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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Radiative Heating Methodology for the Huygens Probe

The radiative heating environment for the Huygens probe near peak heating conditions for Titan entry is investigated in this paper. The task of calculating the radiation-coupled flowfield, accounting for non-Boltzmann and non-optically thin radiation, is simplified to a rapid yet accurate calculation. This is achieved by using the viscous-shock layer (VSL) technique for the stagnation-line flowfield calculation and a modified smeared rotational band (SRB) model for the radiation calculation. These two methods provide a computationally efficient alternative to a Navier-Stokes flowfield and line-by-line radiation calculation. The results of the VSL technique are shown to provide an excellent comparison with the Navier-Stokes results of previous studies. It is shown that a conventional SRB approach is inadequate for the partially optically-thick conditions present in the Huygens shock-layer around the peak heating trajectory points. A simple modification is proposed to the SRB model that improves its accuracy in these partially optically-thick conditions. This modified approach, labeled herein as SRBC, is compared throughout this study with a detailed line-by-line (LBL) calculation and is shown to compare within 5% in all cases. The SRBC method requires many orders-of-magnitude less computational time than the LBL method, which makes it ideal for coupling to the flowfield. The application of a collisional-radiative (CR) model for determining the population of the CN electronic states, which govern the radiation for Huygens entry, is discussed and applied. The non-local absorption term in the CR model is formulated in terms of an escape factor, which is then curve-fit with temperature. Although the curve-fit is an approximation, it is shown to compare well with the exact escape factor calculation, which requires a computationally intensive iteration procedure.

Johnston, Christopher O.↗
NASA NTRS1975

Flight transition data for angles of attack at Mach 22 with correlations of the data

Boundary-layer transition data for angles of attack from 2.5 to 47 deg from a flight experiment with a cone that reentered at angles of attack up to 75 deg were analyzed and their local flow conditions are presented. The transition data were obtained from both acoustic and electrostatic sensors. The data from the acoustic and electrostatic sensors were correlated by use of three different sets of correlating parameters. For each set of correlating parameters, the transitional and turbulent data from the acoustic and electrostatic sensors were plotted separately. Each of the correlations was compared with a linear curve fit of previous cone-flight data at near zero angle of attack. Results indicate that the data from acoustic sensors falls below the linear curve fits to the flight data and indicates the sensitivity of the sensors. It is shown that the transition data from the electrostatic sensors tends to scatter much more than the data from the acoustic sensors. However, the data from the electrostatic sensors tends to scatter about the linear curve fits based on previous flight data.

Johnson, C. B.↗
NASA NTRS2001

Transverse Tension Fatigue Life Characterization Through Flexure Testing of Composite Materials

The transverse tension fatigue life of S2/8552 glass-epoxy and IM7/8552 carbon-epoxy was characterized using flexure tests of 90-degree laminates loaded in 3-point and 4-point bending. The influence of specimen polishing and specimen configuration on transverse tension fatigue life was examined using the glass-epoxy laminates. Results showed that 90-degree bend specimens with polished machined edges and polished tension-side surfaces, where bending failures where observed, had lower fatigue lives than unpolished specimens when cyclically loaded at equal stress levels. The influence of specimen thickness and the utility of a Weibull scaling law was examined using the carbon-epoxy laminates. The influence of test frequency on fatigue results was also documented for the 4-point bending configuration. A Weibull scaling law was used to predict the 4-point bending fatigue lives from the 3-point bending curve fit and vice-versa. Scaling was performed based on maximum cyclic stress level as well as fatigue life. The scaling laws based on stress level shifted the curve fit S-N characterizations in the desired direction, however, the magnitude of the shift was not adequate to accurately predict the fatigue lives. Furthermore, the scaling law based on fatigue life shifted the curve fit S-N characterizations in the opposite direction from measured values. Therefore, these scaling laws were not adequate for obtaining accurate predictions of the transverse tension fatigue lives.

OBrien, T. Kevin↗
NASA NTRS1986

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Rodriguez, Pedro I.↗
NASA NTRS1993

Achieving high data reduction with integral cubic B-splines

During geometry processing, tangent directions at the data points are frequently readily available from the computation process that generates the points. It is desirable to utilize this information to improve the accuracy of curve fitting and to improve data reduction. This paper presents a curve fitting method which utilizes both position and tangent direction data. This method produces G(exp 1) non-rational B-spline curves. From the examples, the method demonstrates very good data reduction rates while maintaining high accuracy in both position and tangent direction.

