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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Study of high speed complex number algorithms

A method of evaluating the radiation integral on the curved surface of a reflecting antenna is presented. A three dimensional Fourier transform approach is used to generate a two dimensional radiation cross-section along a planer cut at any angle phi through the far field pattern. Salient to the method is an algorithm for evaluating a subset of the total three dimensional discrete Fourier transform results. The subset elements are selectively evaluated to yield data along a geometric plane of constant. The algorithm is extremely efficient so that computation of the induced surface currents via the physical optics approximation dominates the computer time required to compute a radiation pattern. Application to paraboloid reflectors with off-focus feeds in presented, but the method is easily extended to offset antenna systems and reflectors of arbitrary shapes. Numerical results were computed for both gain and phase and are compared with other published work.

Heisler, R.↗
NASA NTRS1991

Generalizing Atoms in Constraint Logic

This paper studies the generalization of atomic formulas, or atoms, that are augmented with constraints on or among their terms. The atoms may also be viewed as definite clauses whose antecedents express the constraints. Atoms are generalized relative to a body of background information about the constraints. This paper first examines generalization of atoms with only monadic constraints. The paper develops an algorithm for the generalization task and discusses algorithm complexity. It then extends the algorithm to apply to atoms with constraints of arbitrary arity. The paper also presents semantic properties of the generalizations computed by the algorithms, making the algorithms applicable to such problems as abduction, induction, and knowledge base verification. The paper emphasizes the application to induction and presents a pac-learning result for constrained atoms.

Page, C. David, Jr.↗
NASA NTRS2011

Space Shuttle GN and C Development History and Evolution

Completion of the final Space Shuttle flight marks the end of a significant era in Human Spaceflight. Developed in the 1970 s, first launched in 1981, the Space Shuttle embodies many significant engineering achievements. One of these is the development and operation of the first extensive fly-by-wire human space transportation Guidance, Navigation and Control (GN&C) System. Development of the Space Shuttle GN&C represented first time inclusions of modern techniques for electronics, software, algorithms, systems and management in a complex system. Numerous technical design trades and lessons learned continue to drive current vehicle development. For example, the Space Shuttle GN&C system incorporated redundant systems, complex algorithms and flight software rigorously verified through integrated vehicle simulations and avionics integration testing techniques. Over the past thirty years, the Shuttle GN&C continued to go through a series of upgrades to improve safety, performance and to enable the complex flight operations required for assembly of the international space station. Upgrades to the GN&C ranged from the addition of nose wheel steering to modifications that extend capabilities to control of the large flexible configurations while being docked to the Space Station. This paper provides a history of the development and evolution of the Space Shuttle GN&C system. Emphasis is placed on key architecture decisions, design trades and the lessons learned for future complex space transportation system developments. Finally, some of the interesting flight operations experience is provided to inform future developers of flight experiences.

Zimpfer, Douglas↗
DOE OSTI2025

Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂⁡(𝜅⁢log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837⁢𝜅 at 𝜖 = 10 −10 for Hermitian matrices.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.

Ulbrich, Norbert M.↗
NASA NTRS1988

Spatial compression of Seasat SAR imagery

The results of a study of techniques for spatial compression of synthetic-aperture-radar (SAR) imagery are summarized. Emphasis is on image-data volume reduction for archive and online storage applications while preserving the image resolution and radiometric fidelity. A quantitative analysis of various techniques, including vector quantization (VQ) and adaptive discrete cosine transform (ADCT), is presented. Various factors such as compression ratio, algorithm complexity, and image quality are considered in determining the optimal algorithm. The compression system requirements are established for electronic access of an online archive system based on the results of a survey of the science community. The various algorithms are presented and their results evaluated considering the effects of speckle noise and the wide dynamic range inherent in SAR imagery. The conclusion is that although the ADCT produces the best signal-to-distortion-noise ratio for a given compression ratio, the two-level tree-searched VQ technique is preferred due to its simplicity of decoding and near-optimal performance.

Chang, C. Y.↗
NASA NTRS1993

A highly accurate Voigt function algorithm

A complex Voigt lineshape algorithm is presented whose maximum relative error over the complex plane is less than 1 x 10(exp -8). The algorithm consists of series, rational approximations and Gauss-Hermite integrations which makes it suitable as a general purpose software module for a wide variety of uses, including a Voigt function standard.

