Results for “Integral transforms” — Page 41

NASA NTRS2008

The Nation's Needs in Aviation Formal Methods

Aviation, both on-board systems and the National Airspace System, can be transformed by many current and future technical capabilities. To name but a few, improved efficiency may be achieved by integrating functions; robustness may be improved by distributing functions; and safety may be improved by building in risk mitigation through not only redundant, independent systems but also through operational concepts and effective interaction with human operators. This talk will review the key aspects of verification, validation and certification for which formal methods will provide a critical function in enabling truly revolutionary designs to enter the operational community, illustrating successes in formal modeling to date and posing further questions for the formal modeling community.

Pritchett, Amy R.↗

NASA NTRS2015

Fuel Distribution Estimate via Spin Period to Precession Period Ratio for the Advanced Composition Explorer

The spin period to precession period ratio of a non-axisymmetric spin-stabilized spacecraft, the Advanced Composition Explorer (ACE), was used to estimate the remaining mass and distribution of fuel within its propulsion system. This analysis was undertaken once telemetry suggested that two of the four fuel tanks had no propellant remaining, contrary to pre-launch expectations of the propulsion system performance. Numerical integration of possible fuel distributions was used to calculate moments of inertia for the spinning spacecraft. A Fast Fourier Transform (FFT) of output from a dynamics simulation was employed to relate calculated moments of inertia to spin and precession periods. The resulting modeled ratios were compared to the actual spin period to precession period ratio derived from the effect of post-maneuver nutation angle on sun sensor measurements. A Monte Carlo search was performed to tune free parameters using the observed spin period to precession period ratio over the life of the mission. This novel analysis of spin and precession periods indicates that at the time of launch, propellant was distributed unevenly between the two pairs of fuel tanks, with one pair having approximately 20% more propellant than the other pair. Furthermore, it indicates the pair of the tanks with less fuel expelled all of its propellant by 2014 and that approximately 46 kg of propellant remains in the other two tanks, an amount that closely matches the operational fuel accounting estimate. Keywords: Fuel Distribution, Moments of Inertia, Precession, Spin, Nutation

Moment of Inertia↗

NASA NTRS2018

Action Pathways for Transforming Cities

Transformation is required for cities to fulfil their leadership potential on climate change. Five action pathways can guide them: integrate mitigation and adaptation; coordinate risk reduction and climate adaptation; cogenerate risk information; focus on disadvantaged populations; and improve governance and knowledge networks.

Civil engineering↗

NASA NTRS2020

Dynamic Stability And Adaptive Control of Networked Evolving Formations with Weak Nonlinearities

The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.

Gehlot, Vinod P.↗

NASA NTRS2023

BERT-Based Topic Modeling and Information Retrieval to Support Fishbone Diagramming for Safe Integration of Unmanned Aircraft Systems in Wildfire Response

Recent concepts for emerging wildfire response operations have included unmanned aircraft systems (UAS) due to their increasing accessibility and capabilities. To integrate UAS into wildfire response safely, researchers have studied the use of large repositories of historic incident reports to improve the scope of root cause analysis. Recent work has emphasized applying state-of-the-art natural language processing techniques to extract useful information from these repositories. However, it has not yet been studied how these results can be interpreted and integrated into the systems engineering process. In this work, we propose a process in which Bidirectional Encoder Representations from Transformers (BERT)-based topic modeling and information retrieval are applied to a relevant set of documents in order to support the development of a fishbone diagram in a semiautomated process. High-level themes in the document set are identified using topic modeling, which are then refined and interpreted by a human analyst. Then, the themes are used to guide a finer search using information retrieval, which returns specific incident reports of relevance. This provides traceability to specific incidents as well as broader categorizations that comprise the fishbone branches. We apply the proposed process to relevant documents from NASA’s Aviation Safety Reporting System (ASRS). The proposed process is widely applicable when relevant documents are available, and the results from this study will be useful to identifying potential causes of wildfire response UAS incidents.

Hazard analysis↗

NASA NTRSDate not supplied

BERT-based Topic Modeling and Information Retrieval to Support Fishbone Diagramming for Safe Integration of Unmanned Aircraft Systems in Wildfire Response

