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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 NTRS1988

Robust eigenvalue/eigenvector selection in linear state feedback systems

Design procedures are developed to select both eigenvalues and eigenvectors to improve system robustness. A robustness metric based on the determinant of the normalized eigenvector matrix defined. It is shown that this metric significantly speeds up the convergence of robust eigenvector solutions close to the optimal. A procedure to blend multiple inputs to improve achievable system robustness in the lower dimensional pseudo control space has also been derived.

Srinathkumar, S.↗
NASA NTRS1989

Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria

A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.

Rew, D. W.↗
NASA NTRS1991

A recent case study in system identification

Results of a recent study of a ten-bay truss structure at the NASA Langley Research Center are reported. First, the conditioning of complex eigenvectors derived by the ERA method is discussed. Results of parameter estimation using the SSID (Structural System Identification) code are then presented. Based on the results of the study, it is concluded that (1) parameter estimation based on modal data should include eigenvectors as well as eigenvalues; (2) the eigenvectors should be orthogonalized when orthogonality is poor due to closely spaced modes; and (3) the parameters used in the estimation should enable the model to match the data.

Hasselman, T. K.↗
NASA NTRS1991

Monte Carlo simulation of errors in the anisotropy of magnetic susceptibility - A second-rank symmetric tensor

Monte Carlo perturbations of synthetic tensors to evaluate the Hext/Jelinek elliptical confidence regions for anisotropy of magnetic susceptibility (AMS) eigenvectors are used. When the perturbations are 33 percent of the minimum anisotropy, both the shapes and probability densities of the resulting eigenvector distributions agree with the elliptical distributions predicted by the Hext/Jelinek equations. When the perturbation size is increased to 100 percent of the minimum eigenvalue difference, the major axis of the 95 percent confidence ellipse underestimates the observed eigenvector dispersion by about 10 deg. The observed distributions of the principal susceptibilities (eigenvalues) are close to being normal, with standard errors that agree well with the calculated Hext/Jelinek errors. The Hext/Jelinek ellipses are also able to describe the AMS dispersions due to instrumental noise and provide reasonable limits for the AMS dispersions observed in two Hawaiian basaltic dikes. It is concluded that the Hext/Jelinek method provides a satisfactory description of the errors in AMS data and should be a standard part of any AMS data analysis.

Lienert, Barry R.↗
NASA NTRS1988

Eigenvalue/Eigenvector derivatives for SAVI Gimbalflex nonlinear transient response analysis

An eigenvector expansion method is utilized to predict eigenvalue and eigenvector derivatives due to geometric reconfiguration of a Gimbalflex fine-pointing/vibration isolation system called SAVI (Space Active Vibration Isolation). The eigenvector expansion method used is a modification of the classical method and allows for rigid body roots. Using the resulting modal derivatives, free-free nonlinear equations of motion are developed with Lagrange's Method. These equations represent a nonlinear plant model to be used in conjunction with a control system transient response simulation.

Orr, M. F., Jr.↗
NASA NTRS1992

Evolution of the shock front and turbulence structures in the shock/turbulence interaction

The interaction of a weak shock front with isotropic turbulence has been investigated using Direct Numerical Simulation (DNS). Two problems were considered: the ability of the field equation (the equation for a propagating surface) to model the shock; and a quantitative study of the evolution of turbulence structure using the database generated by Lee et al. Field equation model predictions for front shape have been compared with DNS results; good agreement is found for shock wave interaction with 2D turbulence and for a single steady vorticity wave. In the interaction of 3D isotropic turbulence with a normal shock, strong alignment of vorticity with the intermediate eigenvector of the rate of strain tensor (S(sup *)(sub ij) = S(sub ij) - (1/3)(delta(sub ij))(S(sub kk))) is seen to develop upstream of the shock and to be further amplified on passage through the shock. Vorticity tends to align at 90 deg to the largest eigenvector, but there is no preferred alignment with the smallest eigenvector. Upstream of the shock, the alignments continue to develop even after the velocity derivative skewness saturates. There is a significant tendency, which increases with time throughout the computational domain, for velocity to align with vorticity. The alignment between velocity and vorticity is strongest in eddy regions and weakest in convergence regions.