Shippony, Z.↗
NASA NTRS1993

A Highly Accurate Voight Function Algorithm

A complex Voight lineshape algorithm is presented whose maximum relative error over the complex plane is less than 1 x 10 super minus 8. The algorithm consists of series, rational approximations and Gauss-Hermite integrations which makes it suitable as a general purpose software module for a wide variety of uses, including a Voight function standard.

Voight lineshape Doppler velocity distribution col↗
NASA NTRS1993

Computationally efficient algorithms for real-time attitude estimation

For many practical spacecraft applications, algorithms for determining spacecraft attitude must combine inputs from diverse sensors and provide redundancy in the event of sensor failure. A Kalman filter is suitable for this task, however, it may impose a computational burden which may be avoided by sub optimal methods. A suboptimal estimator is presented which was implemented successfully on the Delta Star spacecraft which performed a 9 month SDI flight experiment in 1989. This design sought to minimize algorithm complexity to accommodate the limitations of an 8K guidance computer. The algorithm used is interpreted in the framework of Kalman filtering and a derivation is given for the computation.

Pringle, Steven R.↗
NASA NTRS2010

A Machine-Checked Proof of A State-Space Construction Algorithm

This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed points, corresponding to a chaotic fixed point strategy. A pencil-and-paper proof of Saturation exists, but a machine checked proof had never been attempted. The key element of the proof is the characterisation theorem of saturated nodes in decision diagrams, stating that a saturated node represents a set of states encoding a local fixed-point with respect to firing all events affecting only the node s level and levels below. For our purpose, we have employed the Prototype Verification System (PVS) for formalising the Saturation algorithm, its data structures, and for conducting the proofs.

Catano, Nestor↗
NASA NTRS1987

An analysis of redundancy management algorithms for asynchronous fault tolerant control systems

Redundancy management algorithms, commonly referred to as voters, are algorithms used in fault-tolerant control systems to vote on incoming redundant data, isolate bad signals, and output a single good value. In a synchronous environment, this algorithm is a straightforward signal-to-signal comparison with relatively low complexity. The technology of asynchronous control systems, recently realized in the Ultrareliable Fault Tolerant Control System research program at NASA Ames Research Center, requires more complex algorithms for fault detection and signal selection. A variety of algorithms used for this process, a means of testing them, and their basic performance under a simulated environment of the ultrareliable fault-tolerant control system are presented.

Davis, Gloria J.↗
NASA NTRS1990

Computation of the fuel optimal degree of controllability

A new algorithm based on discretization is propposed which gives arbitrarily accurate results for fuel-optimal degree of controllability (DOC) as the discretization interval approaches zero. This research on DOC was motivated by the problem of optimizing the actuator locations in the control of large flexible spacecraft, but the concepts can also be applied to model reduction and as a measure of coupling between subsystems in hierarchical or decentralized control. The approach utilized is related closely to the time-optimal DOC algorithm; however, additional constraints must be applied, and a useful approach is found that avoids substantial increase in complexity. Algorithms are developed to calculate both the volume and the minimum distance to the boundary of the recovery region as the two choices of the controllability measure. Accurate methods for computation of both the time-optimal and fuel-optimal DOC for maneuver problems, are also described.

Chen, Xin↗
NASA NTRS2018

Closed Loop Guidance Trade Study for Space Launch System Block-1B Vehicle

NASA is currently building the Space Launch System (SLS) Block-1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. The design of the next evolution of SLS, Block-1B, is well underway. The Block-1B vehicle is more capable overall than Block-1; however, the relatively low thrust-to-weight ratio of the Exploration Upper Stage (EUS) presents a challenge to the Powered Explicit Guidance (PEG) algorithm used by Block-1. To handle the long burn durations (on the order of 1000 seconds) of EUS missions, two algorithms were examined. An alternative algorithm, OPGUID, was introduced, while modifications were made to PEG. A trade study was conducted to select the guidance algorithm for future SLS vehicles. The chosen algorithm needs to support a wide variety of mission operations: ascent burns to LEO, apogee raise burns, trans-lunar injection burns, hyperbolic Earth departure burns, and contingency disposal burns using the Reaction Control System (RCS). Additionally, the algorithm must be able to respond to a single engine failure scenario. Each algorithm was scored based on pre-selected criteria, including insertion accuracy, algorithmic complexity and robustness, extensibility for potential future missions, and flight heritage. Monte Carlo analysis was used to select the final algorithm. This paper covers the design criteria, approach, and results of this trade study, showing impacts and considerations when adapting launch vehicle guidance algorithms to a broader breadth of in-space operations.