Chou, Jin J.↗
NASA NTRS2005

Fitting Nonlinear Curves by use of Optimization Techniques

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Hill, Scott A.↗
NASA NTRS1973

On the reduction of occultation light curves

The two basic methods of reducing occultation light curves - curve fitting and inversion - are reviewed and compared. It is shown that the curve fitting methods have severe problems of nonuniqueness. In addition, in the case of occultation curves dominated by spikes, it is not clear that such solutions are meaningful. The inversion method does not suffer from these drawbacks. Methods of deriving temperature profiles from refractivity profiles are then examined. It is shown that, although the temperature profiles are sensitive to small errors in the refractivity profile, accurate temperatures can be obtained, particularly at the deeper levels of the atmosphere. The ambiguities that arise when the occultation curve straddles the turbopause are briefly discussed.

Wasserman, L.↗
DOE OSTI2024

Low-Cost Heliostat for High-Flux Small-Area Receivers (Final Technical Report)

This project analyzed a two-stage heliostat concept consisting of a tracking stage and a concentrating stage. The tracking stage uses mirrors mounted on a common drive that move to track the sun. The concentrating stage consists of stationary mirrors that each have a unique angle to direct rays towards a small-area, high-flux, point-focused receiver. By splitting the collection and concentrating process into two stages, multiple small, inexpensive mirrors can share a structure and be controlled by a single drive in the tracking stage. The project effort developed modeling techniques that were specifically relevant to this two-stage heliostat concept. Both field-level and unit-level models were developed. The field-level model does not explicitly consider unit-level losses which are predicted by the unit-level model and then integrated into the field-level model through a correlation referred to as an efficiency modifier. This approach is referred to as the two-model approach; the development and demonstration of this two-model approach for a multi-stage heliostat technology is a key outcome of this work. The field-level model is used to design a field that hits a specific design day power given a set of heliostat design parameters. An oversized field is simulated and then heliostat units are removed based on their annual energy production in order to generate the highest performing field. The field reduction procedure fits a smooth curve fit to annual energy production as a function of position in the field which has the effect of reducing the noise that is otherwise caused by the Monte Carlo ray tracing technique. This approach is referred to as the annual energy fit method and substantially reduces computational run time for a given field level modeling accuracy. The annual energy fit approach enables the selection of a properly sized, high-performing field using orders of magnitude fewer rays than would otherwise be possible and the development of this approach is a second key outcome of this work. These models are used within a genetic optimization algorithm in order to optimize the geometric parameters associated with a heliostat in order to achieve the lowest cost per unit of collected design day power. The cost modeling that underlies the optimization is a simple, scaling type analysis backed up by a much more detailed Design for Manufacture and Assembly (DFMA) analysis. Although the figure of merit used for optimization was not cost per mirror area, this metric is reasonable to use as a means of comparison. The optimally designed 500 kW design has a tracking mirror specific cost of $181.85/m 2 , which is significantly larger than the target value and also larger than the current state of the art. The cost of the torque-tube type linkages contributed substantially to the overall cost. Based on this observation, potentially attractive alternative design configuration utilizing a capstan type actuation system should be investigated. Finally, NREL compared the performance of the two-stage heliostat to the performance of a focused and different sized flat conventional heliostats and showed that, as expected, additional losses versus the convention heliostat caused by a worse cosine efficiency, two stages of reflection, and interstage interactions. The two-stage heliostat requires around 75% more reflective area than a flat 1x1 meter conventional heliostat (similar to a focused heliostat) and 40% more than a flat 2x2 meter conventional heliostat.

14 SOLAR ENERGY↗
NASA NTRS1989

Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium

The conservation equations for simulating hypersonic flows in thermal and chemical nonequilibrium and details of the associated physical models are presented. These details include the curve fits used for defining thermodynamic properties of the 11 species air model, curve fits for collision cross sections, expressions for transport properties, the chemical kinetics models, and the vibrational and electronic energy relaxation models. The expressions are formulated in the context of either a two or three temperature model. Greater emphasis is placed on the two temperature model in which it is assumed that the translational and rotational energy models are in equilibrium at the translational temperature, T, and the vibrational, electronic, and electron translational energy modes are in equilibrium at the vibrational temperature, T sub v. The eigenvalues and eigenvectors associated with the Jacobian of the flux vector are also presented in order to accommodate the upwind based numerical solutions of the complete equation set.

Peter A. Gnoffo↗
NASA NTRS1993

Development of a gridless CFD method

The objective of this paper is to stimulate ideas concerning alternative approaches to discretizing fluid flow problems, i.e., the so-called gridless approach. The gridless approach uses only clouds of points and does not require that the points be connected to form a grid as is necessary in conventional CFD algorithms. The governing equations are solved directly by performing local least-squares curve fits in each cloud of points and then analytically differentiating the resulting curve fits to approximate the derivatives. A discussion of these topics is presented in viewgraph form.

