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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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NASA NTRS1990

Applications of truncated QR methods to sinusoidal frequency estimation

Three truncated QR methods are proposed for sinusoidal frequency estimation: (1) truncated QR without column pivoting (TQR), (2) truncated QR with preordered columns, and (3) truncated QR with column pivoting. It is demonstrated that the benefit of truncated SVD for high frequency resolution is achievable under the truncated QR approach with much lower computational cost. Other attractive features of the proposed methods include the ease of updating, which is difficult for the SVD method, and numerical stability. TQR methods thus offer efficient ways to identify sinusoidals closely clustered in frequencies under stationary and nonstationary conditions.

Hsieh, S. F.↗
NASA NTRS1992

Large-scale sparse singular value computations

Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.

Berry, Michael W.↗
NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗
NASA NTRS1994

The Uranian aurora and its relationship to the magnetosphere

About 32 h of Voyager Ultraviolet Spectrometer (UVS) observations of Uranus H2 band airglow emission (875 less than or equal to lambda less than or equal to 1115 A) have been analyzed using the singular value decomposition (SVD) approach to inversion, producing an intensity map showing aurora at both magnetic poles. An H Lyman alpha aurora may also be present but is difficult to separate from scattered solar and local interstellar medium components. SVD analysis of variance shows that the intensity estimate is significantly larger than the error estimate over both Uranographic poles and part of the equatorial region, fortuitously including both magnetic polar regions. The Goddard Space Flight Center Q(sub 3) magnetic field model correctly predicts that the aurora should be larger in area and emit more power at the weaker N magnetic pole than at the stronger S magnetic pole. However, the auroral emissions are quite localized in magnetic longitude and so do not form complete auroral ovals. The brightest auroral emission at each magnetic pole is confined to a range of approximately 90 deg of magnetic longitude centered on the magnetotail direction, at moderate magnetic L parameter (5 less than or equal to L less than or equal to 10), but some emission at each pole is distributed over a range of more than 180 deg of longitude. The magnetic longitudes of the aurora are completely inconsistent with the 'windshield wiper' effect for either ions or electrons, indicating that some other effect, such as rapid depletion of the population of precipitating particles of highly localized strong pitch-angle diffusion, may be acting to localize emission. The low apparent L of the precipitating particles indicates that their energies may be less than or equal to 10 keV. Hence magnetospheric convection is likely to be important, and thus particles exciting the aurora may not remain on constant L shells. The precipitating particles may be a relatively low-energy population at high L that is heated to aurora-exciting energy by adiabatic compression during convection to low L. We estimate that the total auroral power output at H Lyman alpha and shorter wavelengths is about 3 x 10(exp 9) to 7 x 10(exp 9) W, requiring about 10 times that much power for excitation.

Herbert, Floyd↗
NASA NTRS1996

A Feasibility Study on a Parallel Mechanism for Examining the Space Shuttle Orbiter Payload Bay Radiators

The goal of the project was to develop the necessary analysis tools for a feasibility study of a cable suspended robot system for examining the space shuttle orbiter payload bay radiators These tools were developed to address design issues such as workspace size, tension requirements on the cable, the necessary accuracy and resolution requirements and the stiffness and movement requirements of the system. This report describes the mathematical models for studying the inverse kinematics, statics, and stiffness of the robot. Each model is described by a matrix. The manipulator Jacobian was also related to the stiffness matrix, which characterized the stiffness of the system. Analysis tools were then developed based on the singular value decomposition (SVD) of the corresponding matrices. It was demonstrated how the SVD can be used to quantify the robot's performance and to provide insight into different design issues.

Roberts, Rodney G.↗
NASA NTRS1999

East Asian Summer Monsoon Rainfall: A Historical Perspective of the 1998 Flood over Yangtze River

One of the main factors that might have caused the disastrous flood in China during 1998 summer is long-term variations that include a trend indicating increasing monsoon rainfall over the Yangtze River Valley. China's 160-station monthly rainfall anomaly for the summers of 1955-98 is analyzed for exploring such long-term variations. Singular value decomposition (SVD) between the summer rainfall and the global sea surface temperature (SST) anomalies reveals that the rainfall over Yangtze River Valley is closely related to global and regional SST variabilities at both interannual and interdecadal timescales. SVD1 mode links the above normal rainfall condition in central China to an El Nino-like SSTA distribution, varying on interannual timescale modified by a trend during the period. SVD3 mode links positive rainfall anomaly in Yangtze River Valley to the warm SST anomaly in the subtropical western Pacific, varying on interannual timescales modified by interdecadal timescales. This link tends to be stronger when the Nino3 area becomes colder and the western subtropical Pacific becomes warmer. The 1998 summer is a transition season when the 1997/98 El Nino event was in its decaying phase, and the SST in the Nino3 area emerged below normal anomaly while the subtropical western Pacific SST above normal. Thus, the first and third SVD modes become dominant in 1998 summer, favoring more Asian summer monsoon rainfall over the Yangtze River Valley.