Recent concepts for emerging wildfire response operations have included unmanned aircraft systems (UAS) due to their increasing accessibility and capabilities. To integrate UAS into wildfire response safely, researchers have studied the use of large repositories of historic incident reports to improve the scope of root cause analysis. Recent work has emphasized applying state-of-the-art natural language processing techniques to extract useful information from these repositories. However, it has not yet been studied how these results can be interpreted and integrated into the systems engineering process. In this work, we propose a process in which Bidirectional Encoder Representations from Transformers (BERT)-based topic modeling and information retrieval are applied to a relevant set of documents in order to support the development of a fishbone diagram in a semiautomated process. High-level themes in the document set are identified using topic modeling, which are then refined and interpreted by a human analyst. Then, the themes are used to guide a finer search using information retrieval, which returns specific incident reports of relevance. This provides traceability to specific incidents as well as broader categorizations that comprise the fishbone branches. We apply the proposed process to relevant documents from NASA’s Aviation Safety Reporting System (ASRS). The proposed process is widely applicable when relevant documents are available, and the results from this study will be useful to identifying potential causes of wildfire response UAS incidents.

hazard analysis↗

NASA NTRS2023

Digital Engineering Design Center (DEDC): Modelling an ISRU System

The DEDC provides immersive project-based learning on digital engineering toolsets and processes supporting NASA’s digital transformation goals: - Digital Engineering uses authoritative sources of systems' data and models as a continuum across disciplines to support integrated digital approach life cycle activities from concept through disposal. - The digital environment provided includes the state-of-the-art digital engineering suite, Siemens Xcelerator. The pilot project is developing an end-to-end integrated model of an In-Situ Resource Utilization (ISRU) system for commodities production: - ISRU uses local resources to provide mission consumables to enable a sustainable Moon or Mars surface presence. - The final digital twin product will include a methanation reactor, condenser, and electrolyzer subsystem.

Digital Engineering Design Center↗

NASA NTRSDate not supplied

BERT-based Topic Modeling and Information Retrieval to Support Fishbone Diagramming for Safe Integration of Unmanned Aircraft Systems in Wildfire Response

Recent concepts for emerging wildfire response operations have included unmanned aircraft systems (UAS) due to their increasing accessibility and capabilities. To integrate UAS into wildfire response safely, researchers have studied the use of large repositories of historic incident reports to improve the scope of root cause analysis. Recent work has emphasized applying state-of-the-art natural language processing techniques to extract useful information from these repositories. However, it has not yet been studied how these results can be interpreted and integrated into the systems engineering process. In this work, we propose a process in which Bidirectional Encoder Representations from Transformers (BERT)-based topic modeling and information retrieval are applied to a relevant set of documents in order to support the development of a fishbone diagram in a semiautomated process. High-level themes in the document set are identified using topic modeling, which are then refined and interpreted by a human analyst. Then, the themes are used to guide a finer search using information retrieval, which returns specific incident reports of relevance. This provides traceability to specific incidents as well as broader categorizations that comprise the fishbone branches. We apply the proposed process to relevant documents from NASA’s Aviation Safety Reporting System (ASRS). The proposed process is widely applicable when relevant documents are available, and the results from this study will be useful to identifying potential causes of wildfire response UAS incidents.

hazard analysis↗

NASA NTRSDate not supplied

Investigating the Feasibility and Stability for Modeling Broadband Acoustic Wave Scattering using a Time-Domain Boundary Integral Equation

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. Acoustic liners are an effective tool for reducing aircraft noise and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model is discussed in which the liner impedance is specified along a wide range of frequencies. An impedance boundary condition is derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate. It is assumed the flat plate has surfaces treated with acoustic liners. The stability of the numerical algorithm is assessed using eigenvalue analysis.

mathmatics↗

NASA NTRS1975

Stabilization by modification of the Lagrangian

In order to reduce the error growth during a numerical integration, a method of stabilization of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as an independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Liapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.

Baumgarte, J. W.↗

DOE OSTI2026

Use of Digital Real-Time Simulation and Optimization to Identify Maximum Real Power Injection on Banshee Distribution Network

This study investigates the hosting capacity of the Banshee Distribution Network by optimizing the real power injection at carefully selected Distributed Energy Resource (DER) locations. The analysis is conducted within the framework of power system operational constraints, including bus voltage ranges, thermal line ratings, and transformer loading limits. A Python-based Genetic Algorithm (GA), implemented using the PyGAD library, is employed to iteratively identify the optimal power injection configuration that maximizes network utilization while preserving system reliability. The methodology integrates a real-time simulation environment using the Real-Time Digital Simulator (RTDS), allowing high-fidelity evaluation of power flow and voltage behavior under each proposed injection scenario. By coupling the optimization algorithm with real-time simulation feedback, this approach ensures that both static and dynamic constraints are enforced during the evaluation process. The GA leverages evolutionary operators such as selection, crossover, and mutation to navigate the nonlinear search space efficiently. The results of the study delineate the feasible hosting capacity at three targeted buses, reflecting maximum real power levels that can be injected without causing voltage violations, transformer overloading, or line congestion. These findings provide a decision- support tool for distribution planners and utilities aiming to integrate higher penetrations of DERs in existing infrastructure. Additionally, the work lays the foundation for extending such optimization techniques to multi-objective formulations, including economic dispatch and reactive power coordination, in future studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Use of Digital Real-Time Simulation and Optimization to Identify Maximum Real Power Injection on the Banshee Distribution Network: Preprint

