Search NASA⌕ Search

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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Optimization of a corrugated stiffened composite panel under uniaxial compression

An approach of structural optimization has been used to optimize the weight of a simply supported, corrugated hat stiffened composite panel under uniaxial compression. The approach consists of the employment of nonlinear mathematical programming techniques to reach an optimum solution. Some simplifying assumptions are made in the stress analysis to obtain faster convergence to an optimum solution. With these simplifying assumptions the number of unknown design parameters is reduced to twelve.

Agarwal, B. L.↗
NASA NTRS1976

The effects of aircraft design and atmospheric turbulence on handling and ride qualities

The effects of aircraft dynamic characteristics on passenger ride quality were investigated to determine ride-quality isocontours similar to aircraft handling-qualities contours. Measurements were made on a motion-base simulator while varying the aircraft short-period and Dutch Roll frequencies and dampings. Both pilot ratings and subjective ride-quality ratings were obtained during simulator flight. Ride and handling qualities were found to be complimentary for the Dutch Roll mode, but not for the short-period mode. Regions of optimal ride and handling qualities were defined for the short-period mode, and the effects of changes in turbulence level studied using mathematical models.

Jones, C. R.↗
NASA NTRS1977

Optimization of active control systems to suppress flutter and minimize turbulence response

A method for optimizing an active control system which will suppress flutter and minimize the response of a lifting surface to atmospheric turbulence is presented. A mathematical search method is developed which will find a control law which will cause an active control system to flutter at a specified freestream velocity, air density, and Mach number. With the flutter velocity of the system held constant, the control law is then modified in such a way that the peak output power spectral density function of the angular response of a lifting surface (as a result of atmospheric turbulence) is minimized for a specified flight velocity which is less than the flutter velocity. The von Karman generalized power spectrum for the transverse components of turbulence is used in an example problem to increase the flutter velocity and minimize the turbulence response of a simplified delta-wing model which has leading and trailing edge control surfaces.

Rudisill, C. S.↗
NASA NTRS1995

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

Lebiedzik, Catherine↗
NASA NTRS2010

A New Representative for Small-Body Gravity Estimation

One of the options proposed in the 2009 Review of the U. S. Human Spaceflight Plans Committee calls for the consideration of robotic and human missions to asteroids. Beginning in 2000, the NEAR Shoemaker spacecraft inserted into orbit about the asteroid 433 Eros, and studied it for a year before landing. The Hayabusa satellite journeyed to 25143 Itokawa, and operated in a proximity of the asteroid for several months before landing to collect a return sample. Additionally, the DAWN satellite, which was launched in 2007, will explore the dwarf-planet Ceres and the asteroid 4 Vesta in the next three years. These are just several examples of current interests in exploring asteroids. In this paper, we explore an alternative for estimating the gravity field of a small body using observations of an orbiting satellite. Our approach uses two new mathematical tools, the quadratures (on a sphere) invariant under the icosahedral group, and a multiresolution representation of the gravity potential. With the near optimal quadratures on the sphere, we minimize the number of parameters needed to recover a function. Also, instead of estimating the coefficients of the spherical harmonics, the new quadratures allow us to estimate directly the values of the gravity field since they offer an analogue of the Lagrange-type interpolation.

Jones, Brandon A.↗
DOE OSTI2025

Regional Energy Deployment System (ReEDS) Model Documentation: 2025

The Regional Energy Deployment System (ReEDS) model is a capacity expansion and dispatch model that is primarily used for the contiguous U.S. electric power sector. The model relies on system-wide least cost optimization to estimate the type and location of future generation and transmission capacity. This document describes details of how the model is formulated, how it functions, and many of the key inputs.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Prompt Phrase Ordering Using Large Language Models in HPC: Evaluating Prompt Sensitivity

Large language models (LLMs) have demonstrated effective performance in domain-specific tasks, often requiring a well-designed prompt to guide their responses. However, optimizing the right prompt is challenging due to prompt sensitivity—the phenomenon where small changes in the prompt can lead to significant variations in performance. In this study, we evaluate prompt performance by examining all permutations of independent phrases to investigate prompt sensitivity and robustness. We used two datasets: the GSM8k dataset, which assesses mathematical reasoning, and a custom template prompt for summarizing database metadata. Our goal was to evaluate the performance across all permutations of a sequence of prompt phrases. The study was conducted using the llama3-instruct- 7B model hosted on Ollama, with computations parallelized in a high-performance computing environment. By comparing the average index of phrases in the best and worst-performing prompts, we found that the order of independent phrases within a prompt significantly impacts LLM performance. Additionally, we used Hamming distance to assess changes between phrase orderings, concluding that prompt modifications can dramatically affect scores, often by almost random chance. These findings support existing research on prompt sensitivity. We discuss the challenges of prompt optimization, noting that altering phrases in a successful prompt does not always result in another successful prompt.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Analyzing School Bus Electrification in Richmond, Virginia

