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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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The CYBEAN (CYlindrical BEaring ANalysis) program was created to detail radially loaded, aligned and misaligned Cylindrical roller bearing performance under a variety of operating conditions. The models and associated mathematics used within CYBEAN are described. The user is referred to the material for formulation assumptions and algorithm detail.
Mathematical-analytical methods as used in Operations Research approaches are often insufficient for scheduling problems. This is due to three reasons: the combinatorial complexity of the search space, conflicting objectives for production optimization, and the uncertainty in the production process. Knowledge-based techniques, especially approximate reasoning and constraint relaxation, are promising ways to overcome these problems. A case study from an industrial CIM environment, namely high-grade steel production, is presented to demonstrate how knowledge-based scheduling with the desired capabilities could work. By using fuzzy set theory, the applied knowledge representation technique covers the uncertainty inherent in the problem domain. Based on this knowledge representation, a classification of jobs according to their importance is defined which is then used for the straightforward generation of a schedule. A control strategy which comprises organizational, spatial, temporal, and chemical constraints is introduced. The strategy supports the dynamic relaxation of conflicting constraints in order to improve tentative schedules.
The primary aim of this research effort was to advance the current understanding of astronauts' capabilities and limitations in space-suited EVA by developing models of the constitutive and compatibility relations of a space suit, based on experimental data gained from human test subjects as well as a 12 degree-of-freedom human-sized robot, and utilizing these fundamental relations to estimate a human factors performance metric for space suited EVA work. The three specific objectives are to: 1) Compile a detailed database of torques required to bend the joints of a space suit, using realistic, multi- joint human motions. 2) Develop a mathematical model of the constitutive relations between space suit joint torques and joint angular positions, based on experimental data and compare other investigators' physics-based models to experimental data. 3) Estimate the work envelope of a space suited astronaut, using the constitutive and compatibility relations of the space suit. The body of work that makes up this report includes experimentation, empirical and physics-based modeling, and model applications. A detailed space suit joint torque-angle database was compiled with a novel experimental approach that used space-suited human test subjects to generate realistic, multi-joint motions and an instrumented robot to measure the torques required to accomplish these motions in a space suit. Based on the experimental data, a mathematical model is developed to predict joint torque from the joint angle history. Two physics-based models of pressurized fabric cylinder bending are compared to experimental data, yielding design insights. The mathematical model is applied to EVA operations in an inverse kinematic analysis coupled to the space suit model to calculate the volume in which space-suited astronauts can work with their hands, demonstrating that operational human factors metrics can be predicted from fundamental space suit information.
This paper presents the technical background of the Trim and Static module of the Matlab Stability and Control Toolbox. This module performs a low-fidelity stability and control assessment of an aircraft model for a set of flight critical conditions. This is attained by determining if the control authority available for trim is sufficient and if the static stability characteristics are adequate. These conditions can be selected from a prescribed set or can be specified to meet particular requirements. The prescribed set of conditions includes horizontal flight, take-off rotation, landing flare, steady roll, steady turn and pull-up/ push-over flight, for which several operating conditions can be specified. A mathematical model was developed allowing for six-dimensional trim, adjustable inertial properties, asymmetric vehicle layouts, arbitrary number of engines, multi-axial thrust vectoring, engine(s)-out conditions, crosswind and gyroscopic effects.
Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.
The GOES Product Generation System (GPGS) is a set of computer codes and scripts that enable the assimilation of real-time Geostationary Operational Environmental Satellite (GOES) data into regional-weather-forecasting mathematical models. The GPGS can be used to derive such geophysical parameters as land surface temperature, the amount of precipitable water, the degree of cloud cover, the surface albedo, and the amount of insolation from satellite measurements of radiant energy emitted by the Earth and its atmosphere. GPGS incorporates a priori information (initial guesses of thermodynamic parameters of the atmosphere) and radiometric measurements from the geostationary operational environmental satellites along with mathematical models of physical principles that govern the transfer of energy in the atmosphere. GPGS solves the radiative-transfer equation and provides the resulting data products in formats suitable for use by weather-forecasting computer programs. The data-assimilation capability afforded by GPGS offers the potential to improve local weather forecasts ranging from 3 hours to 2 days - especially with respect to temperature, humidity, cloud cover, and the probability of precipitation. The improvements afforded by GPGS could be of interest to news media, utility companies, and other organizations that utilize regional weather forecasts.
Recorded seismic data are generally contaminated by noise from different sources, which masks the signals of interest. In the seismology community, frequency filtering (FF) is the standard method for noise suppression. However, when the signal of interest and noise share the same frequency band, the latter cannot be filtered out without infringing on the former. We implemented a noise suppression approach based on the mathematical morphology theorem. The method involves compound operations of dilation and erosion using structuring elements of varying lengths and decomposes an input noisy waveform into several time functions with differing characteristics. Further, the filtered waveform is constructed from the time functions using a self-adaptive reconstruction technique. Application to a data set of >4700 local waveforms suggests that the implemented mathematical morphological filtering (MMF) approach is efficient for data with low signal-to-noise ratio (SNR) and significantly outperforms FF in that SNR range. For most of the dataset, FF, machine learning (ML) denoising, and continuous wavelet transform (CWT) thresholding result in higher SNR values compared with the MMF method. However, for ~42% of the waveforms, MMF outperforms FF, and the SNR gain achieved with MMF is as large as ~23 dB. Compared to ML denoising and CWT thresholding, this proportion drops to only ~10%–14%. Our results suggests that in an operational setting, MMF cannot replace the other noise suppression methods; however, signal detection can be improved if MMF is used to supplement them in some scenarios. MMF could help detect signals in problematic low-SNR data, which are currently being missed particularly when using FF alone.