Weng, H.-Y.↗
NASA NTRS1999

How to Estimate Attitude from Vector Observations

The most robust estimators minimizing Wahba's loss function are Davenport's q method and the Singular Value Decomposition (SVD) method. The q method is faster than the SVD method with three or more measurements. The other algorithms are less robust since they solve the characteristic polynomial equation to find the maximum eigenvalue of Davenport's K matrix. They are only preferable when speed or processor power is an important consideration. Of these, Fast Optimal Attitude Matrix (FOAM) is the most robust and faster than the q method. Robustness is only an issue for measurements with widely differing accuracies, so the fastest algorithms, Quaternion ESTimator (QUEST), EStimator of the Optimal Quaternion (ESOQ), and ESOQ2, are well suited to star sensor applications.

Markley, F. Landis↗
NASA NTRS1995

Model-Based Obstacle Detention From Image Sequences

This paper proposes a method for detecting obstacles on a runway from monocular image sequences. The surface of the runway is modeled as a plane and the model flow field corresponding to the runway is described by 8 coefficients. The set of 8 coefficients describing the initial model flow field is given by the data from Inertial Navigation System (INS). The uncertainties of this initial model flow field are estimated and used to obtain the accurate model flow field. The residual flow field after warping images by the accurate model flow field is computed by solving over determined gradient-based optical flow equations using a singular value decomposition (SVD). This SVD gives us a new insight of the uncertainties inherent in the optical flow computation. Those pixels with large residual flow vectors are considered as obstacles. Experimental results for two real image sequences are presented.

Sull, Sanghoon↗
NASA NTRS2003

Development of an Efficient Binaural Simulation for the Analysis of Structural Acoustic Data

Applying binaural simulation techniques to structural acoustic data can be very computationally intensive as the number of discrete noise sources can be very large. Typically, Head Related Transfer Functions (HRTFs) are used to individually filter the signals from each of the sources in the acoustic field. Therefore, creating a binaural simulation implies the use of potentially hundreds of real time filters. This paper details two methods of reducing the number of real-time computations required by: (i) using the singular value decomposition (SVD) to reduce the complexity of the HRTFs by breaking them into dominant singular values and vectors and (ii) by using equivalent source reduction (ESR) to reduce the number of sources to be analyzed in real-time by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. The ESR and SVD reduction methods can be combined to provide an estimated computation time reduction of 99.4% for the structural acoustic data tested. In addition, preliminary tests have shown that there is a 97% correlation between the results of the combined reduction methods and the results found with the current binaural simulation techniques

Johnson, Marty E.↗
NASA NTRS2007

Multi-channel System for Beat to Beat QT Interval Variability and its Use in Screening for Coronary Artery Disease and Cardiomyopathy

We investigated the ability of beat-to-beat QT interval variability (QTV) and related parameters to differentiate healthy individuals from patients with obstructive coronary artery disease (CAD) and cardiomyopathy (CM). For this purpose we developed a PC-based ECG software program that in real time, acquires, analyzes and displays QTV in each of the eight independent channels that constitute the 12-lead conventional ECG. The system also analyzes and displays the QTV from QT interval signals that are derived from multiple channels and from singular value decomposition (SVD) to substantially reduce the effect of noise and other artifacts on the QTV results. It also provides other useful SVD-related parameters such as the normalized 3-dimensional volume of the T wave (nTV) = 100*(rho(sub 2)*rho(sub 3)rho(sub 1^2). Advanced high-fidelity 12-lead ECG tests (approx. 5-min supine) were first performed on a "training set" of 99 individuals: 33 with ischemic or dilated CM and low ejection fraction (EF less than 40%); 33 with catheterization-proven obstructive CAD but normal EF; and 33 age-/gender-matched healthy controls. All QTV parameters that were studied for their accuracy in detecting CM and CAD significantly differentiated both CM and CAD from controls (p less than 0.0001). Retrospective areas under the ROC curve (AUC) of SDNN-QTV, rmsSD-QTV, and QTV Index (QTVI) for CM vs. controls in the lead V5 were 0.85, 0.90, and 0.99, respectively, and those for CAD vs. controls in the lead II were 0.82, 0.82, and 0.89. Other advanced ECG parameters, such as HFQRS RAZ score, LF Lomb of RRV or QRS-T angle, differentiated both CM and CAD from controls less significantly, with the respective AUC values of 0.89, 0.88 and 0.98 for CM vs. controls, and 0.73, 0.71 and 0.80 for CAD vs. controls. QTV parameters (especially QTVI, which is QTV as indexed to RRV) were, diagnostically speaking, amongst the best performing of the advanced ECG techniques studied thus far.

