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 343 records · Page 19

Computing Thermodynamic And Transport Properties Of Air

EQAIRS computer program is set of FORTRAN 77 routines for computing thermodynamic and transport properties of equilibrium air for temperatures from 100 to 30,000 K. Computes properties from 11-species, curve-fit mathematical model. Successfully implemented on DEC VAX-series computer running VMS, Sun4-series computer running SunOS, and IBM PC-compatible computer running MS-DOS.

Thompson, Richard A.↗

Determining XV-15 aeroelastic modes from flight data with frequency-domain methods

The XV-15 tilt-rotor wing has six major aeroelastic modes that are close in frequency. To precisely excite individual modes during flight test, dual flaperon exciters with automatic frequency-sweep controls were installed. The resulting structural data were analyzed in the frequency domain (Fourier transformed). All spectral data were computed using chirp z-transforms. Modal frequencies and damping were determined by fitting curves to frequency-response magnitude and phase data. The results given in this report are for the XV-15 with its original metal rotor blades. Also, frequency and damping values are compared with theoretical predictions made using two different programs, CAMRAD and ASAP. The frequency-domain data-analysis method proved to be very reliable and adequate for tracking aeroelastic modes during flight-envelope expansion. This approach required less flight-test time and yielded mode estimations that were more repeatable, compared with the exponential-decay method previously used.

Acree, C. W., Jr.↗

Surface characterization of LDEF materials

The NASA Long Duration Exposure Facility (LDEF), a passive experimental satellite, was placed into low-Earth orbit by the Shuttle Challenger in Apr. 1984. The LDEF spent an unprecedented 69 months in space. The flight and recovery of the LDEF provided a wealth of information on the longterm space environmental effects of a variety of materials exposed to the low-Earth orbit environment. Surface characterization of LDEF materials included polymers, composites, thermal control paints, and aluminum. X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), scanning electron microscopy (SEM), and contact angle analysis were used to document changes in both the surface composition and surface chemistry of these materials. Detailed XPS analysis of the polymer systems, such as Kapton, polyimide polysiloxane copolymers, and fluorinated ethylene propylene thermal blankets on the backside of the LDEF revealed significant changes in both the surface composition and surface chemistry as a result of exposure to the low-Earth orbit environment. Polymer systems such as Kapton, polyimide polysiloxane copolymers, and polysulfone showed a common trend of decreasing carbon content and increasing oxygen content with respect to the control sample. Carbon 1s curve fit XPS analysis of the composite samples, in conjunction with SEM photomicrographs, revealed significant ablation of the polymer matrix resin to expose the carbon fibers of the composite during exposure to the space environment. Surface characterization of anodized aluminum tray clamps, which were located at regular intervals over the entire LDEF frame, provided the first results to evaluate the extent of contamination with respect to position on the LDEF. The XPS results clearly showed that the amount and state of both silicon and fluorine contamination were directly dependent upon the position of the tray clamp on the LDEF.

Wightman, J. P.↗

A fresh look at crater scaling laws for normal and oblique hypervelocity impacts

With the concomitant increase in the amount of man-made debris and an ever increasing use of space satellites, the issue of accidental collisions with particles becomes more severe. While the natural micrometeoroid population is unavoidable and assumed constant, continued launches increase the debris population at a steady rate. Debris currently includes items ranging in size from microns to meters which originated from spent satellites and rocket cases. To understand and model these environments, impact damage in the form of craters and perforations must be analyzed. Returned spacecraft materials such as those from LDEF and Solar Max have provided such a testbed. From these space-aged samples various impact parameters (i.e., particle size, particle and target material, particle shape, relative impact speed, etc.) may be determined. These types of analyses require the use of generic analytic scaling laws which can adequately describe the impact effects. Currently, most existing analytic scaling laws are little more than curve-fits to limited data and are not based on physics, and thus are not generically applicable over a wide range of impact parameters. During this study, a series of physics-based scaling laws for normal and oblique crater and perforation formation has been generated into two types of materials: aluminum and Teflon.

