Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “eigenvalue analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
NASA NTRS1984

Rotordynamic Analysis of the SSME Turbopumps Using Reduced Models

Alternative methods for the rotor-dynamic and sensitivity analysis of large rotor systems are examined. The methods are assessed for their ability to utilize accurate models of reduced size along with effective procedures for describing the dynamic behavior of the systems. Frequency response-based techniques are developed for determining the steady state response to imbalance of the space shuttle main engine (SSME) turbopumps and the related eigenvalue problem. The rotor and housing are represented by reduced receptances associated with their coupling points. The housing may be described by all of its normal modes within a frequency range of interest. The effects of truncated higher and lower modes are accounted for in an approximate manner. A procedure is described for determining the sensitivity of the coupling forces to changes in the coupling elements and rotor speed of the turbopump systems. In addition, an eigenvalue sensitivity analysis technique is adopted for application to the systems. Computer programs were developed for the numerical implementation of the impedance and eigenvalue sensitivity formulated in this study.

Noah, S. T.↗
NASA NTRS1988

Development of an unsteady wake theory appropriate for aeroelastic analyses of rotors in hover and forward flight

The purpose of this research is the development of an unsteady aerodynamic model for rotors such that it can be used in conventional aeroelastic analysis (e.g., eigenvalue determination and control system design). For this to happen, the model must be in a state-space formulation such that the states of the flow can be defined, calculated and identified as part of the analysis. The fluid mechanics of the problem is given by a closed-form inversion of an acceleration potential. The result is a set of first-order differential equations in time for the unknown flow coefficients. These equations are hierarchical in the sense that they may be truncated at any number of radial or azimuthal terms.

Peters, David A.↗
NASA NTRS1981

Effects of displacement and rate saturation on the control of statically unstable aircraft

Methodologies are presented for the analysis and design of stability augmentation control laws for aircraft in which 'hard' displacement and rate limiting are significant. Candidate control laws are derived using the linear-quadratic (LQ) regulator. Analytical and computational estimates of the stability limits imposed by control saturation are presented using state trajectories with control limiting, as well as describing functions and eigenvalue computation. Analysis also includes an investigation of the interaction of the state-space saturation and stability boundaries for various choices of LQ weighting matrices. For minimum-energy control, the saturation and stability boundaries are shown to be parallel. In this case, there is a direct relation between the solution to the matrix Riccati equation and the aircraft's open-loop dynamics.

Hanson, G. D.↗
DOE OSTI2021

Visual Tool for Assessing Stability of DER Configurations on Three-Phase Radial Networks

Here, we present a method and tool for evaluating the placement of Distributed Energy Resources (DER) on distribution circuits in order to control voltages and power flows. Our previous work described Phasor-Based Control (PBC), a novel control framework where DERs inject real and reactive power to track voltage magnitude and phase angle targets. Here, we employ linearized power flow equations and integral controllers to develop a linear state space model for PBC acting on a three-phase unbalanced network. We use this model to evaluate whether a given inverter-based DER configuration admits a stable set of controller gains, which cannot be done by analyzing controllability nor by using the Lyapunov equation. Instead, we sample over a parameter space to identify a stable set of controller gains. Our stability analysis requires only a line impedance model and does not entail simulating the system or solving an optimization problem. We incorporate this assessment into a publicly available visualization tool and demonstrate three processes for evaluating many control configurations on the IEEE 123-node test feeder (123NF).

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

The Cause of Insufficient Damping in Phase-Locked-Loop and Its Influence

Phase-locked loop (PLL) is a critical component that synchronizes grid-following (GFL) inverter-based resources (IBR) to the grid. Insufficient damping in PLL has been identified as a cause associated with real-world weak grid stability issues. This paper reveals that the second-order low-pass filter deployed in a sophisticated PLL structure can have negative influence on damping performance and lead to system instability when the grid is weak and power generation is low. Improving the PLL damping is illustrated as one of the mitigation approaches. The dynamic study is carried out in electromagnetic transient (EMT) simulation environment. In addition to EMT demonstration, a simplified analytical model of PLL is developed to represent a PLL with the sophisticated structure. The resulting overall analytical model of the entire system is then used for eigenvalue- based analysis to illustrate the influence of PLL on dynamic modes.

Wang, Zhengyu↗
DOE OSTI2025

Characterization of Impedance and Stability for Doubly-Fed Induction Generator Based on Voltage-Modulated Direct Power Control

Voltage-modulated direct power control (VM-DPC) applied to the doubly-fed induction generator (DFIG) offers superior steady-state and transient performance but remains underexplored for suppressing wideband oscillations. Here, this article proposes a comprehensive impedance for the VM-DPC-based DFIG, analyzing its impedance characteristics and stability mechanisms compared with the DFIG based on vector-oriented control (VOC). The unified power transfer function is defined for DFIGs employing VM-DPC or VOC to ensure consistent comparison benchmarks. The comprehensive impedance of VM-DPC-based DFIG, incorporating mechanical and grid-side converter (GSC) dynamics, is derived using complex vector modeling in the αβ -frame. Furthermore, the influence of VM-DPC parameters and grid strength on the stability of grid-connected DFIG systems is assessed through eigenvalue trajectory analysis. Impedance analysis reveals the significant contributions of mechanical and GSC dynamics to DFIG impedance, as well as the narrower frequency range of negative resistance in the VM-DPC-based DFIG compared to the VOC-based DFIG. Stability analysis identifies the VM-DPC parameters of the rotor-side converter as dominant factors affecting system stability and confirms that the VM-DPC-based DFIG achieves better stability under weak grid conditions than its VOC-based counterpart. These findings are validated through simulations and experiments.

