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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.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Using Data Assimilation Methods of Prediction of Solar Activity

The variable solar magnetic activity known as the 11-year solar cycle has the longest history of solar observations. These cycles dramatically affect conditions in the heliosphere and the Earth's space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model, complemented by the equation of magnetic helicity conservation and long-term sunspot data series. This approach has allowed us to reproduce the general properties of solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Prediction↗
NASA NTRS2017

Using Data Assimilation Methods for Prediction of Solar Activity

The variability of solar magnetic activity known as the 11-­‐year solar cycles has the longest history of observations. These solar cycles dramatically affect conditions in the heliosphere and the Earth’s space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-­‐term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model complemented by the equation of magnetic helicity conservation and long-­‐term sunspot data series. This approach has allowed us to reproduce the general properties of the solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Solar Activity↗
DOE OSTI2024

Distributed Wind-Energy-Based Hybrids

Presentation defining distributed wind-based hybrids and introducing the Hybrid Optimization Performance Platform (HOPP) an open-source tool that helps design and optimize buildable hybrid power plants.

distributed wind-based hybrids↗
NASA NTRS1992

Computation of near-minimum-time maneuvers of flexible structures by parameter optimization

Near-minimum-time attitude maneuvers of space structures as well as ground based test articles are considered. Switching nature of the controls for rigid body maneuvers are illustrated using a control-cube and a critical control axis of rotation. The presence of torque smoothing and where appropriate, gravitational effects and connections to other bodies are explicitly included in the mathematical models of the systems to be optimized. A maximum fuel consumption constraint is included besides the required terminal conditions on attitude and angular velocities. The switch times, maximum thrust magnitudes, and smoothing parameters are determined using the Sequential Quadratic Programming method for parameter optimization. Results indicating attitude and angular velocity histories, thruster forces, and structural vibrations are presented for three, four, and five switch maneuvers, as well as maneuvers that involve large coasting arcs.

Vadali, S. R.↗
NASA NTRS1987

Application of optimization techniques to spacecaft fuel usage minimization in deep space navigation

Mathematical analysis of the minimization of spacecraft fuel usage for both impulsive and finite motor burns is presented. A high precision integrated trajectory search program (SEPV) and several optimization software libraries are used to solve minimum fuel usage problems. The SEPV program has the capacity to vary either the initial spacecraft state or the finite burn parameters to acquire a specified set of target values. Several test examples for the Voyager 2 Uranus Encounter and the Galileo Jupiter Orbiter are presented to show that spacecraft fuel consumption can be minimized in targeting maneuver strategies. The fuel savings achieved by the optimum solution can be significant.

Wang, Tseng-Chan↗
NASA NTRS1990

A knowledge-based approach to improving optimization techniques in system planning

A knowledge-based (KB) approach to improve mathematical programming techniques used in the system planning environment is presented. The KB system assists in selecting appropriate optimization algorithms, objective functions, constraints and parameters. The scheme is implemented by integrating symbolic computation of rules derived from operator and planner's experience and is used for generalized optimization packages. The KB optimization software package is capable of improving the overall planning process which includes correction of given violations. The method was demonstrated on a large scale power system discussed in the paper.

Momoh, J. A.↗
NASA NTRS1973

An analytic study of near terminal area optimal sequencing and flow control techniques

Optimal flow control and sequencing of air traffic operations in the near terminal area are discussed. The near terminal area model is based on the assumptions that the aircraft enter the terminal area along precisely controlled approach paths and that the aircraft are segregated according to their near terminal area performance. Mathematical models are developed to support the optimal path generation, sequencing, and conflict resolution problems.

Park, S. K.↗
NASA NTRS1973

Optimization of multiple target electric propulsion trajectories.

Development of the mathematical basis for the generation of multiple target low-thrust trajectories. The unique trajectory shaping capabilities of electric propulsion make it ideally suited for modifying the path of the spacecraft to effect close encounters of selected asteroids with only slight penalties in performance. Each intermediate encounter with an asteroid involves the optimization of four parameters, the encounter time and the three components of the relative velocity at encounter. A second type of mission amenable to this analysis is that of asteroid or comet sample return missions. For missions of this type, both launch date and division of departure and return flight times are capable of being optimized. Use is made of the traditional calculus of variations to derive the necessary conditions that must be satisfied for both types of missions. In addition, examples are presented of both a Comet Encke rendezvous mission with multiple encounters of the asteroids Aschera and Alekto and also a sample return mission from the asteroid Flora.