Watts, A. J.↗

On the estimation of the correlation dimension and its application to radar reflector discrimination

Recently, system theorists have recognized that low order systems of nonlinear differential equations can give rise to solutions which are neither periodic, constant, nor predictable in steady state, but which are nonetheless bounded and deterministic. This behavior, which was first described in the study of weather systems, has been termed 'chaotic.' Much study of chaotic systems has concentrated on analysis of the systems' phase space attractors. It has been recognized that invariant measures of the attractor possess inherent information about the system. One such measure is the dimension of the attractors. The dimension of a chaotic attractor has been shown to be noninteger, leading to the term 'strange attractor;' the attractor is said to have a fractal structure. The correlation dimension has become one of the most popular measures of dimension. However, many problems have been identified in correlation dimension estimation from time sequences. The most common methods for obtaining the correlation dimension have been least squares curves fitting to find the slope of the correlation integral and the Takens Estimator. However, these estimates show unacceptable sensitivity to the upper limit on the distance chosen. Here, a new method is proposed which is shown to be rather insensitive to the upper limit and to perform in a very stable manner, at least in the absence of noise. The correlation dimension is also shown to be an effective discriminant in distinguishing between radar returns resulting from weather and those from the ground. The weather returns are shown to have a correlation dimension generally between 2.0 and 3.0, while ground returns have a correlation dimension exceeding 3.0.

Barnett, Kevin D.↗

Establishment of computerized numerical databases on thermophysical and other properties of molten as well as solid materials and data evaluation and validation for generating recommended reliable reference data

The Center for Information and Numerical Data Analysis and Synthesis, (CINDAS), measures and maintains databases on thermophysical, thermoradiative, mechanical, optical, electronic, ablation, and physical properties of materials. Emphasis is on aerospace structural materials especially composites and on infrared detector/sensor materials. Within CINDAS, the Department of Defense sponsors at Purdue several centers: the High Temperature Material Information Analysis Center (HTMIAC), the Ceramics Information Analysis Center (CIAC) and the Metals Information Analysis Center (MIAC). The responsibilities of CINDAS are extremely broad encompassing basic and applied research, measurement of the properties of thin wires and thin foils as well as bulk materials, acquisition and search of world-wide literature, critical evaluation of data, generation of estimated values to fill data voids, investigation of constitutive, structural, processing, environmental, and rapid heating and loading effects, and dissemination of data. Liquids, gases, molten materials and solids are all considered. The responsibility of maintaining widely used databases includes data evaluation, analysis, correlation, and synthesis. Material property data recorded on the literature are often conflicting, diverging, and subject to large uncertainties. It is admittedly difficult to accurately measure materials properties. Systematic and random errors both enter. Some errors result from lack of characterization of the material itself (impurity effects). In some cases assumed boundary conditions corresponding to a theoretical model are not obtained in the experiments. Stray heat flows and losses must be accounted for. Some experimental methods are inappropriate and in other cases appropriate methods are carried out with poor technique. Conflicts in data may be resolved by curve fitting of the data to theoretical or empirical models or correlation in terms of various affecting parameters. Reasons (e.g. phase transitions) must be found for unusual dependence or any anomaly. Such critical evaluation involves knowledge of theory, experience in measurement, familiarity with metallurgy (microstructural behavior) and not inconsiderable judgment. An examination of typical data compiled and analyzed by CINDAS shows that the thermal conductivity of a material reported in the literature may vary by a factor of two of more; the range of reported values increases as temperature increases reflecting the difficulty of high temperature measurements. Often only estimates of melt behavior are available, despite the importance of melt properties in modeling, welding, or other solidification processes. There may be only a few measurements available for properties such as kinematic viscosity, even for widely used materials such as stainless steel. In the face of such a paucity of existing data and in a national environment where too few new data are being generated it is nonetheless the responsibility of CINDAS to select and disseminate recommended values of a wide variety of thermophysical properties.

Ho, C. Y.↗

Implementation of thermal residual stresses in the analysis of fiber bridged matrix crack growth in titanium matrix composites

In this research, thermal residual stresses were incorporated in an analysis of fiber-bridged matrix cracks in unidirectional and cross-ply titanium matrix composites (TMC) containing center holes or center notches. Two TMC were investigated, namely, SCS-6/Timelal-21S laminates. Experimentally, matrix crack initiation and growth were monitored during tension-tension fatigue tests conducted at room temperature and at an elevated temperature of 200 C. Analytically, thermal residual stresses were included in a fiber bridging (FB) model. The local R-ratio and stress-intensity factor in the matrix due to thermal and mechanical loadings were calculated and used to evaluate the matrix crack growth behavior in the two materials studied. The frictional shear stress term, tau, assumed in this model was used as a curve-fitting parameter to matrix crack growth data. The scatter band in the values of tau used to fit the matrix crack growth data was significantly reduced when thermal residual stresses were included in the fiber bridging analysis. For a given material system, lay-up and temperature, a single value of tau was sufficient to analyze the crack growth data. It was revealed in this study that thermal residual stresses are an important factor overlooked in the original FB models.