John T Batina↗
NASA NTRS1996

Studies of Vestibular Neurons in Normal, Hyper- and Hypogravity

During the past year, pre-, in- and postflight studies were conducted in association with the Axon project for Bion 10 (Cosmos 2229). Recordings were made during pre- and postflight studies, from 118 horizontal semicircular canal afferents and 27 vestibular nucleus neurons in 7 rhesus monkeys; 137 pulse rotation protocols alone were executed (548 acceleration and deceleration responses were curve fit). Usable data was obtained from 127 horizontal afferents concerning their spontaneous discharge. Curve fits and analysis was made of sinusoidal and sum of sinusoidal responses from 42 and 35 horizontal afferents, respectively. Also recordings were made from neurons inflight from the two flight animals. The mean spontaneous rate varied from 128 spikes/sec. during preflight to 92 spikes/sec during postflight (day 5) - a change of 28%. In direct contrast to the results of Cosmos 2044, the best fitted neural adaptation operator (k) and the gain of the pulse response were decreased during post flight when compared to preflight. Surprisingly, the best fitted gain and k values for the sum of sines were slightly elevated during post flight tests. The gain and phase of single sine responses were compared for pre- and post flight tests and compared to a larger population of afferents. In contrast to Cosmos 2044 results where on the first day of post flight testing the gains of the best fitted sine response were skewed toward the higher values of the Miles and Braitman distribution, the gain of the best fitted sine responses during the first day of post flight testing (day 2) during Cosmos 2229 were exactly on the mode of the Miles and Braitman distribution. Thus, at least for the periodic stimuli, (pulses and sine waves) we found no change in gain and neural adaptation during post flight testing following Cosmos 2229. This conclusion is different from the one derived following the Cosmos 2044 flight. Cosmos flight 2229 differed from Cosmos flight 2044 in several significant ways: For example, during preflight, (1) The animals preflight training was different (less well trained on the gaze task) and (2) the animals were exposed to more experimental manipulations (surgical and rotational). Inflight, (1) the animals were required to make a pointing gesture (motor response) in association with eye movements to obtain reward, (2) the inflight diet was different (more balanced), (3) the feeder for one of the animals clogged following 9 days of flight resulting in evident dehydration and probably less head motion exposure in that monkey and (4) there was limited video taping of the monkeys in space. During postflight, (1) we were unable to test the flight animals until 26 hours postflight as compared to 14.5 hours during Cosmos 2044, (2) the animals received significantly more exposure to motion stimuli during postflight testing than during Cosmos 2044. These differences in the vestibular environment will require analysis of several parameters other than just neural and eye movement responses. For example, computer programs will have to be written and used to recover and quantify the number of head movements made by each animal during flight. This activity is critical to the production of neural adaptation and increased gain.

Correia, Manning J.↗
NASA NTRS1983

Fitting voltage curves with an electrochemically derived equation

Previous work is refined and extended to describe the discharge curve of Ni-Cd cells. Several models are discussed which are based on chronopotentiometry theory and on a thermodynamic approach. Emphasis is placed on improvement of the fit for the initial portion of discharge. Equations are presented which improve the fit for all regions of the discharge curve.

Spritzer, M. S.↗
NASA NTRS1992

Parameterization of solar cells

The aggregation (sorting) of the individual solar cells into an array is commonly based on a single operating point on the current-voltage (I-V) characteristic curve. An alternative approach for cell performance prediction and cell screening is provided by modeling the cell using an equivalent electrical circuit, in which the parameters involved are related to the physical phenomena in the device. These analytical models may be represented by a double exponential I-V characteristic with seven parameters, by a double exponential model with five parameters, or by a single exponential equation with four or five parameters. In this article we address issues concerning methodologies for the determination of solar cell parameters based on measured data points of the I-V characteristic, and introduce a procedure for screening of solar cells for arrays. We show that common curve fitting techniques, e.g., least squares, may produce many combinations of parameter values while maintaining a good fit between the fitted and measured I-V characteristics of the cell. Therefore, techniques relying on curve fitting criteria alone cannot be directly used for cell parameterization. We propose a consistent procedure which takes into account the entire set of parameter values for a batch of cells. This procedure is based on a definition of a mean cell representing the batch, and takes into account the relative contribution of each parameter to the overall goodness of fit. The procedure is demonstrated on a batch of 50 silicon cells for Space Station Freedom.

