Search NASA⌕ Search

SEARCH · Search NASA

Results for “Curve fitting”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Badavi, F. F.↗
NASA NTRS1981

Statistical model to perform error analysis of curve fits of wind tunnel test data using the techniques of analysis of variance and regression analysis

The considered research had the objective to design a statistical model that could perform an error analysis of curve fits of wind tunnel test data using analysis of variance and regression analysis techniques. Four related subproblems were defined, and by solving each of these a solution to the general research problem was obtained. The capabilities of the evolved true statistical model are considered. The least squares fit is used to determine the nature of the force, moment, and pressure data. The order of the curve fit is increased in order to delete the quadratic effect in the residuals. The analysis of variance is used to determine the magnitude and effect of the error factor associated with the experimental data.

Alston, D. W.↗
NASA NTRS1990

Determination of total column water vapor in the atmosphere at high spatial resolution from AVIRIS data using spectral curve fitting and band ratioing techniques

Techniques are developed for quantitative retrievals of high spatial resolution column atmospheric water vapor that is largely contained in the lower portion of the troposphere. One method consists of curve fitting observed spectra with simulated spectra in the 1.14 microns or the 0.94 micron water vapor band absorption region. The other method is a simple band ratioing technique, which requires less computer time than the curve fitting method. The advantage of the technique over humidity sounding by IR emission measurements is that the retrieved column water vapor amounts over land surfaces have significantly higher precision.

Gao, Bo-Cai↗
NASA NTRS1991

Calculations and curve fits of thermodynamic and transport properties for equilibrium air to 30000 K

A self-consistent set of equilibrium air values were computed for enthalpy, total specific heat at constant pressure, compressibility factor, viscosity, total thermal conductivity, and total Prandtl number from 500 to 30,000 K over a range of 10(exp -4) atm to 10(exp 2) atm. The mixture values are calculated from the transport and thermodynamic properties of the individual species provided in a recent study by the authors. The concentrations of the individual species, required in the mixture relations, are obtained from a free energy minimization calculation procedure. Present calculations are based on an 11-species air model. For pressures less than 10(exp -2) atm and temperatures of about 15,000 K and greater, the concentrations of N(++) and O(++) become important, and consequently, they are included in the calculations determining the various properties. The computed properties are curve fitted as a function of temperature at a constant value of pressure. These curve fits reproduce the computed values within 5 percent for the entire temperature range considered here at specific pressures and provide an efficient means for computing the flowfield properties of equilibrium air, provided the elemental composition remains constant at 0.24 for oxygen and 0.76 for nitrogen by mass.

Gupta, Roop N.↗
NASA NTRS2002

Locally-Based Kernal PLS Smoothing to Non-Parametric Regression Curve Fitting

We present a novel smoothing approach to non-parametric regression curve fitting. This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space. It is our concern to apply the methodology for smoothing experimental data where some level of knowledge about the approximate shape, local inhomogeneities or points where the desired function changes its curvature is known a priori or can be derived based on the observed noisy data. We propose locally-based kernel PLS regression that extends the previous kernel PLS methodology by incorporating this knowledge. We compare our approach with existing smoothing splines, hybrid adaptive splines and wavelet shrinkage techniques on two generated data sets.

Rosipal, Roman↗
NASA NTRS1972

A curve-fitting technique for the determination of gain and saturation intensity in homogeneously-broadened gas lasers: Application to a waveguide CO2 laser

A least squares curve-fitting algorithm is derived which allows the simultaneous estimation of the small signal gain and the saturation intensity from an arbitrary number of data points relating power output to the incidence angle of an internal coupling plate. The method is used to study the dependence of the two parameters on tube pressure and discharge current in a waveguide CO2 laser having a 2 mm diameter capillary. It is found that, at pressures greater than 28 torr, rising CO2 temperature degrades the small signal gain at current levels as low as three milliamperes.

Degnan, J. J.↗
NASA NTRS1975

An interactive graphics program to retrieve, display, compare, manipulate, curve fit, difference and cross plot wind tunnel data

The Aerodynamic Data Analysis and Integration System (ADAIS), developed as a highly interactive computer graphics program capable of manipulating large quantities of data such that addressable elements of a data base can be called up for graphic display, compared, curve fit, stored, retrieved, differenced, etc., was described. The general nature of the system is evidenced by the fact that limited usage has already occurred with data bases consisting of thermodynamic, basic loads, and flight dynamics data. Productivity using ADAIS of five times that for conventional manual methods of wind tunnel data analysis is routinely achieved. In wind tunnel data analysis, data from one or more runs of a particular test may be called up and displayed along with data from one or more runs of a different test. Curves may be faired through the data points by any of four methods, including cubic spline and least squares polynomial fit up to seventh order.

Elliott, R. D.↗
NASA NTRS2021

PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic (LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖, 𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, there are some instances where the fitting needs to be done programmatically. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.

Ianik Plante↗
NASA NTRS2021

PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic(LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖,𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, it is often convenient to do the fitting programmatically, especially when a large number of datasets should be analyzed. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.

Ianik Plante↗
NASA NTRS1981

Modal analysis using a Fourier analyzer, curve-fitting, and modal tuning

The proposed modal test program differs from single-input methods in that preliminary data may be acquired using multiple inputs, and modal tuning procedures may be employed to define closely spaced frquency modes more accurately or to make use of frequency response functions (FRF's) which are based on several input locations. In some respects the proposed modal test proram resembles earlier sine-sweep and sine-dwell testing in that broadband FRF's are acquired using several input locations, and tuning is employed to refine the modal parameter estimates. The major tasks performed in the proposed modal test program are outlined. Data acquisition and FFT processing, curve fitting, and modal tuning phases are described and examples are given to illustrate and evaluate them.

Craig, R. R., Jr.↗
DOE OSTI2020

Fast Automatic Knot Placement Method for Accurate B-spline Curve Fitting

The choice of knot vector has immense influence on the resulting accuracy of a B-spline approximation of a curve. However, despite the significance of this problem and the various solutions that were proposed in the literature, optimizing the number and placement of knots remains a difficult task. This paper presents a novel method for the approximation of a curve by a B-spline of arbitrary order, which automatically determines a knot vector that achieves high approximation quality. Additionally, at the core of our approach is a feature function that characterizes the amount and spatial distribution of geometric details in the input curve by estimating its derivatives. Knots are then selected in such a way as to evenly distribute the feature contents across their intervals. A comparison to the state of the art for a wide variety of curves shows that our method is faster and achieves more accurate reconstruction results, while typically reducing the number of necessary knots.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Huang, Norden E.↗