This study investigates the hosting capacity of the Banshee Distribution Network by optimizing the real power injection at carefully selected Distributed Energy Resource (DER) locations. The analysis is conducted within the framework of power system operational constraints, including bus voltage ranges, thermal line ratings, and transformer loading limits. A Python-based Genetic Algorithm (GA), implemented using the PyGAD library, is employed to iteratively identify the optimal power injection configuration that maximizes network utilization while preserving system reliability. The methodology integrates a real-time simulation environment using the Real-Time Digital Simulator (RTDS), allowing high-fidelity evaluation of power flow and voltage behavior under each proposed injection scenario. By coupling the optimization algorithm with real-time simulation feedback, this approach ensures that both static and dynamic constraints are enforced during the evaluation process. The GA leverages evolutionary operators such as selection, crossover, and mutation to navigate the nonlinear search space efficiently. The results of the study delineate the feasible hosting capacity at three targeted buses, reflecting maximum real power levels that can be injected without causing voltage violations, transformer overloading, or line congestion. These findings provide a decision- support tool for distribution planners and utilities aiming to integrate higher penetrations of DERs in existing infrastructure. Additionally, the work lays the foundation for extending such optimization techniques to multi-objective formulations, including economic dispatch and reactive power coordination, in future studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Computing neutrino cross sections from Euclidian responses

Energy integrated neutrino cross sections are integrals of nuclear responses weighted with kinematic prefactors. We decompose the prefactors into a limited set of functions of energy transfer and show the relevant integrals are the moments of the responses, and integrals weighted with $1/(a+ω)^n$ with $n\leq 2$. These can be directly obtained from the Euclidean response, avoiding the need for inversion of the Laplace transform. As a proof of concept we study the procedure with toy-model responses for the quasielastic peak. We show that the different contributions can be straightforwardly organized in terms of relative importance, and how flux-averaged cross sections can be obtained. Using a realistic model for the response and numerical uncertainty we show that it is feasible to obtain the required integrals from the Euclidean response, with large uncertainties only for the third moment. Due to kinematic restrictions, the integrals contain contributions from the unphysical region for neutrino scattering, coming from high-momentum nucleons. We show that (in the absence of two-body currents) robust corrections for this contamination are obtained from the single-nucleon momentum distribution. These results present an opportunity to compute certain neutrino cross sections with ab-initio methods with controlled uncertainties.

Nikolakopoulos, A. [Washington U., Seattle]↗

DOE OSTI2026

Computing neutrino cross sections from Euclidian responses

Energy integrated neutrino cross sections are integrals of nuclear responses weighted with kinematic prefactors. We decompose the prefactors into a limited set of functions of energy transfer and show the relevant integrals are the moments of the responses, and integrals weighted with $1/(a+ω)^n$ with $n\leq 2$. These can be directly obtained from the Euclidean response, avoiding the need for inversion of the Laplace transform. As a proof of concept we study the procedure with toy-model responses for the quasielastic peak. We show that the different contributions can be straightforwardly organized in terms of relative importance, and how flux-averaged cross sections can be obtained. Using a realistic model for the response and numerical uncertainty we show that it is feasible to obtain the required integrals from the Euclidean response, with large uncertainties only for the third moment. Due to kinematic restrictions, the integrals contain contributions from the unphysical region for neutrino scattering, coming from high-momentum nucleons. We show that (in the absence of two-body currents) robust corrections for this contamination are obtained from the single-nucleon momentum distribution. These results present an opportunity to compute certain neutrino cross sections with ab-initio methods with controlled uncertainties.

Nikolakopoulos, A. [Washington U., Seattle]↗

NASA NTRS1965

The radial heat polynomials and related functions.

