problem instead of N separate 6 DOF problems. The first stage of the solution approach quickly provides a feasible initial solution by solving a simplified version without differential constraints using a bi-directional Rapidly-exploring Random Tree (RRT) planner. A transition algorithm then augments this guess with feasible dynamics that are propagated from the beginning to the end of the trajectory. The resulting output is a feasible initial guess to the complete optimal control problem that is discretized in the second stage using a Gauss pseudospectral method (GPM) and solved using an off-the-shelf nonlinear solver. This paper also places emphasis on the importance of the initialization step in pseudospectral methods in order to decrease their computation times and enable the solution of a more complex class of problems. Several examples are presented and discussed.

Aoude, Georges S.

Overview of US AID-World Bank-NASA Collaboration to Address Water Management Issues in the MENA Region

The World Bank, USAID and NASA have recently established a joint project to study multiple issues pertaining to water related applications in the Middle East North Africa (MENA) region. The main concentration of the project is on utilization of remote sensing data and hydrological models to address crop irrigation and mapping, flood mapping and forecasting, evapotranspiration and drought problems prevalent in this large geographic area. Additional emphases are placed on understanding the climate impact on these areas as well. Per IPCC 2007 report, by the end of this century MENA region is projected to experience an increase of 3 C to 5 C rise in mean temperatures and a 20% decline in precipitation. This poses a serious problem for this geographic zone especially when majority of the hydrological consumption is for the agriculture sector and the remaining amount is for domestic consumption. The remote sensing data from space is one of the best ways to study such complex issues and further feed into the decision support systems. NASA's fleet of Earth Observing satellites offer a great vantage point from space to look at the globe and provide vital signs necessary to maintain healthy and sustainable ecosystem. These observations generate multiple products such as soil moisture, global precipitation, aerosols, cloud cover, normalized difference vegetation index, land cover/use, ocean altimetry, ocean salinity, sea surface winds, sea surface temperature, ozone and atmospheric gases, ice and snow measurements, and many more. All of the data products, models and research results are distributed-via the Internet freely through out the world. This project will utilize several NASA models such as global Land Data Assimilation System (LDAS) to generate hydrological states and fluxes in near real time. These LDAS products will then be further compared with other NASA satellite observations (MODIS, VIIRS, TRMM, etc.) and other discrete models to compare and optimize evapotranspiration, soil moisture and crop irrigation, droUght assessment and water balance. The floods being a critical disaster in many of the MENA countries, NASA's global flood mapping and modeling framework (CREST) will be customized for country specific needs and delivered to the remote sensing organizations for their future use. Finally, capacity building is a critical part of this project and NASA will assist in this effort as well.

Habib, Shahid

Customizing NASA's Earth Science Research Products for addressing MENA Water Challenges

As projected by IPCC 2007 report, by the end of this century the Middle East North Mrica (MENA) region is projected to experience an increase of 3 C to 5 C rise in mean temperatures and a 20% decline in precipitation. This poses a serious problem for this geographic zone especially when majority of the hydrological consumption is for the agriculture sector and the remaining amount is for domestic consumption. In late 2011, the World Bank, USAID and NASA have joined hands to establishing integrated, modem, up to date NASA developed capabilities for various countries in the MENA region for addressing water resource issues and adapting to climate change impacts for improved decision making for societal benefits. The main focus of this undertaking is to address the most pressing societal issues which can be modeled and solved by utilizing NASA Earth Science remote sensing data products and hydrological models. The remote sensing data from space is one of the best ways to study such complex issues and further feed into the decision support systems. NASA's fleet of Earth Observing satellites offer a great vantage point from space to look at the globe and provide vital signs necessary to maintain healthy and sustainable ecosystem. NASA has over fifteen satellites and thirty instruments operating on these space borne platforms and generating over 2000 different science products on a daily basis. Some of these products are soil moisture, global precipitation, aerosols, cloud cover, normalized difference vegetation index, land cover/use, ocean altimetry, ocean salinity, sea surface winds, sea surface temperature, ozone and atmospheric gasses, ice and snow measurements, and many more. All of the data products, models and research results are distributed via the Internet freely through out the world. This project will utilize several NASA models such as global Land Data Assimilation System (LDAS) to generate hydrological states and fluxes in near real time. These LDAS products will then be further compared with other NASA satellite observations (MODIS, VIIRS, TRMM, etc.) and other discrete models to compare and optimize evapotranspiration, soil moisture and crop irrigation, drought assessment and water balance. The floods being a critical disaster in many of the MENA countries, NASA's global flood mapping and modeling framework (CREST) will be customized for country specific needs and delivered to the remote sensing organizations for their future use. Training is an important component under this activity and adequate level of training will be offered to build basic capacity to work with NASA provided data products, models for their future use. This paper provides a comprehensive introduction to NASA's Earth Science mission for understanding the behavior of our home Planet, projecting its health for future generations and applying research results solving societal issues.

Habib, Shahid

Taxi Time Prediction at Charlotte Airport Using Fast-Time Simulation and Machine Learning Techniques

Accurate taxi time prediction is required for enabling efficient runway scheduling that can increase runway throughput and reduce taxi times and fuel consumptions on the airport surface. Currently NASA and American Airlines are jointly developing a decision-support tool called Spot and Runway Departure Advisor (SARDA) that assists airport ramp controllers to make gate pushback decisions and improve the overall efficiency of airport surface traffic. In this presentation, we propose to use Linear Optimized Sequencing (LINOS), a discrete-event fast-time simulation tool, to predict taxi times and provide the estimates to the runway scheduler in real-time airport operations. To assess its prediction accuracy, we also introduce a data-driven analytical method using machine learning techniques. These two taxi time prediction methods are evaluated with actual taxi time data obtained from the SARDA human-in-the-loop (HITL) simulation for Charlotte Douglas International Airport (CLT) using various performance measurement metrics. Based on the taxi time prediction results, we also discuss how the prediction accuracy can be affected by the operational complexity at this airport and how we can improve the fast time simulation model before implementing it with an airport scheduling algorithm in a real-time environment.

airport surface traffic

Estimation With Range Depended Sensor Model

This paper focuses on the improvement of object detection accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. The tracking problem is considered in a mixed continuous-discrete time domain, where the target dynamics is in continuous-time and the measurements are in discrete-time, which is an optimal choice in many tracking and navigation applications. We adopt a commonly used continuous time coordinate-uncoupled white-noise acceleration model for a point object to describe the target motion, and use Extended Kalman Filter (EKF) framework to estimate the target's state and the unknown proportionality coefficient.

Vahram Stepanyan

Algorithms for Maneuvering Spacecraft Around Small Bodies

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Acikmese, A. Bechet