Appelbaum, J.↗
DOE OSTI2022

Extracting single fiber transverse and shear moduli from off-axis misalignment fiber tensile testing

Small diameter (<100 μm) fibers (e.g. carbon fibers, Kevlar, and fiberglass) and wires (e.g. ultrafine copper and aluminum wires) are frequently used in many different engineering applications, such as for light weighting structures, electromagnetic shielding for aircraft/infrastructure/EVs, vibration damping, biological sensors, aerospace electrical devices, and electric windings just to name a few. Due to the manufacturing process, the fibers and wires are pulled and stretched to produce a preferential alignment. Therefore, thin fibers and wires typically display different properties along the length of the fiber as opposed to their cross section and many fibers/wires are considered transversely isotropic. The axial properties of fibers/wires can be ascertained via tensile testing of single-filaments or fiber tows, but the radial properties require much more effort to measure. Knowing these properties is important for the accurate prediction of micromechanical models and manipulation of fibers during micromanufacturing. In this paper, a new technique was developed to determine the transverse/shear moduli and strength of a material by conducting tensile tests of the material at increasing misalignment angles from the tensile axis. Due to the transversely isotropic nature of the material, the transverse/shear moduli and strength influence the experimental results recorded by the test machine to different degrees based on the amount of misalignment in the test setup. An equation was derived to determine the influence of each of the material properties based on the misalignment angle by manipulating the stiffness matrix for transversely isotropic materials using the transformation matrices. Then, curve fitted coefficients were used to identify the material properties. Here, the strengths were similarly determined by curve fitting an off-axis Tsai-Hill failure criteria to determine the influence of transverse, shear, and tensile strengths based on the complex loading condition provided by the off-axis tensile test. Zoltek Panex 35 carbon fibers were used to demonstrate this new technique and the determined properties were then compared to those obtained from nanoindentation and from literature. Fracture surfaces provide insight into the different failure mechanisms at various misalignment angles.

36 MATERIALS SCIENCE↗
NASA NTRS1982

A mathematical model of a single main rotor helicopter for piloted simulation

A mathematical model, suitable for piloted simulation of the flying qualities of helicopters, is a nonlinear, total force and moment model of a single main rotor helicopter. The model has ten degrees of freedom: six rigid body, three rotor flapping, and the rotor rotational degrees of freedom. The rotor model assumes rigid blades with rotor forces and moments radially integrated and summed about the azimuth. The fuselage aerodynamic model uses a detailed representation over a nominal angle of attack and sideslip range of + or - 15 deg., as well as a simplified curve fit at large angles of attack or sideslip. Stabilizing surface aerodynamics are modeled with a lift curve slope between stall limits and a general curve fit for large angles of attack. A generalized stability and control augmentation system is described. Additional computer subroutines provide options for a simplified engine/governor model, atmospheric turbulence, and a linearized six degree of freedom dynamic model for stability and control analysis.

Talbot, P. D.↗
NASA NTRS1999

Method and Apparatus for Evaluating Multilayer Objects for Imperfections

A multilayer object having multiple layers arranged in a stacking direction is evaluated for imperfections such as voids, delaminations and microcracks. First. an acoustic wave is transmitted into the object in the stacking direction via an appropriate transducer/waveguide combination. The wave propagates through the multilayer object and is received by another transducer/waveguide combination preferably located on the same surface as the transmitting combination. The received acoustic wave is correlated with the presence or absence of imperfections by, e.g., generating pulse echo signals indicative of the received acoustic wave. wherein the successive signals form distinct groups over time. The respective peak amplitudes of each group are sampled and curve fit to an exponential curve. wherein a substantial fit of approximately 80-90% indicates an absence of imperfections and a significant deviation indicates the presence of imperfections. Alternatively, the time interval between distinct groups can be measured. wherein equal intervals indicate the absence of imperfections and unequal intervals indicate the presence of imperfections.

Heyman, Joseph S.↗
NASA NTRS1997

Method and apparatus for evaluating multilayer objects for imperfections

A multilayer object having multiple layers arranged in a stacking direction is evaluated for imperfections such as voids, delaminations and microcracks. First, an acoustic wave is transmitted into the object in the stacking direction via an appropriate transducer/waveguide combination. The wave propagates through the multilayer object and is received by another transducer/waveguide combination preferably located on the same surface as the transmitting combination. The received acoustic wave is correlated with the presence or absence of imperfections by, e.g., generating pulse echo signals indicative of the received acoustic wave, wherein the successive signals form distinct groups over time. The respective peak amplitudes of each group are sampled and curve fit to an exponential curve, wherein a substantial fit of approximately 80-90% indicates an absence of imperfections and a significant deviation indicates the presence of imperfections. Alternatively, the time interval between distinct groups can be measured, wherein equal intervals indicate the absence of imperfections and unequal intervals indicate the presence of imperfections.

Heyman, Joseph S.↗