Electronic display unit provides operator of longwall shearer with information needed to control machine. Unit samples sensors on shearer. Using sensor signals, executes mathematical calculations, performs decisionmaking routines and displays results to operator. Unit also logs data for later analysis.
The major goal of this project is to develop mathematical models of heat pipes which can be used to predict transient behavior under normal and adverse conditions. The models and solution techniques are to be formulated so that they can be incorporated into existing NASA structural design codes. The major parameters of interest are heat flux distribution, temperature distribution, working fluid pressure distribution, fluid and containment thermal and mechanical properties and geometry. Normal transient operation is taken to be operating conditions where the capillary structure remains fully wetted. Adverse transient operation occurs when drying, re-wetting, choking, non-continuum flow, thawing, freezing, etc., occur in the internal heat pipe working fluid.
Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.
Review article on connections between Koopman/transfer operator methods and quantum theory
In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.
This research introduces a more efficient way to optimize power grid operations, breaking the problem into manageable steps and using advanced mathematical techniques to speed up calculations. By incorporating smart heuristics, improved preprocessing, and contingency analysis, the approach allows operators to make better decisions faster. These innovations enhance our understanding of how to optimize energy generation, making it possible to anticipate failures before they happen, reduce system costs, and improve overall grid performance. Ultimately, this research helps bridge the gap between theoretical models and real-world applications, paving the way for a smarter, more resilient power grid. This research directly benefits the public by making electricity more affordable, reliable, and sustainable. By improving how power grids schedule and distribute electricity, the project helps energy providers reduce operational costs, which can lead to lower electricity prices for consumers. Additionally, the ability to predict and prevent power system failures enhances grid reliability, reducing the likelihood of blackouts that can disrupt homes, businesses, and critical infrastructure such as hospitals. From an environmental perspective, optimizing power generation reduces energy waste and lowers carbon emissions, contributing to cleaner air and a more sustainable energy system. Furthermore, with extreme weather events becoming more frequent, these advancements make the power grid more resilient, ensuring communities are better prepared for emergencies and natural disasters. By strengthening the nation's energy infrastructure, this research plays a crucial role in improving economic stability, public safety, and environmental sustainability.
This work presents both analytical and simulation studies for defining the minimum safe operational volume needed for aerial vehicles operating in upper Class E airspace. The analytical study is conducted first to investigate factors that affect the minimum safe operational volume, such as position errors, wake/vortex, vehicle maneuverability, communication and surveillance, control/operator response time. A mathematical approach is developed to compute the boundary of the safe operational volume required by the limited aircraft maneuverability and an analytical sensitivity study is then performed with varying parameters. After the analytical study, simulations are then conducted to verify the results from the analytical study. Simulation results will be included in the final paper.
A presentation introducing machine learning operation methods.
Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.
Wind shears can create havoc during aircraft terminal area operations and have been cited as the primary cause of several major aircraft accidents. A simple sensor, potentially having application to the wind-shear problem, was developed to rapidly measure aircraft total energy relative to the air mass. Combining this sensor with either a variometer or a rate-of-climb indicator provides a total energy-rate system which was successfully applied in soaring flight. The measured rate of change of aircraft energy can potentially be used on display/control systems of powered aircraft to reduce glide-slope deviations caused by wind shear. The experimental flight configuration and evaluations of the energy-rate system are described. Two mathematical models are developed: the first describes operation of the energy probe in a linear design region and the second model is for the nonlinear region. The calculated total rate is compared with measured signals for many different flight tests. Time history plots show the tow curves to be almost the same for the linear operating region and very close for the nonlinear region.
Space missions have historically relied upon a large ground staff, numbering in the hundreds for complex missions, to maintain routine operations. When an anomaly occurs, this small army of engineers attempts to identify and work around the problem. A piloted Mars mission, with its multiyear duration, cost pressures, half-hour communication delays and two-week blackouts cannot be closely controlled by a battalion of engineers on Earth. Flight crew involvement in routine system operations must also be minimized to maximize science return. It also may be unrealistic to require the crew have the expertise in each mission subsystem needed to diagnose a system failure and effect a timely repair, as engineers did for Apollo 13. Enter model-based autonomy, which allows complex systems to autonomously maintain operation despite failures or anomalous conditions, contributing to safe, robust, and minimally supervised operation of spacecraft, life support, In Situ Resource Utilization (ISRU) and power systems. Autonomous reasoning is central to the approach. A reasoning algorithm uses a logical or mathematical model of a system to infer how to operate the system, diagnose failures and generate appropriate behavior to repair or reconfigure the system in response. The 'plug and play' nature of the models enables low cost development of autonomy for multiple platforms. Declarative, reusable models capture relevant aspects of the behavior of simple devices (e.g. valves or thrusters). Reasoning algorithms combine device models to create a model of the system-wide interactions and behavior of a complex, unique artifact such as a spacecraft. Rather than requiring engineers to all possible interactions and failures at design time or perform analysis during the mission, the reasoning engine generates the appropriate response to the current situation, taking into account its system-wide knowledge, the current state, and even sensor failures or unexpected behavior.