Bakuckas, John G., Jr.↗

A methodology to predict damage initiation, damage growth and residual strength in titanium matrix composites

In this research, a methodology to predict damage initiation, damage growth, fatigue life, and residual strength in titanium matrix composites (TMC) is outlined. Emphasis was placed on micromechanics-based engineering approaches. Damage initiation was predicted using a local effective strain approach. A finite element analysis verified the prevailing assumptions made in the formulation of this model. Damage growth, namely, fiber-bridged matrix crack growth, was evaluated using a fiber bridging (FB) model which accounts for thermal residual stresses. This model combines continuum fracture mechanics and micromechanics analyses yielding stress-intensity factor solutions for fiber-bridged matrix cracks. It is assumed in the FB model that fibers in the wake of the matrix crack are idealized as a closure pressure, and an unknown constant frictional shear stress is assumed to act along the debond length of the bridging fibers. This frictional shear stress was used as a curve fitting parameter to the available experimental data. Fatigue life and post-fatigue residual strength were predicted based on the axial stress in the first intact 0 degree fiber calculated using the FB model and a three-dimensional finite element analysis.

Bakuckas, J. G., Jr.↗

Full-spectrum multiwavelength pyrometry for nongray surfaces

A full-spectrum (encompassing radiation on both sides of the Wien displacement peak) multiwavelength pyrometer was developed. It measures the surface temperature of arbitrary nongray ceramics by curve fitting a spectrum in this spectral region to a Planck function of temperature T. This function of T is modified by the surface spectral emissivity. The emissivity function was derived experimentally from additional spectra that were obtained by using an auxiliary radiation source and from application of Kirchhoff's law. This emissivity was verified by results that were obtained independently by using electromagnetic and solid-state theories. In the presence of interfering reflected radiation this general pyrometry improves the accuracy of the measured temperature by measuring an additional spectrum that characterizes the interfering radiation source.

Ng, Daniel↗

Applications of data compression techniques in modal analysis for on-orbit system identification

Data compression techniques have been investigated for use with modal analysis applications. A redundancy-reduction algorithm was used to compress frequency response functions (FRFs) in order to reduce the amount of disk space necessary to store the data and/or save time in processing it. Tests were performed for both single- and multiple-degree-of-freedom (SDOF and MDOF, respectively) systems, with varying amounts of noise. Analysis was done on both the compressed and uncompressed FRFs using an SDOF Nyquist curve fit as well as the Eigensystem Realization Algorithm. Significant savings were realized with minimal errors incurred by the compression process.

Carlin, Robert A.↗

Robust control design with real parameter uncertainty using absolute stability theory

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.

How, Jonathan P.↗

Strain gage selection in loads equations using a genetic algorithm

Traditionally, structural loads are measured using strain gages. A loads calibration test must be done before loads can be accurately measured. In one measurement method, a series of point loads is applied to the structure, and loads equations are derived via the least squares curve fitting algorithm using the strain gage responses to the applied point loads. However, many research structures are highly instrumented with strain gages, and the number and selection of gages used in a loads equation can be problematic. This paper presents an improved technique using a genetic algorithm to choose the strain gages used in the loads equations. Also presented are a comparison of the genetic algorithm performance with the current T-value technique and a variant known as the Best Step-down technique. Examples are shown using aerospace vehicle wings of high and low aspect ratio. In addition, a significant limitation in the current methods is revealed. The genetic algorithm arrived at a comparable or superior set of gages with significantly less human effort, and could be applied in instances when the current methods could not.

Source record↗

Computer modeling the fatigue crack growth rate behavior of metals in corrosive environments

The objective of this task was to develop a method to digitize FCP (fatigue crack propagation) kinetics data, generally presented in terms of extensive da/dN-Delta K pairs, to produce a file for subsequent linear superposition or curve-fitting analysis. The method that was developed is specific to the Numonics 2400 Digitablet and is comparable to commercially available software products as Digimatic(sup TM 4). Experiments demonstrated that the errors introduced by the photocopying of literature data, and digitization, are small compared to those inherent in laboratory methods to characterize FCP in benign and aggressive environments. The digitizing procedure was employed to obtain fifteen crack growth rate data sets for several aerospace alloys in aggressive environments.

