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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A geometric theory for the QR, LU and power iterations.

Consideration of the task of computing the invariant subspaces of a given matrix. For this purpose the LU, QR, treppen and bi-iterations have been presented, used, and studied more or less independently of the old-fashioned power method. Each of these methods generates implicitly a sequence of subspaces which determines the convergence properties of the method. The iterations differ in the way in which a basis is constructed to represent each subspace. This aspect largely determines the usefulness of the method. It is shown that the first four iterations produce exactly the same sequence of subspaces as do direct and inverse iteration started from appropriate subspaces. Their convergence properties are therefore the same, and a complete geometric convergence theory is presented in terms of the power method. It is shown that Hessenberg matrices are associated with ideal starting spaces.

Parlett, B. N.↗
NASA NTRS1992

Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods

Let F(z) be a vectored-valued function F: C approaches C sup N, which is analytic at z=0 and meromorphic in a neighborhood of z=0, and let its Maclaurin series be given. We use vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series in conjunction with power iterations to develop bona fide generalizations of the power method for an arbitrary N X N matrix that may be diagonalizable or not. These generalizations can be used to obtain simultaneously several of the largest distinct eigenvalues and the corresponding invariant subspaces, and present a detailed convergence theory for them. In addition, it is shown that the generalized power methods of this work are equivalent to some Krylov subspace methods, among them the methods of Arnoldi and Lanczos. Thus, the theory provides a set of completely new results and constructions for these Krylov subspace methods. This theory suggests at the same time a new mode of usage for these Krylov subspace methods that were observed to possess computational advantages over their common mode of usage.

Sidi, Avram↗
NASA NTRSDate not supplied

High-Fidelity Aeropropulsive Assessment of Distributed Electric Propulsion and Boundary Layer Ingestion for the SUSAN Electrofan

This paper presents a high-fidelity aeropropulsive assessment of the SUSAN Electrofan’s distributed electric propulsion (DEP) and boundary layer ingestion (BLI) aft fuselage turbofan technologies. This is achieved through the application of computational tools for aerodynamic and aeropropulsive design and analysis based on the Reynolds-averaged Navier-Stokes (RANS) equations. Representative aircraft models are first developed in 3D for the SUSAN Electrofan concept, a non-DEP variant, and a year 2020 technology level reference aircraft based on the Boeing 737-8. These include airframes developed through the application of RANS-based aerodynamic shape optimization, with the objective of drag minimization at cruise while subject to constant lift and zero pitching moment constraints. Wing propulsors are also included and modeled as free-flying ducted fans. These are developed through RANS-based aeropropulsive shape optimization, with the objective of shaft power minimization while subject to constant net thrust and maximum fan face Mach number constraints. An iterative power balance method is then used to trim each of the decoupled aircraft configurations, providing estimates of relative aerodynamic performance, shaft power, and range efficiency. Results also include power on and off analyses, which indicate reduced thrust-induced drag for the SUSAN Electrofan’s DEP and BLI aft fuselage turbofan propulsors when compared to those of the Boeing 737-8-like reference aircraft.

CAS↗
NASA NTRS2009

Highly Scalable Matching Pursuit Signal Decomposition Algorithm

Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.

Christensen, Daniel↗
NASA NTRS1976

Calculations of the Electron Energy Distribution Function in a Uranium Plasma by Analytic and Monte Carlo Techniques

Electron energy distribution functions were calculated in a U235 plasma at 1 atmosphere for various plasma temperatures and neutron fluxes. The distributions are assumed to be a summation of a high energy tail and a Maxwellian distribution. The sources of energetic electrons considered are the fission-fragment induced ionization of uranium and the electron induced ionization of uranium. The calculation of the high energy tail is reduced to an electron slowing down calculation, from the most energetic source to the energy where the electron is assumed to be incorporated into the Maxwellian distribution. The pertinent collisional processes are electron-electron scattering and electron induced ionization and excitation of uranium. Two distinct methods were employed in the calculation of the distributions. One method is based upon the assumption of continuous slowing and yields a distribution inversely proportional to the stopping power. An iteration scheme is utilized to include the secondary electron avalanche. In the other method, a governing equation is derived without assuming continuous electron slowing. This equation is solved by a Monte Carlo technique.