Kevlahan, N.↗
NASA NTRS1994

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Kenny, Sean P.↗
NASA NTRS1996

REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination

In order to find the attitude of a spacecraft with respect to a reference coordinate system, vector measurements are taken. The vectors are pairs of measurements of the same generalized vector, taken in the spacecraft body coordinates, as well as in the reference coordinate system. We are interested in finding the best estimate of the transformation between these coordinate system.s The algorithm called QUEST yields that estimate where attitude is expressed by a quarternion. Quest is an efficient algorithm which provides a least squares fit of the quaternion of rotation to the vector measurements. Quest however, is a single time point (single frame) batch algorithm, thus measurements that were taken at previous time points are discarded. The algorithm presented in this work provides a recursive routine which considers all past measurements. The algorithm is based on on the fact that the, so called, K matrix, one of whose eigenvectors is the sought quaternion, is linerly related to the measured pairs, and on the ability to propagate K. The extraction of the appropriate eigenvector is done according to the classical QUEST algorithm. This stage, however, can be eliminated, and the computation simplified, if a standard eigenvalue-eigenvector solver algorithm is used. The development of the recursive algorithm is presented and illustrated via a numerical example.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1993

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

Barnard, Stephen T.↗
NASA NTRS1998

Using Solar Radiation Pressure to Control L2 Orbits

The main perturbations at the Sun-Earth Lagrange points L1 and L2 are from solar radiation pressure (SRP), the Moon and the planets. Traditional approaches to trajectory design for Lagrange-point orbits use maneuvers every few months to correct for these perturbations. The gravitational effects of the Moon and the planets are small and periodic. However, they cannot be neglected because small perturbations in the direction of the unstable eigenvector are enough to cause exponential growth within a few months. The main effect of a constant SRP is to shift the center of the orbit by a small distance. For spacecraft with large sun-shields like the Microwave Anisotropy Probe (MAP) and the Next Generation Space Telescope (NGST), the SRP effect is larger than all other perturbations and depends mostly on spacecraft attitude. Small variations in the spacecraft attitude are large enough to excite or control the exponential eigenvector. A closed-loop linear controller based on the SRP variations would eliminate one of the largest errors to the orbit and provide a continuous acceleration for use in controlling other disturbances. It is possible to design reference trajectories that account for the periodic lunar and planetary perturbations and still satisfy mission requirements. When such trajectories are used the acceleration required to control the unstable eigenvector is well within the capabilities of a continuous linear controller. Initial estimates show that by using attitude control it should be possible to minimize and even eliminate thruster maneuvers for station keeping.

Tene, Noam↗
NASA NTRS2001

Characterizing Aeroelastic Systems Using Eigenanalysis, Explicitly Retaining The Aerodynamic Degrees of Freedom

Discrete time aeroelastic models with explicitly retained aerodynamic modes have been generated employing a time marching vortex lattice aerodynamic model. This paper presents analytical results from eigenanalysis of these models. The potential of these models to calculate the behavior of modes that represent damped system motion (noncritical modes) in addition to the simple harmonic modes is explored. A typical section with only structural freedom in pitch is examined. The eigenvalues are examined and compared to experimental data. Issues regarding the convergence of the solution with regard to refining the aerodynamic discretization are investigated. Eigenvector behavior is examined; the eigenvector associated with a particular eigenvalue can be viewed as the set of modal participation factors for that particular mode. For the present formulation of the equations of motion, the vorticity for each aerodynamic element appears explicitly as an element of each eigenvector in addition to the structural dynamic generalized coordinates. Thus, modal participation of the aerodynamic degrees of freedom can be assessed in M addition to participation of structural degrees of freedom.

Heeg, Jennifer↗
NASA NTRS2001

Principal Components Analysis of Triaxial Vibration Data From Helicopter Transmissions

Research on the nature of the vibration data collected from helicopter transmissions during flight experiments has led to several crucial observations believed to be responsible for the high rates of false alarms and missed detections in aircraft vibration monitoring systems. This work focuses on one such finding, namely, the need to consider additional sources of information about system vibrations. In this light, helicopter transmission vibration data, collected using triaxial accelerometers, were explored in three different directions, analyzed for content, and then combined using Principal Components Analysis (PCA) to analyze changes in directionality. In this paper, the PCA transformation is applied to 176 test conditions/data sets collected from an OH58C helicopter to derive the overall experiment-wide covariance matrix and its principal eigenvectors. The experiment-wide eigenvectors. are then projected onto the individual test conditions to evaluate changes and similarities in their directionality based on the various experimental factors. The paper will present the foundations of the proposed approach, addressing the question of whether experiment-wide eigenvectors accurately model the vibration modes in individual test conditions. The results will further determine the value of using directionality and triaxial accelerometers for vibration monitoring and anomaly detection.