Von der Porten, Paul↗
NASA NTRS2010

Recent Advancements in Lightning Jump Algorithm Work

In the past year, the primary objectives were to show the usefulness of total lightning as compared to traditional cloud-to-ground (CG) networks, test the lightning jump algorithm configurations in other regions of the country, increase the number of thunderstorms within our thunderstorm database, and to pinpoint environments that could prove difficult for any lightning jump configuration. A total of 561 thunderstorms have been examined in the past year (409 non-severe, 152 severe) from four regions of the country (North Alabama, Washington D.C., High Plains of CO/KS, and Oklahoma). Results continue to indicate that the 2 lightning jump algorithm configuration holds the most promise in terms of prospective operational lightning jump algorithms, with a probability of detection (POD) at 81%, a false alarm rate (FAR) of 45%, a critical success index (CSI) of 49% and a Heidke Skill Score (HSS) of 0.66. The second best performing algorithm configuration was the Threshold 4 algorithm, which had a POD of 72%, FAR of 51%, a CSI of 41% and an HSS of 0.58. Because a more complex algorithm configuration shows the most promise in terms of prospective operational lightning jump algorithms, accurate thunderstorm cell tracking work must be undertaken to track lightning trends on an individual thunderstorm basis over time. While these numbers for the 2 configuration are impressive, the algorithm does have its weaknesses. Specifically, low-topped and tropical cyclone thunderstorm environments are present issues for the 2 lightning jump algorithm, because of the suppressed vertical depth impact on overall flash counts (i.e., a relative dearth in lightning). For example, in a sample of 120 thunderstorms from northern Alabama that contained 72 missed events by the 2 algorithm 36% of the misses were associated with these two environments (17 storms).

Schultz, Christopher J.↗
NASA NTRS1997

Bounds Estimation Via Regression with Asymmetric Cost Functions

This paper addresses a significant but mostly-neglected class of problems that we call bounds estimation. This includes learning empirical best-case and worst-case algorithmic complexity bounds and red-line bounds on sensor data.

regression-based learning algorithm bounds estimat↗
NASA NTRS1974

A comparison of computational methods and algorithms for the complex gamma function

A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries.

Ng, E. W.↗
NASA NTRS1990

A computational study of the impingement region of an unsteady subsonic jet

Vertical/Short Take-Off and Landing (V/STOL) aircraft may encounter operating difficulties while hovering near the ground. Lift loss, hot gas and debris ingestion, and landing surface damage are some of the potential problems which can result from the interaction of the propulsive jets with the airframe and ground. The purpose of the present work is to develop a detailed understanding of a flowfield, a jet exiting from a flat plate impacting a ground plane, that contains much of the essential physics of the complex flows encountered by V/STOL aircraft in hover. To achieve this, a high-resolution time-accurate numerical simulation of the impinging jet flow was performed. The numerical simulation is based on the solution of the laminar compressible Navier-Stokes equations using the Beam-Warming algorithm. Complex start-up and periodic jet and jet-induced vortex structures were captured, including the formation of primary and secondary jet-induced vortices and wall-jet separation. The formation and development of these phenomena are supported by experimental measurements and smoke visualization. Results are compared with appropriate experiments.

Jalamani, Zakaria A.↗
NASA NTRS2019

Evaluation of Classifier Complexity for Delay Tolerant Network Routing

The growing popularity of small cost effective satellites (SmallSats, CubeSats, etc.) creates the potential for a variety of new science applications involving multiple nodes functioning together or independently to achieve a task, such as swarms and constellations. As this technology develops and is deployed for missions in Low Earth Orbit and beyond, the use of delay tolerant networking (DTN) techniques may improve communication capabilities within the network. In this paper, a network hierarchy is developed from heterogeneous networks of SmallSats, surface vehicles, relay satellites and ground stations which form an integrated network. There is a tradeoff between complexity, flexibility, and scalability of user defined schedules versus autonomous routing as the number of nodes in the network increases. To address these issues, this work proposes a machine learning classifier based on DTN routing metrics. A framework is developed which will allow for the use of several categories of machine learning algorithms (decision tree, random forest and deep learning) to be applied to a dataset of historical network statistics, which allows for the evaluation of algorithm complexity versus performance to be explored. We develop the emulation of a hierarchical network, consisting of tens of nodes which form a cognitive network architecture. CORE (Common Open Research Emulator) is used to emulate the network using bundle protocol and DTN IP neighbor discovery.

Dudukovich, Rachel↗