School buses are an essential component of the transportation infrastructure, serving as a lifeline for students across the globe. However, the widespread use of diesel school buses has raised concerns about the health impact on millions of students exposed to harmful emissions daily. Recognizing this issue, school districts worldwide are urgently seeking cleaner energy alternatives. Electric school buses emerge as an environmentally friendly and sustainable option, fostering a healthier environment for both students and communities. However, school bus electrification faces the challenges of high upfront cost, cumbersome charging management, and constraints from power grids. To help school bus operators address those challenges, this study presents a data-driven analysis for school bus electrification. This study considered a real-world school bus system in Richmond, VA, and developed a mathematical programming model to analyze the system design, charging strategies, and charging load profiles for the electrification scenario. The study evaluated different charging strategies based on model outcomes, aiming to optimize efficiency and effectiveness. Ultimately, this research generated electric school bus charging demand profiles under various scenarios, shedding light on the feasibility and implications of transitioning to electric-powered school buses.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

A framework and tool for designing cost-effective, resilient, and circular net-zero supply chains under uncertainty with an application to multilayer plastic films

While 55% of Fortune 500 companies have committed to achieving net-zero emissions and/or zero-waste operations by 2035, only 2% are currently on track, revealing a critical gap between ambition and action. Designing supply chains that reduce both emissions and waste is a complex non-intuitive, multi-objective challenge, compounded by the high costs of new technologies and the need for resilient, profitable solutions. This paper aims to address this challenge by presenting a generic framework and multi-objective optimization formulation for designing cost-effective, circular, and resilient supply chains under uncertainty, implemented through a user-friendly decision-support tool with intuitive data visualization capabilities, enabling communication of results to both technical and non-technical stakeholders. We demonstrate the application of this framework in the context of multilayer plastic films (barrier films), which are widely used in food packaging and composite materials. The model quantifies trade-offs across three objectives: minimizing global warming potential, maximizing circularity, and minimizing cost. A key contribution of this work is the explicit modeling of technological resilience, the ability of supply chains to maintain function under disruption. In the cost-minimization case, the resilience constraint makes the design approximately three times more expensive in the short-term metric, but shifts the system from relying on a single recovery pathway to a portfolio of four recovery pathways, improving the robustness of the optimization solution under uncertainty. Lastly, we introduce TranZero, a decision-support tool that integrates material flow analysis, hotspot identification, and optimization-based scenario planning to support net-zero and circularity decisions.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

Economic NMPC for a Reversible Solid Oxide Cell

Reversible solid oxide fuel cells (rSOCs) offer the flexibility to operate in tandem with the electric grid by switching between fuel cell and electrolysis modes based on real-time electricity prices. However, their complex, tightly coupled dynamic behavior poses significant challenges in determining optimal operating strategies. In this work, we present an economic nonlinear model predictive control (E-NMPC) framework to optimize the operation of rSOCs. The proposed E-NMPC is applied to a detailed rSOC flowsheet model that includes a utility scale rSOC module as well as balance-of-plant equipment necessary for thermal management. Our results demonstrate that in fuel cell mode, the E-NMPC strategy reduces hydrogen consumption compared to conventional set-point tracking NMPC, while maintaining the same level of electricity output. Also, in electrolysis mode, the E-NMPC yields a marginal improvement in hydrogen production. In addition, we explore the integration of a battery with the rSOC system to enhance flexibility in meeting electricity production and consumption targets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Deep Reinforcement Learning for Distribution System Operations: A Tutorial and Survey

Here, the rapid evolution of modern electric power distribution systems into complex networks of interconnected active devices, distributed generation (DG), and storage poses increasing difficulties for system operators. The large-scale integration of distributed energy resources (DERs) and the rapid exchange of measurement data via communication networks present major opportunities for advancing grid operations but also introduce greater uncertainty, higher data dimensionality, more complex network and device models, and challenging control and optimization problems. Deep reinforcement learning (DRL) algorithms are promising in addressing these challenges. However, they have not been effectively adapted for power systems applications, requiring extensive customization for implementation and evaluation. This has resulted in reproducibility challenges and a steep learning curve for researchers new to applying DRL algorithms to the power systems domain. To bridge these gaps, this tutorial aims to serve as a valuable resource for researchers interested in exploring learning-based algorithms to operate active power distribution networks. Specifically, this work presents a generalized process for translating sequential decision-making problems in power distribution systems into Markov decision process (MDP) formulations, illustrated through concrete grid service examples. Additionally, we introduce a simple environment design strategy to develop and evaluate example DRL algorithms for distribution system applications, complete with an included code repository to guide users through environment construction.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRSDate not supplied

