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NASA NTRS1989

Laser transit anemometer software development program

Algorithms were developed for the extraction of two components of mean velocity, standard deviation, and the associated correlation coefficient from laser transit anemometry (LTA) data ensembles. The solution method is based on an assumed two-dimensional Gaussian probability density function (PDF) model of the flow field under investigation. The procedure consists of transforming the data ensembles from the data acquisition domain (consisting of time and angle information) to the velocity space domain (consisting of velocity component information). The mean velocity results are obtained from the data ensemble centroid. Through a least squares fitting of the transformed data to an ellipse representing the intersection of a plane with the PDF, the standard deviations and correlation coefficient are obtained. A data set simulation method is presented to test the data reduction process. Results of using the simulation system with a limited test matrix of input values is also given.

Abbiss, John B.↗

NASA NTRS1989

Analysis of lightning field changes during active Florida thunderstorms

A computer algorithm for deriving accurate values of lightning-caused changes in cloud electric fields under active storm conditions was developed and applied to data obtained during two thunderstorms from a network of ground-based electric field mills at the NASA Kennedy Space Center and the Cape Canaveral Air Force Station. The resulting field changes were analyzed using a least-squares optimization procedure and point-charge (Q) and point-dipole (P) models. The values and the time variations of the Q-model parameters under active storm conditions were found to be similar to those reported by Maier and Krider (1986) for small storms, when the computations were carried out with the same analysis criteria and comparable biases. The parameters of the P solutions were found to vary with time within the storm interval and from storm to storm.

Koshak, William J.↗

NASA NTRS1992

An improved plate theory of order (1,2) for thick composite laminates

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.

Tessler, A.↗

NASA NTRS1987

The corrosion mechanisms for primer coated 2219-T87 aluminum

To investigate metal surface corrosion and the breakdown of metal protective coatings, the ac Impedance Method was applied to zinc chromate primer coated 2219-T87 aluminum. The EG&GPARC Model 368 ac Impedance Measurement System, along with dc measurements with the same system using the Polarization Resistance Method, was used to monitor changing properties of coated aluminum disks immersed in 3.5 percent NaCl solutions buffered at pH 5.5 and pH 8.2 over periods of 40 days each. The corrosion system can be represented by an electronic analog called an equivalent circuit consisting of resistors and capacitors in specific arrangements. This equivalent circuit parallels the impedance behavior of the corrosion system during a frequency scan. Values for resistances and capacitances, that can be assigned in the equivalent circuit following a least squares analysis of the data, describe changes occurring on the corroding metal surface and in the protective coatings. A suitable equivalent circuit has been determined which predicts the correct Bode phase and magnitude for the experimental sample. The dc corrosion current density data are related to equivalent circuit element parameters.

Danford, Merlin D.↗

NASA NTRS1988

An electrochemical study of corrosion protection by primer-topcoat systems on 4130 steel with ac impedance and dc methods

To investigate metal surface corrosion and the breakdown of metal protective coatings, the ac impedance method is applied to six systems of primer coated and primer topcoated 4130 steel. Two primers were used: a zinc-rich epoxy primer and a red lead oxide epoxy primer. The epoxy-polyamine topcoat was used in four of the systems. The EG and G-PARC Model 368 ac impedance measurement system, along with dc measurements with the same system using the polarization resistance method, were used to monitor changing properties of coated 4230 steel disks immersed in 3.5 percent NaCl solutions buffered at pH 5.4 over periods of 40 to 60 days. The corrosion system can be represented by an electronic analog called an equivalent circuit consisting of resistors and capacitors in specific arrangements. This equivalent circuit parallels the impedance behavior of the corrosion system during a frequency scan. Values for the resistors and capacitors, that can be assigned in the equivalent circuit following a least-squares analysis of the data, describe changes that occur on the corroding metal surface and in the protective coatings. Two equivalent circuits have been determined that predict the correct Bode phase and magnitude of the experimental sample at different immersion times. The dc corrosion current density data are related to equivalent circuit element parameters. Methods for determining corrosion rate with ac impedance parameters are verified by the dc method.

Mendrek, M. J.↗

NASA NTRS1995

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

Bui, Trong T.↗

NASA NTRS2001

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Tessler, A.↗

NASA NTRS1974

Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry

Curve-fit formulas are presented for the stagnation-point radiative heating rate, cooling factor, and shock standoff distance for inviscid flow over blunt bodies at conditions corresponding to high-speed earth entry. The data which were curve fitted were calculated by using a technique which utilizes a one-strip integral method and a detailed nongray radiation model to generate a radiatively coupled flow-field solution for air in chemical and local thermodynamic equilibrium. The range of free-stream parameters considered were altitudes from about 55 to 70 km and velocities from about 11 to 16 km.sec. Spherical bodies with nose radii from 30 to 450 cm and elliptical bodies with major-to-minor axis ratios of 2, 4, and 6 were treated. Powerlaw formulas are proposed and a least-squares logarithmic fit is used to evaluate the constants. It is shown that the data can be described in this manner with an average deviation of about 3 percent (or less) and a maximum deviation of about 10 percent (or less). The curve-fit formulas provide an effective and economic means for making preliminary design studies for situations involving high-speed earth entry.

