The operator theory of the pseudo-inverse. II - Unbounded operators with arbitrary range.
Pseudo-inverse concept extended to Hilbert space unbounded operators with arbitrary range
SEARCH · Search NASA
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.
Pseudo-inverse concept extended to Hilbert space unbounded operators with arbitrary range
The VIIRS sensor provides measurements for 22 Environmental Data Records (EDRs) addressing the atmosphere, ocean surface temperature, ocean color, land parameters, aerosols, imaging for clouds and ice, and more. That is, the VIIRS collects visible and infrared radiometric data of the Earth's atmosphere, ocean, and land surfaces. Data types include atmospheric, clouds, Earth radiation budget, land/water and sea surface temperature, ocean color, and low light imagery. This wide scope of measurements calls for the preparation of a multiplicity of Algorithm Theoretical Basis Documents (ATBDs), and, additionally, for intermediate products such as cloud mask, et al. Furthermore, the VIIRS interacts with three or more other sensors. This paper addresses selected and crucial elements of the process being used to convert and test an immense volume of a maturing and changing science code to the initial operational source code in preparation for launch of NPP. The integrity of the original science code is maintained and enhanced via baseline comparisons when re-hosted, in addition to multiple planned code performance reviews.
This paper briefly outlines EOS Aura's Tropospheric Emmision Spectrometer (TES) experiment and TES instrument activities on operations.
Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.
Microgrids are becoming critical assets in power distribution systems. This is partly due to the resiliency and reliability challenges faced by power distribution systems in the last decade and partly due to the increased integration of distributed energy resource assets, such as solar photovoltaic. This increased need for microgrids has created a multitude of needs for microgrid controllers. Most microgrid controllers in the past decade have been uniquely programmed or custom programmed to meet the needs of a specific microgrid. Currently, IEEE standards aim to integrate the needs and capabilities of microgrid controllers under a unified umbrella. But the standards do not recommend necessary or appropriate software development practices for microgrid controllers. In addition, the programmable nature and maintenance of controllers are also key characteristics that fall outside the coverage of the standards. In this paper, we present the best software practices that utility engineers and microgrid operators should consider in the microgrid software platform. This paper can be used as an information document for developing documentation of controller requirements and assessing microgrid controller requirements.
Since hydrogen vehicles can be implemented in heavy-duty transportation applications such as buses, it is important to understand safety hazards and risks of hydrogen fuel cell electric bus (FCEB) and refueling technology. We conducted a hazard and operability analysis for FCEB operation/driving, refueling, and maintenance/inspection. We identified failure modes and consequences and defined a qualitative risk metric as the product of the likelihood of a failure and the severity of the worst-ca
Manned space flight and preflight operations
Surveyor Mission G flight operations from transit phase to second lunar day
Supersonic transport performance during real time simulated operations in future air traffic control system environments
Complex relationships between two directorates of research and development and industrial operations at MSFC
An anesthetic gas flow pop-off valve canister is described that is airtight and permits the patient to breath freely. Once its release mechanism is activated, the exhaust gases are collected at a hose adapter and passed through activated coal for adsorption. A survey of laminar air flow clean rooms is presented and the installation of laminar cross flow air systems in operating rooms is recommended. Laminar flow ventilation experiments determine drying period evaporation rates for chicken intestines, sponges, and sections of pig stomach.
The operation plans are presented for the oceanic Gamefish/Skylab Experiment 240, which was conducted to obtain fish catch data for the northeast area of the Gulf of Mexico. The plans for surface measurements, aerial observations, and communications are included.
Current aircraft operating problems that must be alleviated for future high-density terminal areas are safety, dependence on weather, congestion, energy conservation, noise, and atmospheric pollution. The Microwave Landing System (MLS) under development by FAA provides increased capabilities over the current ILS. The development of the airborne system's capability to take maximum advantage of the MLS capabilities in order to solve terminal area problems are discussed. A major limiting factor in longitudinal spacing for capacity increase is the trailing vortex hazard. Promising methods for causing early dissipation of the vortices were explored. Flight procedures for avoiding the hazard were investigated. Terminal configured vehicles and their flight test development are discussed.
The activities and results of the test and operations program performed on the three orbiter spacecraft (VO-1, VO-2, and VO-3) are described.
The mode of operation that is of interest in this discussion is a solar array battery load-sharing mode. The battery is loaded for a fraction of a second and then charged, so the cycle is a 100 millisecond load, followed by a 500 millisecond charge. The purpose of the experiment was to evaluate the charge efficiency and the state of charge. Charge/discharge ratio graphs are presented.
Hardware description and operational procedures for the ATS-3 Hawaii-Ames satellite computer link are presented in basic step-by-step instructions. Transmit and receive channels and frequencies are given. Details such as switch settings for activating the station to the sequence of turning switches on are provided. Methods and procedures for troubleshooting common problems encountered with communication stations are also provided.
Spacecraft navigation to the outer planets (Jupiter and beyond) places very stringent demands upon the performance of frequency and time (F&T) reference standards. The Deep Space Network (DSN) makes use of hydrogen masers as an aid in meeting the routine F&T operational requirements within the 64 m antenna network. Results as of October 1980 indicate the hydrogen masers are performing within the required specifications. Two problem areas are discussed: insufficient control over the environment in which the reference standards reside; and frequency drift.
The system and program requirements for a space operations center as defined by systems analysis studies are presented as a guide for future study and systems definition. Topics covered include general requirements for safety, maintainability, and reliability, service and habitat modules, the health maintenance facility; logistics modules; the docking tunnel; and subsystem requirements (structures, electrical power, environmental control/life support; extravehicular activity; data management; communications and tracking; docking/berthing; flight control/propulsion; and crew support). Facilities for flight support, construction, satellite and mission servicing, and fluid storage are included as well as general purpose support equipment.