Bathke, C. G.↗
NASA NTRS1981

Eigenvector determination by iterative optical methods

Three power algorithms are considered by which an iterative optical processor can be used to compute the eigenvalues and eigenvectors of a matrix. The algorithms are appropriate for three applications: (1) calculating the largest eigenvalue; (2) calculating the eigenvalues in order of decreasingly dominant eigenvalues; and (3) calculating the eigenvector whose eigenvalue is closest to a given value.

Vijaya Kumar, B. V. K.↗
NASA NTRS1976

Voltage profile program for the Kennedy Space Center electric power distribution system

The Kennedy Space Center voltage profile program computes voltages at all busses greater than 1 Kv in the network under various conditions of load. The computation is based upon power flow principles and utilizes a Newton-Raphson iterative load flow algorithm. Power flow conditions throughout the network are also provided. The computer program is designed for both steady state and transient operation. In the steady state mode, automatic tap changing of primary distribution transformers is incorporated. Under transient conditions, such as motor starts etc., it is assumed that tap changing is not accomplished so that transformer secondary voltage is allowed to sag.

Source record↗
NASA NTRS1983

Frequency-multiplexed and pipelined iterative optical systolic array processors

Optical matrix processors using acoustooptic transducers are described, with emphasis on new systolic array architectures using frequency multiplexing in addition to space and time multiplexing. A Kalman filtering application is considered in a case study from which the operations required on such a system can be defined. This also serves as a new and powerful application for iterative optical processors. The importance of pipelining the data flow and the ordering of the operations performed in a specific application of such a system are also noted. Several examples of how to effectively achieve this are included. A new technique for handling bipolar data on such architectures is also described.

Casasent, D.↗
NASA NTRS1974

Solution of an eigenvalue problem for the Laplace operator on a spherical surface

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Walden, H.↗
NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗
NASA NTRS1990

Ideal efficiency of propellers - Theodorsen revisited

Theodorsen's 1948 analog evaluation of the parameters governing the ideal (friction-free) efficiency of propellers is updated and extended by computer. The results are presented both in his format and in a much more convenient one by Kramer that avoids iteration: curves of power coefficient at constant ideal efficiency are plotted vs propeller advance coefficient. The curves for a wide range of blade numbers are collapsed into just three sets (with some approximation) by use of multiple, shifted (and distorted) abscissae scales. Along with an overview of Theodorsen's theory, analytic asymptotic results at low and high advance coefficients are given. At the low end, the disagreement with actuator disk theory is given support and physical interpretation. At the high end, exact agreement is found with the thrust of a slender twisted delta propeller.

Ribner, H. S.↗
NASA NTRS2004

Power Lander for Support of Long-Term Lunar Presence

Emerging industrial base and the consequent sustained manned Lunar presence will require consistent high power capacities. This paper proposes a first iteration design of a flyable electric power platform which could serve as an enabler of Lunar Development and Exploration. It is intended to support a small facility solo or an emerging industrial base as part of a grid. Lunar Missions, Habitats and Facilities stand to benefit from an expected decade of non-stop operation, the economics of scale, Commercial Off-The-Shelf (COTS) availability, standardization of design, and logistical support for Lunar encampments provided by this architecture. The unattended and unmanned vehicle design is to be man- and robotics-serviceable after delivery by current and proposed heavy-lift boosters. Design continuity within a family of systems will improve reliability through "lessons learned'' in the field. Further, various configurations of the proposed scalable architecture will provide reference platforms for the indigenous construction of similar power plant facilities from in-situ Lunar resources (ISRU). The baseline design should be directed towards those materials available on the Moon and expected to be manufacturable on-site within the first decade of operation.

Joyner, Russ↗
NASA NTRS2014

Doppler Lidar System Design via Interdisciplinary Design Concept at NASA Langley Research Center - Part III

Optimized designs of the Navigation Doppler Lidar (NDL) instrument for Autonomous Landing Hazard Avoidance Technology (ALHAT) were accomplished via Interdisciplinary Design Concept (IDEC) at NASA Langley Research Center during the summer of 2013. Three branches in the Engineering Directorate and three students were involved in this joint task through the NASA Langley Aerospace Research Summer Scholars (LARSS) Program. The Laser Remote Sensing Branch (LRSB), Mechanical Systems Branch (MSB), and Structural and Thermal Systems Branch (STSB) were engaged to achieve optimal designs through iterative and interactive collaborative design processes. A preliminary design iteration was able to reduce the power consumption, mass, and footprint by removing redundant components and replacing inefficient components with more efficient ones. A second design iteration reduced volume and mass by replacing bulky components with excessive performance with smaller components custom-designed for the power system. The existing power system was analyzed to rank components in terms of inefficiency, power dissipation, footprint and mass. Design considerations and priorities are compared along with the results of each design iteration. Overall power system improvements are summarized for design implementations.