Parallel Hybrid Turboprop Performance Modeling and Optimization

NASA’s Electrified Powertrain Flight Demonstration (EPFD) project conducts ground and flight tests of integrated Megawatt (MW) class hybrid-electric powertrain systems on regional turboprop aircraft demonstrators. To meet the increased demand for assessment of potential capabilities and benefits from these novel vehicle configurations, NASA is developing tooling and models to estimate the performance of hybridized regional turboprops. This paper covers the development of a parametrically driven performance model for a De Havilland Canada Dash 8-400 (Q400) regional turboprop integrated with a novel parallel hybrid architecture using the Gascon framework. Gascon is a modern reimplementation of the General Aviation Synthesis Program (GASP) built using the Condor mathematical modeling framework in Python. Within Gascon, a parametric representation of the parallel hybrid architecture was synthesized, which features the electric motor coupled to the power turbine. This capability allows for in-the-loop optimization of the parametric parallel hybrid architecture to characterize the mission capabilities and fuel savings of the design and determine optimal power scheduling strategies for efficient electric power management for a given mission. The study shows that a fuel savings of up to 20% can be achieved, but that increased fuel savings comes at the expense of payload capacity.

Gascon↗
NASA NTRSDate not supplied

Parallel Hybrid Turboprop Performance Modeling and Optimization

NASA’s Electrified Powertrain Flight Demonstration (EPFD) project conducts ground and flight tests of integrated Megawatt (MW) class hybrid-electric powertrain systems on regional turboprop aircraft demonstrators. To meet the increased demand for assessment of potential capabilities and benefits from these novel vehicle configurations, NASA is developing tooling and models to estimate the performance of hybridized regional turboprops. This paper covers the development of a parametrically driven performance model for a De Havilland Canada Dash 8-400 (Q400) regional turboprop integrated with a novel parallel hybrid architecture using the Gascon framework. Gascon is a modern reimplementation of the General Aviation Synthesis Program (GASP) built using the Condor mathematical modeling framework in Python. Within Gascon, a parametric representation of the parallel hybrid architecture was synthesized, which features the electric motor coupled to the power turbine. This capability allows for in-the-loop optimization of the parametric parallel hybrid architecture to characterize the mission capabilities and fuel savings of the design and determine optimal power scheduling strategies for efficient electric power management for a given mission. The study shows that a fuel savings of up to 20% can be achieved, but that increased fuel savings comes at the expense of payload capacity.

Gascon↗
DOE OSTI2025

A Demand Bidding Model for Multi-Product Industrial Plants

The growing contribution of renewable energy sources has increased volatility and uncertainty in electricity markets, challenging traditional grid operation paradigms. Demand bidding (DB), a market participation model where (large) electricity users communicate their willingness to pay for electricity to the grid operator, was shown in previous work to enhance grid stability and lower generation cost. We present a DB model for multi-product industrial plants, based on an extended optimal power flow problem where the plant dynamics are represented using autoregressive with extra inputs (ARX) models. We compare DB to price-based demand-side management, showing that, under certain assumptions, the two approaches are equivalent, while DB provides more transparency and predictability to the grid operator. A case study based on an industrial air separation unit is discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1975

A new structural analysis/synthesis capability - ACCESS

The creation of an efficient automated capability for minimum weight design of structures is reported. The ACCESS 1 computer program combines finite element analysis techniques and mathematical programming algorithms using an innovative collection of approximation concepts. Design variable linking, constraint deletion techniques and approximate analysis methods are used to generate a sequence of small explicit mathematical programming problems which retain the essential features of the design problem. Organization of the finite element analysis is carefully matched to the design optimization task. The efficiency of the ACCESS 1 program is demonstrated by giving results for several example problems.

Schmit, L. A.↗
NASA NTRS1976

Acoustoelasticity

Internal sound fields are considered. Specifically, the interaction between the (acoustic) sound pressure field and the (elastic) flexible wall of an enclosure is discussed. Such problems frequently arise when the vibrating walls of a transportation vehicle induce a significant internal sound field. Cabin noise in various flight vehicles and the internal sound field in an automobile are representative examples. A mathematical model, simplified solutions, and numerical results and comparisons with representative experimental data are briefly considered. An overall conclusion is that reasonable grounds for optimism exist with respect to available theoretical models and their predictive capability.

Dowell, E. H.↗