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Results for “nonlinear least squares”

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NASA NTRS1990

Polarization studies of Zeeman affected spectral lines using the MSFC magnetograph

The Marshall Space Flight Center (MSFC) vector magnetograph records polarization images of absorption lines that are sensitive to magnetic fields. A method is presented for analyzing the Stokes spectral-line profiles of a photospheric Fe I absorption line (5250.2 A) which is influenced by the Zeeman effect. Using nonlinear least-square optimization, the observed Stokes profiles are compared with those generated from the theoretical solution of the polarized radiative transfer equations. The optimization process accounts for the spectral convolution of the source and the MSFC vector magnetograph. The resulting physical properties of the active region producing the polarized light are discussed.

Balasubramaniam, K. S.↗

NASA NTRS1992

Multiwavelength pyrometry for nongray bodies

A multiwavelength technique was developed and applied to measure the temperatures of nongray surfaces. The instruments required are a spectral radiometer, a dedicated auxiliary radiation source, and a computer. In general, three radiation spectra are recorded: (1) spectrum S sub 0 of the auxiliary radiation source; (2) spectrum S sub 1 of the surface-emitted radiation; and (3) spectrum S sub 2, the sum of the radiation of S sub 1 plus the reflected radiation due to the incidence of the auxiliary radiation source on the surface. Subtracting spectrum S sub 1 from spectrum Sub 2 yields the reflection spectrum resulting from the incidence radiation. From these spectra, a quantity z(lambda) is derived and is related to the reflectivity r(lambda) by r(lambda) = z(lambda)/f, where f is a constant. Spectrum S sub 1 is represented mathematically as the product of a wavelength-dependent emissivity obtained from Kirchhoff's law and a Planck function of temperature T. Application of two-variable (lambda and z), nonlinear, least-squares curve-fitting computer software to fit spectrum S sub 1 to this mathematical expression yielded the surface temperature. This technique also measured the spectral reflectivity and emissivity of the surface. Instrumentation necessary to extend measurement to elevated temperatures and in the presence of reflective interference is discussed.

Ng, Daniel↗

NASA NTRS1991

Vector magnetic fields in sunspots. I - Stokes profile analysis using the Marshall Space Flight Center magnetograph

The Marshall Space Flight Center (MSFC) vector magnetograph is a tunable filter magnetograph with a bandpass of 125 mA. Results are presented of the inversion of Stokes polarization profiles observed with the MSFC vector magnetograph centered on a sunspot to recover the vector magnetic field parameters and thermodynamic parameters of the spectral line forming region using the Fe I 5250.2 A spectral line using a nonlinear least-squares fitting technique. As a preliminary investigation, it is also shown that the recovered thermodynamic parameters could be better understood if the fitted parameters like Doppler width, opacity ratio, and damping constant were broken down into more basic quantities like temperature, microturbulent velocity, or density parameter.

Balasubramaniam, K. S.↗

NASA NTRS1992

Mt. Pinatubo SO2 column measurements from Mauna Loa

Absorption features of the nu sub 1 band of SO2 are identified in high-resolution IR solar-absorption spectra recorded from Mauna Loa, Hawaii, on July 9 and 12, 1991, shortly after the arrival of the first eruption plume from the Mt. Pinatubo volcano. A total SO2 vertical column amount of (5.1 +/- 0.5) x 10 exp 16 molecules/sq cm on July 9 is retrieved based on nonlinear least-squares spectral fittings of 9 selected SO2 absorption features with an updated set of SO2 spectral parameters. A SO2 total-column upper limit of 0.9 x 10 exp 16 molecules/sq cm deduced from measurements on September 20-24, 1991, is consistent with the dispersion of the SO2 cloud and the rapid conversion of the SO2 vapor into volcanic aerosol particles.

Goldman, A.↗

NASA NTRS1991

Measurements of Lorentz-broadening coefficients and pressure-induced line shift coefficients in the nu2 band of D2(O-16)

Lorentz-broadening and pressure-induced line-shift coefficients are determined experimentally for 126 transitions in the nu2 band of D2(O-16) from laboratory spectra with a Fourier-transform spectrometer. A nonlinear least-squares fitting procedure is employed to measure transitions up to J double-prime = 12 in the buffer gases air, nitrogen, and oxygen. The N2-broadening/O2-broadening coefficient ratio is correlated with the magnitude of the O2-broadening coefficient, and the pressure coefficients are not correlated with line widths.

