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Results for “nonlinear least squares”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Improvement of structural models using covariance analysis and nonlinear generalized least squares

The next generation of large, flexible space structures will be too light to support their own weight, requiring a system of structural supports for ground testing. The authors have proposed multiple boundary-condition testing (MBCT), using more than one support condition to reduce uncertainties associated with the supports. MBCT would revise the mass and stiffness matrix, analytically qualifying the structure for operation in space. The same procedure is applicable to other common test conditions, such as empty/loaded tanks and subsystem/system level tests. This paper examines three techniques for constructing the covariance matrix required by nonlinear generalized least squares (NGLS) to update structural models based on modal test data. The methods range from a complicated approach used to generate the simulation data (i.e., the correct answer) to a diagonal matrix based on only two constants. The results show that NGLS is very insensitive to assumptions about the covariance matrix, suggesting that a workable NGLS procedure is possible. The examples also indicate that the multiple boundary condition procedure more accurately reduces errors than individual boundary condition tests alone.

Glaser, R. J.↗
NASA NTRS2017

Statistical Approaches for the Definition of Landslide Rainfall Thresholds and their Uncertainty Using Rain Gauge and Satellite Data

Models for forecasting rainfall-induced landslides are mostly based on the identification of empirical rainfall thresholds obtained exploiting rain gauge data. Despite their increased availability, satellite rainfall estimates are scarcely used for this purpose. Satellite data should be useful in ungauged and remote areas, or should provide a significant spatial and temporal reference in gauged areas. In this paper, the analysis of the reliability of rainfall thresholds based on rainfall remote sensed and rain gauge data for the prediction of landslide occurrence is carried out. To date, the estimation of the uncertainty associated with the empirical rainfall thresholds is mostly based on a bootstrap resampling of the rainfall duration and the cumulated event rainfall pairs (D,E) characterizing rainfall events responsible for past failures. This estimation does not consider the measurement uncertainty associated with D and E. In the paper, we propose (i) a new automated procedure to reconstruct ED conditions responsible for the landslide triggering and their uncertainties, and (ii) three new methods to identify rainfall threshold for the possible landslide occurrence, exploiting rain gauge and satellite data. In particular, the proposed methods are based on Least Square (LS), Quantile Regression (QR) and Nonlinear Least Square (NLS) statistical approaches. We applied the new procedure and methods to define empirical rainfall thresholds and their associated uncertainties in the Umbria region (central Italy) using both rain-gauge measurements and satellite estimates. We finally validated the thresholds and tested the effectiveness of the different threshold definition methods with independent landslide information. The NLS method among the others performed better in calculating thresholds in the full range of rainfall durations. We found that the thresholds obtained from satellite data are lower than those obtained from rain gauge measurements. This is in agreement with the literature, where satellite rainfall data underestimate the 'ground' rainfall registered by rain gauges.

landslide prediction↗
NASA NTRS1992

Phasing of a space based segmented submillimeter wavelength telescope using focal plane measurements

As part of a technology development program for realizing a space based submillimeter telescope, two different approaches to the absolute phasing of a segmented primary mirror using focal plane measurements have been implemented for feasibility. The method of optimization by simulated annealing evaluates the image quality of a point spread function after all the telescope segments have been randomly moved. It accepts each iteration which improves the image quality, as well as a random number of iterations which do not, thus keeping the Strehl in the initialization procedure from falling into local maxima. Methods for determining the annealing schedule, and the step size for random segment movements are presented and discussed. Using phase diversity and a model for the telescope imaging system, a nonlinear least squares algorithm has also been implemented which parameterizes each of the segment actuator movements. Using multiple out of focus images, the segment actuator positions are estimated using an iterative procedure. Nonlinear least squares, although computationally intensive, offers a large savings in the actuator movements over simulated annealing and pairwise phasing methods for large numbers of segments. These algorithms have been integrated into a general simulation program which models the behavior of the telescope under anticipated space conditions.

Levine, B. M.↗
NASA NTRS1990

Analysis of pressure-broadened ozone spectra in the 3 micron region

The Molecular Spectroscopy Lab at NASA-Langley has been involved in a long term effort to carefully characterize the infrared spectra of small molecules of atmospheric interest, including methane, water vapor, ozone, and their isotopic counterparts. High resolution gas phase infrared spectra are obtained using both a tunable diode laser system, and the McMath Fourier transform spectrometer at the Kitt Peak Solar Observatory. Spectra are obtained at various pressures and temperatures for pure gas samples, and for samples containing mixtures of the species of interest in nitrogen, oxygen, or air. From these spectra, using a nonlinear least squares fitting technique, spectral parameters of position, intensity, and half-width were determined for varying laboratory conditions that approximate atmospheric conditions experienced in remote sensing situations. These parameters are of interest in theoretical studies of these species, as well as in allowing more accurate interpretation of remote sensing data. The current work involves the analysis of a series of McMath FTIR spectra of ozone broadened by mixing with air, nitrogen, or oxygen. Each spectrum covers the region from 2396 to 4057/cm. Each vibrational band is analyzed by first diving its region into small intervals containing a few well isolated absorption lines of reasonable intensity. Each of these small intervals is fit by multiple iterations of the nonlinear least square program until residuals are minimized to a reasonable value which corresponds to the noise level of the measured spectrum. Intervals for the 3 nu(sub 3) ozone band in the region from 3000 to 3060 wavenumbers are being examined.

Prochaska, Eleanor S.↗
NASA NTRS1984

Stratospheric HNO3 quantification from line-by-line nonlinear least-squares analysis of high-resolution balloon-borne solar absorption spectra in the 870/cm region

Line parameters for the nu(5) and 2nu(9) bands and associated hot bands of HNO3 have been calculated and compared with laboratory spectra, and the results are presented. Spectral intervals near 870/cm for which best agreement was obtained are used to quantitatively analyze HNO3 absorption features in 0.02/cm resolution stratospheric solar absorption spectra.

Goldman, A.↗
NASA NTRS1991

A Newton algorithm for complex curve fitting

The problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type which converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions.

Spanos, J. T.↗
NASA NTRS1993

Newton algorithm for fitting transfer functions to frequency response measurements

In this paper the problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type that converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second-order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions. Two numerical examples demonstrate the effectiveness of the algorithm.

Spanos, J. T.↗
NASA NTRS2000

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Tzikang, Chen↗
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.↗
DOE OSTI2020

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (User's Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a users manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user’s manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.15 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