Suttles, J. T.↗

NASA NTRS1982

Modeling the thermal structure and magnetic properties of the crust of active regions with application to the Rio Grande rift

Experiments in Curie depth estimation from long wavelength magnetic anomalies are summarized. The heart of the work is equivalent-layer-type magnetization models derived by inversion of high-elevation, long wavelength magnetic anomaly data. The methodology is described in detail in the above references. A magnetization distribution in a thin equivalent layer at the Earth's surface having maximum detail while retaining physical significance, and giving rise to a synthetic anomaly field which makes a best fit to the observed field in a least squares sense is discussed. The apparent magnetization contrast in the equivalent layer is approximated using an array of dipoles distributed in equal area at the Earth's surface. The dipoles are pointed in the direction of the main magnetic field, which carries the implicit assumption that crustal magnetization is dominantly induced or viscous. The determination of the closest possible dipole spacing giving a stable inversion to a solution having physical significance is accomplished by plotting the standard deviation of the solution parameters against their spatial separation for a series of solutions.

Source record↗

NASA NTRS1992

Finite element computation of incompressible flows

Among the solution techniques presented for FEM computation of incompressible flows are stabilized formulations designed to prevent the numerical oscillations that may be generated by (1) the presence of dominant advection terms in the governing equations, or (2) the failure to use an acceptable combination of interpolation functions to represent velocity and pressure fields. It is shown that the space-time formulation, in conjunction with the Galerkin-least squares methods, can be used to compute steady incompressible flows involving moving boundaries and interfaces; it is recommended that iteration methods be used to reduce the associated computational costs.

Tezduyar, T. E.↗

NASA NTRS2000

Autonomous Performance Monitoring System: Monitoring and Self-Tuning (MAST)

Maintaining the long-term performance of software onboard a spacecraft can be a major factor in the cost of operations. In particular, the task of controlling and maintaining a future mission of distributed spacecraft will undoubtedly pose a great challenge, since the complexity of multiple spacecraft flying in formation grows rapidly as the number of spacecraft in the formation increases. Eventually, new approaches will be required in developing viable control systems that can handle the complexity of the data and that are flexible, reliable and efficient. In this paper we propose a methodology that aims to maintain the accuracy of flight software, while reducing the computational complexity of software tuning tasks. The proposed Monitoring and Self-Tuning (MAST) method consists of two parts: a flight software monitoring algorithm and a tuning algorithm. The dependency on the software being monitored is mostly contained in the monitoring process, while the tuning process is a generic algorithm independent of the detailed knowledge on the software. This architecture will enable MAST to be applicable to different onboard software controlling various dynamics of the spacecraft, such as attitude self-calibration, and formation control. An advantage of MAST over conventional techniques such as filter or batch least square is that the tuning algorithm uses machine learning approach to handle uncertainty in the problem domain, resulting in reducing over all computational complexity. The underlying concept of this technique is a reinforcement learning scheme based on cumulative probability generated by the historical performance of the system. The success of MAST will depend heavily on the reinforcement scheme used in the tuning algorithm, which guarantees the tuning solutions exist.

Peterson, Chariya↗

NASA NTRS1992

A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds

We contrast two different solutions of the constant alpha, force-free MHD equation, both of which have been suggested as models for magnetic clouds: a solution in cylindrical coordinates and one in spherical coordinates. In line with the observation that magnetic clouds expand, we generalize these static models and construct their expanding counterparts. We find that expansion introduces in both cases a large asymmetry in the field strength signature which is in the same sense as that seen the the data, i.e. towards the leading edge of the cloud. We then do a least squares fit of the respective models to one-spacecraft data on a magnetic cloud. We find that the fitting routine converges in both cases. However, while purely formally we cannot distinguish between the two models using data from one spacecraft, the field components in the 'spherical' model have features not compatible with data on magnetic clouds.

Farrugia, C. J.↗

NASA NTRS1992

MIMO system identification using frequency response data

A solution to the problem of obtaining a multi-input, multi-output statespace model of a system from its individual input/output frequency responses is presented. The Residue Identification Algorithm (RID) identifies the system poles from a transfer function model of the determinant of the frequency response data matrix. Next, the residue matrices of the modes are computed guaranteeing that each input/output frequency response is fitted in the least squares sense. Finally, a realization of the system is computed. Results of the application of RID to experimental frequency responses of a large space structure ground test facility are presented and compared to those obtained via the Eigensystem Realization Algorithm.