Rinsland, Curtis P.↗

NASA NTRS1992

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Korte, John J.↗

NASA NTRS1993

Multiwavelength Pyrometry To Correct For Reflections

Computerized curve fitting yields more and better information on thermal radiation. Multiwavelength pyrometry involves measurement of spectrum of thermal radiation emitted by and reflected from specimen. Auxiliary source enables determination of spectral reflectance of specimen. Spectral reflectance and temperature of specimen obtained from spectral measurements by nonlinear least-squares curve-fitting routine.

Ng, Daniel↗

NASA NTRS1993

Inverting Image Data For Optical Testing And Alignment

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

Shao, Michael↗

NASA NTRS1992

A method for modeling discontinuities in a microwave coaxial transmission line

A method for modeling discontinuities in a coaxial transmission line is presented. The methodology involves the use of a nonlinear least-squares fit program to optimize the fit between theoretical data (from the model) and experimental data. When this method was applied to modeling discontinuities in a slightly damaged Galileo spacecraft S-band (2.295-GHz) antenna cable, excellent agreement between theory and experiment was obtained over a frequency range of 1.70-2.85 GHz. The same technique can be applied for diagnostics and locating unknown discontinuities in other types of microwave transmission lines, such as rectangular, circular, and beam waveguides.

Otoshi, T. Y.↗

NASA NTRS1992

Reconstruction of internal density distributions in porous bodies from laser ultrasonic data

It is presently shown that, for density-reconstruction problems in which information about the inhomogeneity is known a priori, the nonlinear least-squares algorithm yields satisfactory results on the basis of limited projection data. The back-projection algorithm, which obviates assumptions about the objective function to be reconstructed, does not recover the boundary of the inhomogeneity when the number of projections is limited and ray-bending is ignored.

Lu, Yichi↗

NASA NTRS1992

Measurements of pressure broadening and pressure shifting by nitrogen in the 4.3-micron band of (C-12)(O-16)2

Lorentz-broadening coefficients and pressure-induced line-shift coefficients of 34 individual lines have been determined for the P(40) to R(40) vibration-rotation transitions in the nu(3) fundamental of CO2 using N2 as the buffer gas. The parameters were derived from 0.01/cm resolution infrared absorption spectra recorded using the McMath Fourier transform spectrometer and a nonlinear, least-squares fitting algorithm. It is concluded that the N2-broadening coefficients obtained in the present study agree well with recent high resolution measurements. The results are considered to be of importance not only for predicting the infrared spectrum of the atmosphere due to CO2 absorption or emission but also for verifying theoretical calculations.

Devi, V. M.↗

NASA NTRS1993

The millimeter-wave spectrum of the MgH and MgD radicals

The pure rotational spectrum of MgH radical (X 2 Sigma (+)) in its ground state v = 0 and v = 1 vibrational modes has been observed in the laboratory using millimeter/submillimeter direct absorption spectroscopy. The rotational spectra of two isotopically substituted species, MgD and (Mg-26)H, have been detected as well. All six hyperfine components of the N = 0 -1 transition of MgH in its v = 0 and v = 1 states have been directly measured to an accuracy of +/-50 kHz, and the five components have been observed for (Mg-26)H. The N = 0 +/-1 and N = 1 -2 transitions of MgD have also been detected. Rotational, fine structure, and hyperfine constants were determined for all species from a nonlinear least-squared fit to the data using a 2 Sigma Hamiltonian.

Ziurys, L. M.↗

NASA NTRS1993

Statistical fitting accuracy in photon correlation spectroscopy

Continuing our experimental investigation of the fitting accuracy associated with photon correlation spectroscopy, we collect 150 correlograms of light scattered at 90 deg from a thermostated sample of 91-nm-diameter, polystyrene latex spheres in water. The correlograms are taken with two correlators: one with linearly spaced channels and one with geometrically spaced channels. Decay rates are extracted from the single-exponential correlograms with both nonlinear least-squares fits and second-order cumulant fits. We make several statistical comparisons between the two fitting techniques and verify an earlier result that there is no sample-time dependence in the decay rate errors. We find, however, that the two fitting techniques give decay rates that differ by 1 percent.

Shaumeyer, J. N.↗

NASA NTRS1993

The millimeter-wave spectrum of AlOH

The pure rotational spectrum of the AlOH and AlOD molecules in their X 1Sigma(+) (v = 0) ground electric states has been measured in the laboratory using direct absorption millimeter/submillimeter spectroscopy. The species were produced by the reaction of aluminum vapor, created in a Broida-type oven, with hydrogen peroxide or D2O2. Eight rotational transitions of AlOH and five transitions for AlOD were measured in the frequency range of 157-378 GHz to an accuracy better than +/- 75 kHz. Electric quadrupole interactions, arising from the aluminum nuclear spin of 5/2, were observed in the J = 4 - 5 and the J = 5 - 6 transitions of AlOH. The rotational constants of these molecules have been determined from a nonlinear least-squares fit to the data. The electric quadrupole coupling constant, eqQ, has been measured as well, and was found to have a value of -42.4 +/- 4.3 MHz. The spectra are consistent with quasi-linear ground states for AlOH and AlOD, as predicted by theory. AlOH is of astrophysical interest because of the relatively high cosmic abundance of aluminum.