Starc, V.↗
NASA NTRS2007

Construction and Use of Resting 12-Lead High Fidelity ECG "SuperScores" in Screening for Heart Disease

We investigated the accuracy of several conventional and advanced resting ECG parameters for identifying obstructive coronary artery disease (CAD) and cardiomyopathy (CM). Advanced high-fidelity 12-lead ECG tests (approx. 5-min supine) were first performed on a "training set" of 99 individuals: 33 with ischemic or dilated CM and low ejection fraction (EF less than 40%); 33 with catheterization-proven obstructive CAD but normal EF; and 33 age-/gender-matched healthy controls. Multiple conventional and advanced ECG parameters were studied for their individual and combined retrospective accuracies in detecting underlying disease, the advanced parameters falling within the following categories: 1) Signal averaged ECG, including 12-lead high frequency QRS (150-250 Hz) plus multiple filtered and unfiltered parameters from the derived Frank leads; 2) 12-lead P, QRS and T-wave morphology via singular value decomposition (SVD) plus signal averaging; 3) Multichannel (12-lead, derived Frank lead, SVD lead) beat-to-beat QT interval variability; 4) Spatial ventricular gradient (and gradient component) variability; and 5) Heart rate variability. Several multiparameter ECG SuperScores were derivable, using stepwise and then generalized additive logistic modeling, that each had 100% retrospective accuracy in detecting underlying CM or CAD. The performance of these same SuperScores was then prospectively evaluated using a test set of another 120 individuals (40 new individuals in each of the CM, CAD and control groups, respectively). All 12-lead ECG SuperScores retrospectively generated for CM continued to perform well in prospectively identifying CM (i.e., areas under the ROC curve greater than 0.95), with one such score (containing just 4 components) maintaining 100% prospective accuracy. SuperScores retrospectively generated for CAD performed somewhat less accurately, with prospective areas under the ROC curve typically in the 0.90-0.95 range. We conclude that resting 12-lead high-fidelity ECG employing and combining the results of several advanced ECG software techniques shows great promise as a rapid and inexpensive tool for screening of heart disease.

Schlegel, T. T.↗
NASA NTRS2009

Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

Gurgiolo, Chris↗
NASA NTRS2016

Erasing the Milky Way: New Cleaning Technique Applied to GBT Intensity Mapping Data

We present the first application of a new foreground removal pipeline to the current leading HI intensity mapping dataset, obtained by the Green Bank Telescope (GBT). We study the 15- and 1-h field data of the GBT observations previously presented in Masui et al. (2013) and Switzer et al. (2013), covering about 41 square degrees at 0.6 less than z is less than 1.0, for which cross-correlations may be measured with the galaxy distribution of the WiggleZ Dark Energy Survey. In the presented pipeline, we subtract the Galactic foreground continuum and the point source contamination using an independent component analysis technique (fastica), and develop a Fourier-based optimal estimator to compute the temperature power spectrum of the intensity maps and cross-correlation with the galaxy survey data. We show that fastica is a reliable tool to subtract diffuse and point-source emission through the non-Gaussian nature of their probability distributions. The temperature power spectra of the intensity maps is dominated by instrumental noise on small scales which fastica, as a conservative sub-traction technique of non-Gaussian signals, can not mitigate. However, we determine similar GBT-WiggleZ cross-correlation measurements to those obtained by the Singular Value Decomposition (SVD) method, and confirm that foreground subtraction with fastica is robust against 21cm signal loss, as seen by the converged amplitude of these cross-correlation measurements. We conclude that SVD and fastica are complementary methods to investigate the foregrounds and noise systematics present in intensity mapping datasets.

Wolz, L.↗
NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper discusses the Dynamic Mode Decomposition (DMD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected with four Phantom high-speed cameras at a constant sample frequency in the Ascent Transient Aerodynamics Test (ATAT) of the Space Launch System (SLS) Block 1 cargo vehicle with the Unitary Plan Wind Tunnel (UPWT) 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD). For the data with zero mean, the DMD is equivalent to the Discrete Fourier Transform (DFT). Since the uPSP is mainly used to determine the unsteady property of the aerodynamic flow, the DMD of the uPSP measurements is implemented in two steps: (1) subtract the mean value from the uPSP measurement; (2) apply the Fast Fourier Transform (FFT) on the resulting data with zero mean. The DMD of the uPSP measurements with FFT has two advantages: (1) the FFT algorithm is well known for its computational efficiency, therefore, compared to the SVD-based DMD algorithm, the DMD with FFT reduces the computation time; (2) the DMD with FFT can be easily implemented in parallel processing. The DMD outputs were generated with the execution in parallel of a code in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, on the NASA Pleiades supercomputer. In this paper, the results of DMD of the uPSP measurements in the tests of Mach sweep runs of the SLS ATAT are presented, and the effectiveness of the DMD of the uPSP measurements in the diagnosis of the unsteady, aerodynamic phenomena is demonstrated. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding for this research was provided by the NASA Aeroscience Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
NASA NTRS1984

Acoustooptic linear algebra processors - Architectures, algorithms, and applications

Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.

Casasent, D.↗
NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗
NASA NTRS1988

Statistical analysis of effective singular values in matrix rank determination

A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

Konstantinides, Konstantinos↗
NASA NTRS1989

Constraint elimination in dynamical systems

Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

Singh, R. P.↗