42 ENGINEERING↗
DOE OSTI2023

Insights on the Effects of Magnetic Forces on the Efficiency of Vibration Energy Harvesting Absorbers in Controlling Dynamical Systems

This study investigates the effects of magnetic constraints on a piezoelectric energy harvesting absorber while simultaneously controlling a primary structure and harnessing energy. An accurate forcing representation of the magnetic force is investigated and developed. A reduced-order model is derived using the Euler–Lagrange principle, and the impact of the magnetic force is evaluated on the absorber’s static position and coupled natural frequency of the energy harvesting absorber and the coupled primary absorber system. The results show that attractive magnet configurations cannot improve the system substantially before pull-in occurs. A rigorous eigenvalue problem analysis is performed on the absorber’s substrate thickness and tip mass to effectively design an energy harvesting absorber for multiple initial gap sizes for the repulsive configurations. Then, the effects of the forcing amplitude on the primary structure absorber are studied and characterized by determining an effective design of the system for a simultaneous reduction in the primary structure’s motion and improvement in the harvester’s efficiency.

42 ENGINEERING↗
DOE OSTI2022

A Nonlocal Magneto-curvature Instability in a Differentially Rotating Disk

A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1983

Enhancement of the CAVE computer code

The computer code CAVE (Conduction Analysis via Eigenvalues) is a convenient and efficient computer code for predicting two dimensional temperature histories within thermal protection systems for hypersonic vehicles. The capabilities of CAVE were enhanced by incorporation of the following features into the code: real gas effects in the aerodynamic heating predictions, geometry and aerodynamic heating package for analyses of cone shaped bodies, input option to change from laminar to turbulent heating predictions on leading edges, modification to account for reduction in adiabatic wall temperature with increase in leading sweep, geometry package for two dimensional scramjet engine sidewall, with an option for heat transfer to external and internal surfaces, print out modification to provide tables of select temperatures for plotting and storage, and modifications to the radiation calculation procedure to eliminate temperature oscillations induced by high heating rates. These new features are described.

Rathjen, K. A.↗
NASA NTRS1988

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Lerch, F. J.↗
NASA NTRS1989

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the GEM-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient by coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment.

Lerch, F. J.↗
NASA NTRS1991

An improved error assessment for the GEM-T1 gravitational model

Several tests have been designed to estimate the correct error variances for the GEM-T1 gravitational solution that was derived exclusively from satellite tracking data. The basic method uses both independent and dependent subset data solutions and produces a coefficient-by-coefficient estimate of the model uncertainties. The GEM-T1 errors have been further analyzed using a method based on eigenvalue-eigenvector analysis, which calibrates the entire covariance matrix. Dependent satellite data sets and independent altimetric, resonant satellite, and surface gravity data sets all confirm essentially the same error assessment. The calibration test results yield very stable calibration factors, which vary only by approximately 10 percent over the range of tests performed. Based on these calibrated error estimates, GEM-T1 is a significantly improved solution, which to degree and order 8 is twice as accurate as earlier satellite derived models like GEM-L2. Also, by being complete to degree and order 36, GEM-T1 is more complete and has significantly reduced aliasing effects that were present in previous models.

Lerch, F. J.↗
NASA NTRS1994

Structural design criteria for filament-wound composite shells

Advanced composite cylinders, manufactured by filament winding, provide a cost effective solution to many present structural applications; however, the compressive performance of filament-wound cylinders is lower than comparable shells fabricated from unidirectional tape. The objective of this study was to determine the cause of this reduction in thin filament-wound cylinders by relating the manufacturing procedures to the quality of the cylinder and to its compressive performance. The experiments on cylinder buckling were complemented by eigenvalue buckling analysis using a detailed geometric model in a finite element analysis. The applicability of classical buckling analyses was also investigated as a design tool.

Hahn, H. T.↗
DOE OSTI2023

Beyond Generalized Eigenvalues in Lattice Quantum Field Theory

Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.

Fleming, George T.↗
NASA NTRS1989

Solution and sensitivity analysis of a complex transcendental eigenproblem with pairs of real eigenvalues

This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.

Murthy, Durbha V.↗
NASA NTRS1989

Solution and sensitivity analysis of a complex transcendental eigenproblem with pairs of real eigenvalues

This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.

Murthy, D. V.↗