Tumer, Irem Y.↗
NASA NTRS2005

The Application of Infrared Thermographic Inspection Techniques to the Space Shuttle Thermal Protection System

The Nondestructive Evaluation Sciences Branch at NASA s Langley Research Center has been actively involved in the development of thermographic inspection techniques for more than 15 years. Since the Space Shuttle Columbia accident, NASA has focused on the improvement of advanced NDE techniques for the Reinforced Carbon-Carbon (RCC) panels that comprise the orbiter s wing leading edge. Various nondestructive inspection techniques have been used in the examination of the RCC, but thermography has emerged as an effective inspection alternative to more traditional methods. Thermography is a non-contact inspection method as compared to ultrasonic techniques which typically require the use of a coupling medium between the transducer and material. Like radiographic techniques, thermography can be used to inspect large areas, but has the advantage of minimal safety concerns and the ability for single-sided measurements. Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. A typical implementation of PCA is when the eigenvectors are generated from the data set being analyzed. Although it is a powerful tool for enhancing the visibility of defects in thermal data, PCA can be computationally intense and time consuming when applied to the large data sets typical in thermography. Additionally, PCA can experience problems when very large defects are present (defects that dominate the field-of-view), since the calculation of the eigenvectors is now governed by the presence of the defect, not the "good" material. To increase the processing speed and to minimize the negative effects of large defects, an alternative method of PCA is being pursued where a fixed set of eigenvectors, generated from an analytic model of the thermal response of the material under examination, is used to process the thermal data from the RCC materials. Details of a one-dimensional analytic model and a two-dimensional finite-element model will be presented. An overview of the PCA process as well as a quantitative signal-to-noise comparison of the results of performing both embodiments of PCA on thermographic data from various RCC specimens will be shown. Finally, a number of different applications of this technology to various RCC components will be presented.

Cramer, K. E.↗
NASA NTRS2012

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Orr, Jeb S.↗
NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗
NASA NTRS2019

Matrix Exponential in C/C++ Version of Vector Radiative Transfer Code IPOL

We use only left eigenvectors to evaluate the matrix exponential in the method of discrete ordinates for the vector radiative transfer equation, which neglects circular polarization, in a plane-parallel atmosphere. This is contrary to a common practice of using the right eigenvectors to evaluate the matrix exponential combined with the left eigenvectors to avoid the inversion of the matrix of the right ones. Two numerical tests for Rayleigh and Aerosol scattering confirm our idea. For better explanation of our approach and for independent crosscheck of our results, we distribute an example in C/C++.

Sergey Korkin↗
DOE OSTI2025

Toward shell model interactions with credible uncertainties

Background: The nuclear shell model is a powerful framework for predicting nuclear structure observables, but relies on interaction matrix elements fit to experimental data as its inputs. Extending the shell model's applicability, particularly toward dripline nuclei, requires efficient fitting methods and credible uncertainty quantification. Traditional approaches face computational challenges and may underestimate uncertainties. Purpose: We develop and test a framework combining eigenvector continuation and Markov chain Monte Carlo to efficiently fit shell model interaction matrix elements and quantify their uncertainties. Methods: Eigenvector continuation is used to emulate shell model calculations, reducing computational costs. The emulator enables Markov chain Monte Carlo sampling to optimize interaction matrix elements and rigorously assess parametric uncertainties. Here, the framework is benchmarked using the USDB interaction in the 𝑠⁢𝑑 shell. Results: The emulator reproduces the USDB interaction with negligible error, validating its use in shell model fitting applications. However, we find that to obtain credible predictive intervals, the model defect of the shell model itself, rather than experimental or emulator error, must be taken into account in order to obtain credible uncertainties. Conclusions: The proposed framework provides an efficient and rigorous approach for fitting shell model interactions and quantifying uncertainties. Further, the normality assumption used in the past appears sufficient to describe the distribution of interaction matrix elements. However, it is crucial to account for model correlations to avoid underestimating uncertainties.

Nuclear forces↗
DOE OSTI2026

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