Sauer, C. G., Jr.↗
DOE OSTI2025

A matheuristic for design and dispatch of a utility-connected distributed energy system

Modeling distributed power generation systems often requires complicated mathematical expressions that present challenges for commercial optimization solvers. Here, this paper presents a matheuristic to solve a mixed-integer optimization model that informs decisions regarding the design and dispatch of a utility-connected microgrid. We deploy a genetic algorithm to search the system design space and a linear program to solve the economic dispatch problem. The model is a component of a web tool that requires solutions within a few minutes. Our method yields objective function values within 5% of an exogenously produced optimal in fewer than 30 seconds for 90% of our test cases compared to only 10% of our test cases by a traditional optimization solver in the same amount of time.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1986

Impact of mismodeled idle engine performance on calculation and tracking of optimal 4-D descent trajectories

Advanced flight management systems are being developed which are capable of calculating optimal 3-D and 4-D flight trajectories for arbitrary fuel and time costs. These systems require mathematical models of airplane performance in order to compute the optimal profiles. Mismodeled idle engine characteristics can result in descent trajectories requiring excessive throttle and/or speedbrake activity in order to achieve the desired end conditions. This paper evaluates the cost and fuel penalties, trajectory variations, and flight control requirements associated with typical idle engine modeling errors for a twin-jet transport airplane. Variations in idle power setting, thrust, fuel flow, and surge bleed operation were evaluated for a cruise/descent flight segment. The results of this analysis provide insight into the penalties associated with uncertainties in idle engine performance and suggest methods of modeling which minimize these penalties.

Williams, D. H.↗
NASA NTRS1986

The development of optimal control laws for orbiting tethered platform systems

A mathematical model of the open and closed loop in orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Langrangian formulation yields equations describing platform pitch, subsatellite tetherline swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

Bainum, P. M.↗
NASA NTRS1986

The development of optimal control laws for orbiting tethered platform systems

A mathematical model of the open and closed loop in-orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Lagrangian formulation yields equations describing platform pitch, subsatellite tether-line swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

Bainum, P. M.↗
NASA NTRS1994

Optimal Empirical Z-R Relations

We attempt to mathematically justify the two empirical approaches to the problem of deriving Z-R relations, namely the power-law regression and the 'probability matching method'.

mathematical assumptions power-law Z-R relation pr↗
NASA NTRS2017

Model-Based Thermal System Design Optimization for the James Webb Space Telescope

Spacecraft thermal model validation is normally performed by comparing model predictions with thermal test data and reducing their discrepancies to meet the mission requirements. Based on thermal engineering expertise, the model input parameters are adjusted to tune the model output response to the test data. The end result is not guaranteed to be the best solution in terms of reduced discrepancy and the process requires months to complete. A model-based methodology was developed to perform the validation process in a fully automated fashion and provide mathematical bases to the search for the optimal parameter set that minimizes the discrepancies between model and data. The methodology was successfully applied to several thermal subsystems of the James Webb Space Telescope (JWST). Global or quasiglobal optimal solutions were found and the total execution time of the model validation process was reduced to about two weeks. The model sensitivities to the parameters, which are required to solve the optimization problem, can be calculated automatically before the test begins and provide a library for sensitivity studies. This methodology represents a crucial commodity when testing complex, large-scale systems under time and budget constraints. Here, results for the JWST Core thermal system will be presented in detail.

Cataldo, Giuseppe↗
DOE OSTI2024

Identifying Bayesian optimal experiments for uncertain biochemical pathway models

Abstract Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

Disturbance decoupling, decentralized control and the Riccati equation

The disturbance decoupling and optimal decentralized control problems are looked at using identical mathematical techniques. A statement of the problems and the development of their solution approach is presented. Preliminary results are given for the optimal decentralized control problem.

Garzia, M. R.↗
NASA NTRSDate not supplied

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of A Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗
NASA NTRSDate not supplied

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of a Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