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Results for “least square approximations”

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 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1975

Comparison of techniques for approximating ocean bottom topography in a wave-refraction computer model

A study of the effects of using different methods for approximating bottom topography in a wave-refraction computer model was conducted. Approximation techniques involving quadratic least squares, cubic least squares, and constrained bicubic polynomial interpolation were compared for computed wave patterns and parameters in the region of Saco Bay, Maine. Although substantial local differences can be attributed to use of the different approximation techniques, results indicated that overall computed wave patterns and parameter distributions were quite similar.

Poole, L. R.↗

NASA NTRS1992

Optimizing Reduced-Order Transfer Functions

Transfer-function approximations made optimal in special least-squares sense. Algorithm computes reduced-order rational-fraction approximates to single-input/single-output transfer functions. Reduces amount of computation needed for such purposes as numerical simulation of dynamics and design of control subsystems.

Spanos, John T.↗

NASA NTRS1980

Design of a recursive vector processor using polynomial splines

The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.

Kim, C. S.↗

NASA NTRS1982

Least-squares sequential parameter and state estimation for large space structures

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Thau, F. E.↗

NASA NTRS1978

Simplified contact analysis

A simple and straightforward method for calculating the elastic deformation at the center of contact between two solids with different radii of curvature is proposed instead of the conventional contact deformation analysis for ball bearings, gears, and cams, which usually involves tedious iterative procedures or the use of design charts. Ellipticity of the contact is approximated from a least-squares power fit. Simplified expressions are derived which allow rapid calculation of deformation from the material properties and geometry of the contacting elements.

Brewe, D. E.↗

NASA NTRS1990

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

Sohn, J. L.↗

NASA NTRS1991

Numerical recovery of certain discontinuous electrical conductivities

The inverse problem of recovering an electrical conductivity of the form Gamma(x) = 1 + (k-1)(sub Chi(D)) (Chi(D) is the characteristic function of D) on a region omega is a subset of 2-dimensional Euclid space from boundary data is considered, where D is a subset of omega and k is some positive constant. A linearization of the forward problem is formed and used in a least squares output method for approximately solving the inverse problem. Convergence results are proved and some numerical results presented.

Bryan, Kurt↗

NASA NTRS1992

Development of an efficient analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is described. It uses an inviscid/viscid interaction approach, wherein the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation. The viscous-layer solution is obtained using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and the wake streamline. A semiinverse global iteration procedure permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for two cascades where a range of inlet flow conditions was considered for one of them including conditions leading to large-scale flow separation.

Barnett, M.↗

NASA NTRS1993

An analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

Barnett, Mark↗

NASA NTRS1986

Parameter identifiability under approximation

The problem of injectivity of the parameter-to-state map is discussed for Galerkin approximations of a linear parabolic equation. A necessary and sufficient condition is derived and illustrated by means of simple examples. Finally, output least squares identifiability of the Galerkin approximations is discussed.

Kunisch, K.↗

NASA NTRS1986

Least squares finite element simulation of transonic flows

Finite difference approximation of transonic flow problems is a well-developed and largely successful approach. Nevertheless, there is still a real need to develop finite element methods for applications arising from fluid-structure interactions and problems with complicated boundaries. In this paper a least squares based finite element scheme is introduced. It is shown that, if suitably formulated, such an approach can lead to physically meaningful results. Bottlenecks that arise from such schemes are also discussed.

Chen, T. F.↗

NASA NTRS1995

Aerodynamic parameter estimation via Fourier modulating function techniques

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Pearson, A. E.↗

DOE OSTI2022

Preconditioning for Hyper-reduction in Reduced Order Models

Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Hyper Suprime-Cam Legacy Archive

Abstract We present the launch of the Hyper Suprime-Cam Legacy Archive (HSCLA), a public archive of processed, science-ready data from the Hyper Suprime-Cam (HSC). HSC is an optical wide-field imager installed at the prime focus of the Subaru Telescope and has been in operation since 2014. While ∼1/3 of the total observing time of HSC has been used for the Subaru Strategic Program (SSP), the remainder of the time is used for Principal Investigator (PI)-based programs. We have processed the data from these PI-based programs and make the processed, high-quality data available to the community through HSCLA. The current version of HSCLA includes data taken in the first year of science operation, 2014. We provide both individual and coadd images as well as photometric catalogs. The photometric catalog from the coadd is loaded to the database, which offers a fast access to the large catalog. There are other online tools such as an image browser and an image cutout tool and they will be useful for science analyses. The coadd images reach 24–27th magnitudes at 5σ for point sources and cover approximately 580 square degrees in at least one filter with 150 million objects in total. We perform extensive quality assurance tests and verify that the photometric and astrometric quality of the data is good enough for most scientific explorations. However, the data are not without problems and users are referred to the list of known issues before exploiting the data for science. All the data and documentations can be found at the data release site, 〈https://hscla.mtk.nao.ac.jp/〉.

Tanaka, Masayuki↗

NASA NTRS1975

Geodetic and Astrometric Measurements with Very-Long-Baseline Interferometry

The use of very-long-baseline interferometry (VLBI) observations for the estimation of geodetic and astrometric parameters is discussed. Analytic models for the dependence of delay and delay rate on these parameters are developed and used for parameter estimation by the method of weighted least squares. Results are presented from approximately 15,000 delay and delay-rate observations, obtained in a series of nineteen VLBI experiments involving a total of five stations on two continents. The closure of baseline triangles is investigated and found to be consistent with the scatter of the various baseline-component results. Estimates are made of the wobble of the earth's pole and of the irregularities in the earth's rotation rate. Estimates are also made of the precession constant and of the vertical Love number, for which a value of 0.55 + or - 0.05 was obtained.

Robertson, D. S.↗

NASA NTRS1988

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗

NASA NTRS1990

Estimation of time- and state-dependent delays and other parameters in functional differential equations

Murphy, K. A.↗

DOE OSTI2021

Practical algorithms for multivariate rational approximation

We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation (in particular, constraints demanding the absence of singularities), resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

97 MATHEMATICS AND COMPUTING↗