Generalized heat equation solution expansion in terms of radial heat polynomials, Appel transforms and Laguerre polynomials

RADIAL DISTRIBUTION↗

NASA NTRS2025

Distributed Sensing Node Configuration

A vision and radar sensor integration strategy for surveillance of Advance Air Mobility Mission concept of airspace is contained in the CAD drawing in this publication developed as part of NASA's Transformational Tools and Technology project. High-density airspace operations with multiple aircraft type and potentially noncooperative aircraft require distributed sensor detection and tracking systems to monitor airspace for safe, autonomous flight operations for advanced air mobility, urban air mobility, and high density small uncrewed air systems (SUAS) flight concepts. Contained herein are drawings that are available in the stp and creo file formats of the distributed sensing nodes. Additional dovetail integration is included to enable rapid changing of embedded system. A day in the life node deployment is included in the 2023_last_flight_day.mp4. Please cite this publication if you use these drawings. This sensor configuration methodology is presented in detail in the publication reference below. Chester Dolph, Thomas Lombaerts, Corey A. Ippolito, Vahram Stepanyan, Evan Kawamura, Keerthana Kannan, George Szatkowski, Todd Ferante, Christopher Morris, Federica Vitiello, Flavia Causa, Roberto Opromolla and Giancarmine Fasano. "Distributed Sensor Fusion of Ground and Air Nodes using Vision and Radar Modalities for Tracking Multirotor Small Uncrewed Air Systems and Birds," AIAA 2024-1781. AIAA SCITECH 2024 Forum. January 2024.

Chester V Dolph↗

DOE OSTI2024

Modular Subsurface Sensors and Integrated Software for Advanced Subsurface Characterization and Monitoring using Unoccupied Vehicles

The advent and subsequent proliferation of autonomous airborne, waterborne, and groundbased vehicles (i.e., “drones”) promises to broadly transform the geosciences and associated industries, including fossil energy exploration and development, mineral resource exploration and development, water-resource management, and environmental remediation. For geophysical characterization and monitoring, the prospect of programming highly repeatable and low-cost drone missions for subsurface imaging will allow for deployments in hazardous and previously inaccessible areas. Coupled with autonomous workflows for data processing, management, and visualization, drone-based geophysical characterization and monitoring will enable unprecedented, real-time insight into diverse subsurface properties and processes of scientific and engineering importance. Toward this end, the objectives of this Lab Directed Research and Development (LDRD) project were to develop new (1) instrumentation for dronebased electromagnetic induction (EMI) geophysical imaging, including separated transmitter and receivers and associated electronics, (2) software for real-time data telemetry, processing, management, and visualization. Although EMI has been previously deployed using unoccupied aerial systems (UASs), these applications failed to capitalize on the game-changing capabilities of drone platforms. Whereas drone-based data acquisition allows for collection of rich, three-dimensional (3D) multi-offset/multi-angle configurations between transmitters and receivers, past efforts have relied on conventional instrumentation that was designed for ground-based data collection with the transmitter and a single receiver housed in the same unit; nor did these previous applications demonstrate real-time delivery of results to support rapid management decisions in the field. In this 1-year project, we (1) designed and constructed new lightweight independent transmitter and receiver antenna platforms that communicate with a laptop computer; (2) developed software to control data acquisition, manage/transfer data, and visualize data as its collected; and (3) demonstrated the operation of the new hardware and software systems in a ground-based field test. Our work entails major technological advances for EMI and established a foundation on which to build a new drone-based, real-time geophysical EMI imaging capability to support diverse challenges facing the nation.

47 OTHER INSTRUMENTATION↗

NASA NTRSDate not supplied

Harnessing the Digital Transformation for Development of Hybrid Electric Aircraft Propulsion Control Systems

Hybrid electric aircraft propulsion is an emerging technology that presents a variety of potential benefits along with technical integration challenges. Developing these new propulsion architectures with their complex control systems, and ultimately proving their benefit, is a multistep process that goes from concept, to analysis, to dynamic simulation, to hardware in the loop testing, to full scale testing and beyond. This effort is being revolutionized and indeed enabled by new digital tools that support the increasing technology readiness level throughout the maturation process. NASA has developed and made available a suite of digital tools that ease the path from concept to implementation. The three packages are the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS), the Electrical Modeling and Thermal Analysis Toolbox (EMTAT), and the Thermal Systems Analysis Toolbox (TSAT). These tools are interactive, complementary, and compatible with each other. T-MATS is a modular thermodynamic modeling framework designed for creating custom component level models of jet engines. EMTAT is a modeling framework used to simulate a variety of power electronic devices, using both physics-based and power flow calculations. TSAT is a framework for modeling and analysis of dynamic heat transfer. These packages all consist of graphical, drag-and-drop, parameterizable building blocks representing various components of the system to be modeled, e.g., compressors, turbines, motors, energy storage devices, etc. They are designed to enable the user to model and simulate the end-to-end dynamic operation of a hybrid powertrain at the timescale of the turbomachinery, capturing mechanical, electrical, and thermal interactions. This paper will describe through multiple examples how these tools have been used successfully in several of the early stages of hybrid electric propulsion system development, from the initial system modeling to real-time interactive pilot-in-the-loop simulation to physical hardware-in-the-loop testing, each step bringing the technology closer to fruition.

Electrified Propulsion↗