Apponi, A. J.↗

NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

NASA NTRS1994

Measurement uncertainty and feasibility study of a flush airdata system for a hypersonic flight experiment

Presented is a feasibility and error analysis for a hypersonic flush airdata system on a hypersonic flight experiment (HYFLITE). HYFLITE heating loads make intrusive airdata measurement impractical. Although this analysis is specifically for the HYFLITE vehicle and trajectory, the problems analyzed are generally applicable to hypersonic vehicles. A layout of the flush-port matrix is shown. Surface pressures are related airdata parameters using a simple aerodynamic model. The model is linearized using small perturbations and inverted using nonlinear least-squares. Effects of various error sources on the overall uncertainty are evaluated using an error simulation. Error sources modeled include boundarylayer/viscous interactions, pneumatic lag, thermal transpiration in the sensor pressure tubing, misalignment in the matrix layout, thermal warping of the vehicle nose, sampling resolution, and transducer error. Using simulated pressure data for input to the estimation algorithm, effects caused by various error sources are analyzed by comparing estimator outputs with the original trajectory. To obtain ensemble averages the simulation is run repeatedly and output statistics are compiled. Output errors resulting from the various error sources are presented as a function of Mach number. Final uncertainties with all modeled error sources included are presented as a function of Mach number.

Whitmore, Stephen A.↗

NASA NTRS1992

Size-reduction techniques for the determination of efficient aeroservoelastic models

Size-reduction techniques for determining efficient time-domain state-space aeroservoelastic models are presented. Various rational function approximation methods of the unsteady aerodynamic force coefficients are brought to a common motion, emphasizing their differences. Among these, the classic Roger's method is the easier to apply but its resulting number of aerodynamic states is typically equal to or larger than the number of structural states. On the other hand, the minimum-state (MS) method, which typically reduces the number of aerodynamic states by 70 percent or more, requires the solution of an iterative nonlinear least-square solution. The MS computational efforts are reduced significantly when three approximation constraints are applied.

Karpel, Mordechay↗

NASA NTRS1994

Optimized design of a hypersonic nozzle

Conventional procedures for designing nozzles involve the design of an inviscid contour (using the method of characteristics) that is corrected with a displacement thickness calculated from boundary-layer theory. However, nozzles designed using this classical procedure have been shown to exhibit poor flow quality at Mach numbers characteristic of hypersonic applications. The nozzle to be designed will be a part of the NASA HYPULSE facility which is being used for hypervelocity flight research. Thus, the flow quality of the nozzle is a critical question that needs to be addressed. Design of nozzles for hypersonic applications requires a proper assessment of the effects of the thick boundary layer on the inviscid flowfield. Since the flow field is largely supersonic, the parabolized form of the Navier-Stokes (PNS) equations can be used. The requirement of a uniform flow at the exit plane of the nozzle can be used to define an objective function as part of an optimization procedure. The design procedure used in this study involves the coupling of a nonlinear (least-squares) optimization algorithm with an efficient, explicit PNS solver. The thick boundary layers growing on the walls of the nozzle limit the extent of the usable core region (region with uniform flow) for testing models (especially rectangular). In order to maximize the region of uniform flow, it was decided to have the exit plane of this nozzle to be (nearly) rectangular. Thus, an additional constraint on the nozzle shape resulted, namely the nozzle will have a shape transitioning from a circular one at the inlet to that of a rectangle at the exit. In order to provide for a smooth shape transition, the cross sectional contour of the nozzle is defined by a superellipse. The nozzle is taken to be a meter in length. The axial variations of the major and minor radii of the superellipse are governed by cubic splines. The design parameters are the coefficients of the splines associated with the local nozzle wall slopes. Extensive calculations have been made (with a three-dimensional Euler code) to understand the effects of various parameters such as location of the knot points of the spline function, different ways of characterizing the uniformity of the flow in the exit plane, as well as the effect of constraining the area of the nozzle to be invariant. Turbulent flow (measurements indicate that the flow at the nozzle inlet is turbulent) calculations are now being performed (with the inviscidly designed nozzle contours) to assess the flow quality.

Krishnamurthy, Ramesh↗