Richey, Edward, III↗

An incremental database access method for autonomous interoperable databases

We investigated a number of design and performance issues of interoperable database management systems (DBMS's). The major results of our investigation were obtained in the areas of client-server database architectures for heterogeneous DBMS's, incremental computation models, buffer management techniques, and query optimization. We finished a prototype of an advanced client-server workstation-based DBMS which allows access to multiple heterogeneous commercial DBMS's. Experiments and simulations were then run to compare its performance with the standard client-server architectures. The focus of this research was on adaptive optimization methods of heterogeneous database systems. Adaptive buffer management accounts for the random and object-oriented access methods for which no known characterization of the access patterns exists. Adaptive query optimization means that value distributions and selectives, which play the most significant role in query plan evaluation, are continuously refined to reflect the actual values as opposed to static ones that are computed off-line. Query feedback is a concept that was first introduced to the literature by our group. We employed query feedback for both adaptive buffer management and for computing value distributions and selectivities. For adaptive buffer management, we use the page faults of prior executions to achieve more 'informed' management decisions. For the estimation of the distributions of the selectivities, we use curve-fitting techniques, such as least squares and splines, for regressing on these values.

Roussopoulos, Nicholas↗

Pressure and higher-order spectra for homogeneous isotropic turbulence

The spectra of the pressure, and other higher-order quantities including the dissipation, the enstrophy, and the square of the longitudinal velocity derivative are computed using data obtained from direct numerical simulation of homogeneous isotropic turbulence at Taylor-Reynolds numbers R(sub lambda) in the range 38 - 170. For the pressure spectra we find reasonable collapse in the dissipation range (of the velocity spectrum) when scaled in Kolmogorov variables and some evidence, which is not conclusive, for the existence of a k(exp -7/3) inertial range where k = absolute value of K, is the modulus of the wavenumber. The power spectra of the dissipation, the enstrophy, and the square of the longitudinal velocity derivative separate in the dissipation range, but appear to converge together in the short inertial range of the simulations. A least-squares curve-fit in the dissipation range for one value of R(sub lambda) = 96 gives a form for the spectrum of the dissipation as k(exp 0)exp(-Ck eta), for k(eta) greater than 0.2, where eta is the Kolmogorov length and C is approximately equal to 2.5.

Pullin, D. I.↗

SEEK: A FORTRAN optimization program using a feasible directions gradient search

This report describes the use of computer program 'SEEK' which works in conjunction with two user-written subroutines and an input data file to perform an optimization procedure on a user's problem. The optimization method uses a modified feasible directions gradient technique. SEEK is written in ANSI standard Fortran 77, has an object size of about 46K bytes, and can be used on a personal computer running DOS. This report describes the use of the program and discusses the optimizing method. The program use is illustrated with four example problems: a bushing design, a helical coil spring design, a gear mesh design, and a two-parameter Weibull life-reliability curve fit.

Savage, M.↗

A comparison of spectral mixture analysis an NDVI for ascertaining ecological variables

In this study, we compare the performance of spectral mixture analysis to the Normalized Difference Vegetation Index (NDVI) in detecting change in a grassland across topographically-induced nutrient gradients and different management schemes. The Konza Prairie Research Natural Area, Kansas, is a relatively homogeneous tallgrass prairie in which change in vegetation productivity occurs with respect to topographic positions in each watershed. The area is the site of long-term studies of the influence of fire and grazing on tallgrass production and was the site of the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE) from 1987 to 1989. Vegetation indices such as NDVI are commonly used with imagery collected in few (less than 10) spectral bands. However, the use of only two bands (e.g. NDVI) does not adequately account for the complex of signals making up most surface reflectance. Influences from background spectral variation and spatial heterogeneity may confound the direct relationship with biological or biophysical variables. High dimensional multispectral data allows for the application position of techniques such as derivative analysis and spectral curve fitting, thereby increasing the probability of successfully modeling the reflectance from mixed surfaces. The higher number of bands permits unmixing of a greater number of surface components, separating the vegetation signal for further analyses relevant to biological variables.

Wessman, Carol A.↗

Surface characterization of LDEF carbon fiber/polymer matrix composites

XPS (x-ray photoelectron spectroscopy) and SEM (scanning electron microscopy) analysis of both carbon fiber/epoxy matrix and carbon fiber/polysulfone matrix composites revealed significant changes in the surface composition as a result of exposure to low-earth orbit. The carbon 1s curve fit XPS analysis in conjunction with the SEM photomicrographs revealed significant erosion of the polymer matrix resins by atomic oxygen to expose the carbon fibers of the composite samples. This erosion effect on the composites was seen after 10 months in orbit and was even more obvious after 69 months.

Grammer, Holly L.↗