Barnes, Bruce W.↗
NASA NTRS1978

Analytical study of STOL Aircraft in ground effect. Part 1: Nonplanar, nonlinear wing/jet lifting surface method

A nonlinear, nonplanar three dimensional jet flap analysis, applicable to the ground effect problem, is presented. Lifting surface methodology is developed for a wing with arbitrary planform operating in an inviscid and incompressible fluid. The classical, infintely thin jet flap model is employed to simulate power induced effects. An iterative solution procedure is applied within the analysis to successively approximate the jet shape until a converged solution is obtained which closely satisfies jet and wing boundary conditions. Solution characteristics of the method are discussed and example results are presented for unpowered, basic powered and complex powered configurations. Comparisons between predictions of the present method and experimental measurements indicate that the improvement of the jet with the ground plane is important in the analyses of powered lift systems operating in ground proximity. Further development of the method is suggested in the areas of improved solution convergence, more realistic modeling of jet impingement and calculation efficiency enhancements.

Shollenberger, C. A.↗
NASA NTRS1971

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Gatewood, B. E.↗
NASA NTRS1988

Analysis of spectra using correlation functions

A novel method is presented for the quantitative analysis of spectra based on the properties of the cross correlation between a real spectrum and either a numerical synthesis or laboratory simulation. A new goodness-of-fit criterion called the heteromorphic coefficient H is proposed that has the property of being zero when a fit is achieved and varying smoothly through zero as the iteration proceeds, providing a powerful tool for automatic or near-automatic analysis. It is also shown that H can be rendered substantially noise-immune, permitting the analysis of very weak spectra well below the apparent noise level and, as a byproduct, providing Doppler shift and radial velocity information with excellent precision. The technique is in regular use in the Atmospheric Trace Molecule Spectroscopy (ATMOS) project and operates in an interactive, realtime computing environment with turn-around times of a few seconds or less.

Beer, Reinhard↗
NASA NTRSDate not supplied

Microbial Optical Data Processing: A Key Step in the Metabolic Assessment of Lunar Explorer Instrument for Space Biology Applications (LEIA) and Biosentinel’s Payload Data

The BioSensor payload platform on BioSentinel and LEIA autonomously collects optical data from microbial model organisms in liquid culture. The BioSensor is designed to monitor metabolic activity using absorbance measurements of cell density and alamarBlue, a readily available colorimetric redox indicator dye. BioSentinel, a pioneering NASA CubeSat, uses yeast to study deep space radiation. LEIA investigates radiation and lunar gravity response. The experimental setup includes 16 wells equipped with three LEDs (570, 630, and 850 nm) and their corresponding photodetectors. One well is a calibration control without biology while the rest have desiccated cultures. Autonomous rehydration initiates the experiment. Data from the BioSensor are received from the flight and ground units, enabling comparison to uncover location-based metabolic rate variations. This study presents a Python Jupyter notebook developed for efficient data processing of multiple CSV files containing date and time columns, temperature, and well illumination data. It offers a user-friendly interface while maintaining computational power, automatically recognizing and iteratively processing data files in a user-input path. A Hampel filter with a short window eliminates outlier artifacts from sensor dropout. Because absorbance is a relative measurement, conversion from raw illumination requires defining a “blank” value, so the first data points are averaged to provide the necessary denominator. A cube-root function correction mitigates undesired drift caused by air pockets during the fluidic card filling phase, maintaining optical path length consistency. Beer-Lambert's law is applied to further convert absorbance values to cell and dye form concentrations, the desired science parameters. The processed data are saved and visualized as SVG plots. Future plans include extracting specific science parameters from the processed data like growth rate and metabolic rate, and identification of features corresponding to metabolic and phenotypic shifts such as starvation, shifts from aerobic to anaerobic growth, and osmotic stresses.

Space biology↗