Search NASA⌕ Search

SEARCH · Search NASA

Results for “least squares solution”

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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Recursive inversion of externally defined linear systems

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.

Bach, Ralph E., Jr.↗
NASA NTRS1989

Recursive inversion of externally defined linear systems by FIR filters

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.

Bach, Ralph E., Jr.↗
NASA NTRS1989

Gravity field determination and error assessment techniques

Linear estimation theory, along with a new technique to compute relative data weights, was applied to the determination of the Earth's geopotential field and other geophysical model parameters using a combination of satellite ground-based tracking data, satellite altimetry data, and the surface gravimetry data. The relative data weights for the inhomogeneous data sets are estimated simultaneously with the gravity field and other geophysical and orbit parameters in a least squares approach to produce the University of Texas gravity field models. New techniques to perform calibration of the formal covariance matrix for the geopotential solution were developed to obtain a reliable gravity field error estimate. Different techniques, which include orbit residual analysis, surface gravity anomaly residual analysis, subset gravity solution comparisons and consider covariance analysis, were applied to investigate the reliability of the calibration.

Yuan, D. N.↗
NASA NTRS2006

Multiple concurrent recursive least squares identification with application to on-line spacecraft mass-property identification

The present invention is a method for identifying unknown parameters in a system having a set of governing equations describing its behavior that cannot be put into regression form with the unknown parameters linearly represented. In this method, the vector of unknown parameters is segmented into a plurality of groups where each individual group of unknown parameters may be isolated linearly by manipulation of said equations. Multiple concurrent and independent recursive least squares identification of each said group run, treating other unknown parameters appearing in their regression equation as if they were known perfectly, with said values provided by recursive least squares estimation from the other groups, thereby enabling the use of fast, compact, efficient linear algorithms to solve problems that would otherwise require nonlinear solution approaches. This invention is presented with application to identification of mass and thruster properties for a thruster-controlled spacecraft.

Wilson, Edward↗
NASA NTRS2017

Full Gradient Solution to Adaptive Hybrid Control

This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.

Bean, Jacob↗
NASA NTRS1992

AVIRIS study of Death Valley evaporite deposits using least-squares band-fitting methods

Minerals found in playa evaporite deposits reflect the chemically diverse origins of ground waters in arid regions. Recently, it was discovered that many playa minerals exhibit diagnostic visible and near-infrared (0.4-2.5 micron) absorption bands that provide a remote sensing basis for observing important compositional details of desert ground water systems. The study of such systems is relevant to understanding solute acquisition, transport, and fractionation processes that are active in the subsurface. Observations of playa evaporites may also be useful for monitoring the hydrologic response of desert basins to changing climatic conditions on regional and global scales. Ongoing work using Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data to map evaporite minerals in the Death Valley salt pan is described. The AVIRIS data point to differences in inflow water chemistry in different parts of the Death Valley playa system and have led to the discovery of at least two new North American mineral occurrences. Seven segments of AVIRIS data were acquired over Death Valley on 31 July 1990, and were calibrated to reflectance by using the spectrum of a uniform area of alluvium near the salt pan. The calibrated data were subsequently analyzed by using least-squares spectral band-fitting methods, first described by Clark and others. In the band-fitting procedure, AVIRIS spectra are fit compared over selected wavelength intervals to a series of library reference spectra. Output images showing the degree of fit, band depth, and fit times the band depth are generated for each reference spectrum. The reference spectra used in the study included laboratory data for 35 pure evaporite spectra extracted from the AVIRIS image cube. Additional details of the band-fitting technique are provided by Clark and others elsewhere in this volume.

Crowley, J. K.↗
NASA NTRS2016

Full Gradient Solution to Adaptive Hybrid Control

This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered-reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.

Bean, Jacob↗
DOE OSTI2023

A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Remote Americium Detection Using an Optical Sensor: A D-Optimal Strategy for Efficient PLS-Based Modeling

A fiber-optic visible–near-infrared absorption spectroscopy system in a glove box was demonstrated for remote quantification of Am(III) (0–500 µM) and HNO 3 (0.1–9 M) using partial least squares regression (PLSR) models. The sensor platform, featuring a simple plug-and-play spectrophotometer, can enable noninvasive, real-time monitoring of actinide process solutions. To establish a flexible PLSR model calibration strategy, a D-optimal design developed using Nd(III) in previous studies was successfully extended to an actinide system with Am(III) to effectively minimize sample set size while maintaining robust prediction performance. The results suggest strong spectral similarities between Nd(III) and Am(III) and validate Nd(III) as an effective optical surrogate for trivalent actinide species. This work also supports the generalizability of a D-optimal training set selection approach for two-factor systems. The PLS1 models for Am(III) and HNO 3 outperformed a PLS2 model and maintained reasonable performance in the presence of interfering U(VI). The resulting sensor system and multivariate approach provides a flexible and scalable solution for process monitoring, control, and safety in diverse nuclear applications.

actinide↗
NASA NTRS1979

M2, S2, K1 models of the global ocean tide

Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each contituent are presented.