Medina, Enrique A.↗

NASA NTRS1973

Geodetic analysis of Skylab altimetry preliminary data - SL/2 EREP pass 9

The author has identified the following significant results. The analysis was based on a time series intrinsic relationship between the satellite ephemeris, altimeter measured ranges, and the corresponding a priori values of subsatellite geoidal heights. Using sequential least squares processing with parameter weighting, the objective was to recover (1) the absolute geoidal heights of the subsatellite points, and (2) the associated altimeter calibration constant(s). Preliminary results from Skylab altimetry are given, using various combinations of orbit ephemeris and altimeter ranges as computed differently by NASA/JSC and NASA/Wallops. The influences of orbit accuracy, weighting functions, and a priori ground truth are described, based on the various combination solutions. It is shown that to deduce geoidal height by merely subtracting the height of the satellite from the altimeter range is inadmissible. The results of such direct subtraction can be very misleading if the orbit used is computed from data that included altimeter data used as height constraints. In view of the current state of knowledge, the use of geodetic ground truth samples as control benchmarks appears indispensable for the recovery of absolute geoidal heights with correct scale.

Mourad, A. G.↗

NASA NTRS1992

The spin vector of Venus determined from Magellan data

A control network of the north polar region of Venus has been established by selecting and measuring control points on full-resolution radar strips. The measurements were incorporated into a least-squares adjustment program that improved initial estimates of the coordinates of the control points, pole direction, and rotation rate of Venus. The current dataset contains 4206 measurements of 606 points on 619 radar strips. The accuracy of the determination is driven by spacecraft ephemeris errors. An accurate estimate of the rotation period of Venus was obtained by applying an ephemeris improvement technique. The second cycle closure orbits improved ephemeris solutions for 40 orbits (376-384, 520-528, 588-592, 658-668, 1002-1010, 1408-1412, 1746-1764, and 2166-2170) are included and fixed in the geodetic control computations, thus trying the network to the J2000 coordinate system.

Davies, M. E.↗

NASA NTRS1980

An equivalent source model of the satellite-altitude magnetic anomaly field over Australia

The low-amplitude, long-wavelength magnetic anomaly field measured between 400 and 700 km elevation over Australia by the POGO satellites is modeled by means of the equivalent source technique. Magnetic dipole moments are computed for a latitude-longitude array of dipole sources on the earth's surface such that the dipoles collectively give rise to a field which makes a least squares best fit to that observed. The distribution of magnetic moments is converted to a model of apparent magnetization contrast in a layer of constant (40 km) thickness, which contains information equivalent to the lateral variation in the vertical integral of magnetization down to the Curie isotherm and can be transformed to a model of variable thickness magnetization. It is noted that the closest equivalent source spacing giving a stable solution is about 2.5 deg, corresponding to about half the mean data elevation, and that the magnetization distribution correlates well with some of the principle tectonic elements of Australia.

Mayhew, M. A.↗

NASA NTRS1972

Synthesis of stiffened conical shells.

The development of a method to effect the automated minimum weight design of ring and stringer stiffened shells is presented. Membrane theory is used for the shell prebuckling analysis. The buckling analysis is based upon an arbitrary shell of revolution computer program. The structural analysis includes both buckling and yielding modes of failure. The synthesis involves the coupling of an exterior penalty function with a method for the unconstrained minimization of a function comprised of a sum of squares. Results of the application of the method to the design of the Viking Aeroshell cone are presented. The least weight Viking Aeroshell appears to be an all magnesium shell with ring stiffeners of hollow circular cross section. Because the method incorporates a general shell of revolution buckling analysis, it can be readily modified and applied to the design of any axisymmetrically loaded uniformly stiffened shell of revolution for which a membrane prebuckling solution exists.

Thornton, W. A.↗

NASA NTRS1976

DHARMA - Discriminant hyperplane abstracting residuals minimization algorithm for separating clusters with fuzzy boundaries

Learning of discriminant hyperplanes in imperfectly supervised or unsupervised training sample sets with unreliably labeled samples along the fuzzy joint boundaries between sample clusters is discussed, with the discriminant hyperplane designed to be a least-squares fit to the unreliably labeled data points. (Samples along the fuzzy boundary jump back and forth from one cluster to the other in recursive cluster stabilization and are considered unreliably labeled.) Minimization of the distances of these unreliably labeled samples from the hyperplanes does not sacrifice the ability to discriminate between classes represented by reliably labeled subsets of samples. An equivalent unconstrained linear inequality problem is formulated and algorithms for its solution are indicated. Landsat earth sensing data were used in confirming the validity and computational feasibility of the approach, which should be useful in deriving discriminant hyperplanes separating clusters with fuzzy boundaries, given supervised training sample sets with unreliably labeled boundary samples.

Dasarathy, B. V.↗