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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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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Analytical Identification Method of Generalized Short‐Circuit Ratio Using Phasor Measurement Units

This paper introduces a novel analytical approach for the identification of the admittance matrix and the generalized short-circuit ratio (gSCR) in power systems integrated with renewable energy sources. The proposed method leverages voltage and current measurements from phasor measurement units (PMUs) to construct a least squares objective function, which is then solved using matrix calculus and partial derivatives. Unlike conventional optimization algorithms, this approach provides an analytical solution that substantially reduces data requirements, enabling the efficient and accurate identification of the gSCR with smaller datasets. Additionally, its fixed computational complexity allows for real-time updates as new data are collected, ensuring continuous refinement of the system of equations and enabling rapid, precise gSCR calculations. The method also exhibits strong robustness against measurement noise, making it well-suited for practical applications in dynamic power systems. The combination of reduced data requirements, real-time adaptability, noise robustness and fixed computational load establishes this method as a highly efficient and reliable tool for real-time power system stability analysis. Case studies on an EPRI 36-bus system demonstrate the method's effectiveness, highlighting its accuracy in closely matching true gSCR values, even under diverse disturbances and noisy conditions.

Han, Zelei [Hohai University, Nanjing (China)] (OR↗
NASA NTRS1974

Least squares adjustment with relatively large observation errors, inaccurate initial approximations, or both

Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.

Eichhorn, H.↗
NASA NTRS1981

On the method of least squares. II

A least squares method proposed previously for solving a general class of problems is expanded in two ways. First, covariance matrices related to the solution are calculated and their interpretation is given. Second, improved methods of solving the normal equations related to those of Marquardt (1963) and Fletcher and Powell (1963) are developed for this approach. These methods may converge in cases where Newton's method diverges or converges slowly.

Jefferys, W. H.↗
NASA NTRS1995

A study of various methods for calculating locations of lightning events

This article reports on the results of numerical experiments on finding the location of lightning events using different numerical methods. The methods include linear least squares, nonlinear least squares, statistical estimations, cluster analysis and angular filters and combinations of such techniques. The experiments involved investigations of methods for excluding fake solutions which are solutions that appear to be reasonable but are in fact several kilometers distant from the actual location. Some of the conclusions derived from the study are that bad data produces fakes, that no fool-proof method of excluding fakes was found, that a short base-line interferometer under development at Kennedy Space Center to measure the direction cosines of an event shows promise as a filter for excluding fakes. The experiments generated a number of open questions, some of which are discussed at the end of the report.

Cannon, John R.↗
NASA NTRS1996

Optimum Transonic Airfoils Based on the Euler Equations

We solve the problem of determining airfoils that approximate, in a least square sense, given surface pressure distributions in transonic flight regimes. The flow is modeled by means of the Euler equations and the solution procedure is an adjoint- based minimization algorithm that makes use of the inverse Theodorsen transform in order to parameterize the airfoil. Fast convergence to the optimal solution is obtained by means of the pseudo-time method. Results are obtained using three different pressure distributions for several free stream conditions. The airfoils obtained have given a trailing edge angle.

Iollo, Angelo↗
NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1993

Euler solutions for blunt bodies using triangular meshes - Artificial viscosity forms and numerical boundary conditions

A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.

Winterstein, R.↗
DOE OSTI2020

XRD-PUAT (X-Ray Diffraction - Parameter Uncertainty Analysis Toolkit)

This XRD uncertainty toolkit was built to investigate uncertainty and local least squares topology over a specified parameter space on a single histogram in a gpx GSAS-II file. The parameter uncertainty can be investigated using either a frequentist F-test approach or a Bayesian Inference statistical inversion method on a weighted least squares or peak fit refinements.SAND Number: SAND2020-12227 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Moore, Alexander↗
DOE OSTI2021

TAO Users Manual (Rev. 3.15)

The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints. The development of TAO was motivated by the scattered support for parallel computations and the lack of reuse of external toolkits in current optimization software. Our aim is to produce high-quality optimization software for computing environments ranging from workstations and laptops to massively parallel high-performance architectures. Our design decisions are strongly motivated by the challenges inherent in the use of large-scale distributed memory architectures and the reality of working with large, often poorly structured legacy codes for specific applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗
NASA NTRS1993

Objective determination of image end-members in spectral mixture analysis

Spectral mixture analysis was shown to be a powerful, multifaceted tool for analysis of multi- and hyper-spectral data. The essence of the first phase of the approach is to determine a set of image end-members that best account for the spectral variance in an image cube within a constrained, linear least squares mixing model. The selection of the image end-member is usually achieved using a priori knowledge and successive trial and error solutions to refine the total number and physical location of the end-members. However, in many situations a more objective method of determining these essential components is desired. The problem of image end-member determination was approached objectively by using the inherent variance of the data. Unlike purely statistical methods such as factor analysis, this approach derives solutions that conform to a physically realistic model.

Tompkins, Stefanie↗
NASA NTRS1990

Least-squares finite element methods for compressible Euler equations

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Jiang, Bo-Nan↗
DOE OSTI2020

Algorithms in Diffraction Profile Analysis

This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.

Singh, Susheela↗
NASA NTRS1978

The radii of Uranian rings alpha, beta, gamma, delta, epsilon, eta, 4, 5, and 6 from their occultations of SAO 158687

All available timing data for the occultations of SAO 158687 on March 10, 1977, by the cited rings of Uranus are analyzed. Least-squares fits to the data are performed using a model which postulates that rings alpha, beta, gamma, and delta are circular and coplanar. A solution obtained under the assumption that the ring plane coincides with the plane of the satellite orbits is adopted which yields radii of 44,844 km for ring alpha, 45,799 km for ring beta, 47,746 km for ring gamma, and 48,423 km for ring delta. The uncertainties in these values are discussed along with the apparent shapes and inclinations of these main rings. The mean radii estimated for the other rings are: 47,323 km for ring eta, 42,663 km for ring 4, 42,360 km for ring 5, and 41,980 km for ring 6.

Elliot, J. L.↗
NASA NTRS1981

Development of an unsteady aerodynamic analysis for finite-deflection subsonic cascades

An unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, was developed to predict aerodynamic forces and moments associated with free vibration or flutter phenomena in the fan, compressor, or turbine stages of modern jet engines. Based on the assumption of small amplitude blade motions, the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady low. These equations were approximated using difference expressions determined from an implicit least squares development and applicable on arbitrary grids. The resulting linear system of algebraic equations is block tridiagonal, which permits an efficient, direct (i.e., noniterative) solution. The solution procedure was extended to treat blades with rounded or blunt edges at incidence relative to the inlet flow.

Verdon, J. M.↗