Parke, M. E.↗
NASA NTRS1987

Polynomial compensation, inversion, and approximation of discrete time linear systems

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Baram, Yoram↗
NASA NTRS2001

A Combined HIPPARCOS and Multichannel Astrometric Photometer Study of the Proposed Planetary System of Rho Coronae Borealis

Hipparcos and Multichannel Astrometric Photometer (MAP) observations of rho Coronae Borealis independently display astrometric motion at the period of the proposed extrasolar planetary companion to the star. Individual least-squares fits to each astrometric data set yield independent estimates of the semimajor axis, inclination, and node angle that are in excellent agreement. A combined solution of the Hipparcos and MAP data yields an inclination of 0.5 deg, a node at 30.5 +/- 12.4, and a semimajor axis of 1.66 +/- 0.35 mas, indicating a companion mass of 0.14 +/- 0.05 solar masses over two orders of magnitude greater than the minimum mass for the companion as determined by radial velocity studies. This mass is approximately that of an M dwarf star, the companion cannot be a planetary object.

Gatewood, George↗
DOE OSTI2024

Subsampling of Parametric Models with Bifidelity Boosting

Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are generated using an experimental design process (e.g., a quadrature grid) involving computationally expensive models, or when the data size is large, sketching techniques have shown promise at reducing the cost of the construction of the regression model while ensuring accuracy comparable to that of the full data. However, random sketching strategies, such as those based on leverage scores, lead to regression errors that are random and may exhibit large variability. To mitigate this issue, we present a novel boosting approach that leverages cheaper, lower-fidelity data of the problem at hand to identify the best sketch among a set of candidate sketches. This in turn specifies the sketch of the intended high-fidelity model and the associated data. We provide theoretical analyses of this bifidelity boosting (BFB) approach and discuss the conditions the low- and high-fidelity data must satisfy for a successful boosting. In doing so, we derive a bound on the residual norm of the BFB sketched solution relating it to its ideal, but computationally expensive, high-fidelity boosted counterpart. Finally, empirical results on both manufactured and PDE data corroborate the theoretical analyses and illustrate the efficacy of the BFB solution in reducing the regression error, as compared to the nonboosted solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1], [2], [3], [4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Towards non-contact pollution monitoring in sewers with hyperspectral imaging

Monitoring water quality in sewers is challenging, particularly because state-of-the-art technologies require contact with the raw wastewater. The presence of fat, oil, grease, and solids makes automated grab sampling difficult and causes sensor fouling. To overcome these limitations, non-contact methods based on light reflectance, such as hyperspectral imaging (HSI), are gaining attention. However, HSI has never been tested for raw wastewater. To assess its accuracy for measuring pollution, we developed a laboratory setup and performed targeted experiments with a combination of raw and diluted wastewater, as well as synthetic turbidity stock solutions. We measured seven pollution variables: chemical oxygen demand, turbidity, dissolved organic compounds, ammonium, total nitrogen, phosphate, and sulphates. We used automated pixel selection and partial least squares regression to retrieve pollution information from the hyperspectral images. Our results, based on 144 samples, suggest that HSI can estimate pollution levels with a precision in the range of state-of-the-art absorbance spectrophotometric methods. Additionally, we found that the combination of pixel and wavelength selection, enabled by the hyperspectral data structure, significantly influences the performance of partial least square modelling. Overall, our findings indicate that HSI is a promising technology for non-contact monitoring of water quality in raw wastewater.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Samoa Updater: An Application of the Levenberg-Marquardt Method to Update DELFIC Predictions Using Field Measurements

The US Department of Energy (DOE) Forensics Operations (DFO) is a member of the Ground Collections Task Force (GCTF), which is responsible for sample collection of radiological debris for attribution should a nuclear detonation ever occur in the United States. The DFO runs the Defense Land Fallout Interpretive Code (DELFIC) Fallout Planning Tool to predict the deposition of fallout from a nuclear detonation. This prediction is refined using the DELFIC Updater tool, which takes ground measurements and adjusts DELFIC inputs to minimize the difference between prediction and observation, yielding improved predictions of fallout in locations both measured and not yet measured. Samoa, a framework for uncertainty analysis and optimization, is used to improve DELFIC predictive fallout modeling. This new capability using Samoa, dubbed “Samoa Updater,” is compared with the current DELFIC Updater, a brute-force sampling approach. Samoa Updater uses the Levenberg– Marquardt (LM) method, a gradient-based nonlinear least squares approach that uses the functional shape of the input space to increase optimization speed. In simulated test cases Samoa Updater yields faster and more accurate solutions than the current Updater.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1981

Considerations of open-loop, closed-loop, and adaptive multicyclic control systems

Four different types of self-tuning regulators were studied for multicyclic control of helicopter vibration. A numerical simulation of the helicopter is made, using a multivariable frequency-domain model, in terms of transfer function with six input control harmonics and six output harmonics. The model characteristics vary with flight speed. An off-line identification of model characteristics is made, using the least-squared-error method and using a succession of input and output measurements. The on-line identification of model characteristics is made using the Kalman filter solution. The optimal controls are calculated from the minimization of quadratic performance function based on response and multicyclic inputs. The performance of various regulators or controllers is judged from the stability, transient response, convergence time, and amplitude of the steady state.

Chopra, I.↗