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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Weighted SAW reflector gratings for orthogonal frequency coded SAW tags and sensors

Weighted surface acoustic wave reflector gratings for coding identification tags and sensors to enable unique sensor operation and identification for a multi-sensor environment. In an embodiment, the weighted reflectors are variable while in another embodiment the reflector gratings are apodized. The weighting technique allows the designer to decrease reflectively and allows for more chips to be implemented in a device and, consequently, more coding diversity. As a result, more tags and sensors can be implemented using a given bandwidth when compared with uniform reflectors. Use of weighted reflector gratings with OFC makes various phase shifting schemes possible, such as in-phase and quadrature implementations of coded waveforms resulting in reduced device size and increased coding.

Puccio, Derek↗
NASA NTRSDate not supplied

Aero-Propulsive Modeling for eVTOL Aircraft Using Wind Tunnel Testing with Multisine Inputs

A novel approach for modeling the aero-propulsive characteristics of an electric vertical takeoff and landing (eVTOL) aircraft was developed and demonstrated in wind tunnel testing. The approach was applied to the NASA LA-8 tandem tilt-wing eVTOL aircraft, using an efficient, hybrid experiment design composed of a static I-optimal response surface design for slowly-varying test variables, and dynamic orthogonal phase-optimized multisine excitations for the control surfaces and electric propulsors. Both the static and dynamic experiment designs were executed simultaneously to collect informative data for model identification. Statistically-weighted multivariate orthogonal function modeling was used to combine local modeling results computed in the frequency domain using data collected with dynamic excitations operating on the control effectors to form an aggregate aero-propulsive model. The final identified model exhibited good predictive capability when compared to validation data acquired separately from the data used to develop the model. The required test time using these new techniques was reduced by at least a factor of five compared to previous static wind tunnel testing for the LA-8 aircraft, while providing more informative data, greater parameterization flexibility, and high-quality models.

system identification↗
NASA NTRS1999

30 Years of Wahba's Problem

This article discusses a problem proposed by Grace Wahba: Find the orthogonal matrix A with determinant +1 that minimizes the loss function L(A) is identical with the 1/2(summation from i( a(sub i) * absolute value of (b(sub i)- Ar(sub i))squared). where {b(sub i)} is a set of unit vectors measured in a spacecraft's body frame, {r(sub i)} e the corresponding unit vectors in a reference frame and {a(sub i) are non-negative weights). The orthogonal Procrustes problem is to find the orthogonal matrix A that is closest to B in the sense of the Fobenius norm, so that Wahba's Problem is equivalent to the orthogonal Procrustes problem with the provision that the determinant of A must be +1. The article reviews various solutions to this problem and the implementations of the various solutions.

Markley, F. Landis↗
NASA NTRS1990

Orthogonal subspaces for correlation masking

A digital correlation mask that induces orthogonality among a prescribed set of reference imagery is described. In this particular implementation, the resulting correlation is undersampled and shift-variant, though if it is applied to optical correlators, those limitations are removed. A method of introducing orthogonality among the weights among the training set from which filter values are obtained is derived, so that the correlation value from a given filter is representative of the unique nature of the reference object as compared against the other objects in the training class.

Juday, Richard D.↗
NASA NTRS1996

The weight hierarchies and chain condition of a class of codes from varieties over finite fields

The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.

Wu, Xinen↗
NASA NTRS1973

Preliminary numerical analysis of improved gas chromatograph model

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Woodrow, P. T.↗
NASA NTRS1982

A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

Emukashvily, I. M.↗
NASA NTRS2001

A Canonical Ensemble Correlation Prediction Model for Seasonal Precipitation Anomaly

This report describes an optimal ensemble forecasting model for seasonal precipitation and its error estimation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. This new CCA model includes the following features: (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States precipitation field. The predictor is the sea surface temperature.

Shen, Samuel S. P.↗
NASA NTRS2001

Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model

This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.

Shen, Samuel S. P.↗
NASA NTRS1997

Neural Learning Using Orthogonal Arrays

The paper proposes the use of the orthogonal arrays for neural network learning. Learning can be seen as a search for the neural weights that give an optimal network performance.

orthogonal arrays weight values robust design opti↗
NASA NTRS1986

Development of a reaction wheel attitude control system for sounding rocket experiments and small Shuttle-based free flyers

A three-axis reaction wheel control system is currently under development. Initial emphasis is on a magnetic field reference, although the system is easily adaptable to other positional references, e.g., the gyroscopic. The system is housed in a skin section 17.25 inches in diameter and approximately 10 inches long. Current weight estimate is 75 pounds. An orthogonal triad of dc motors forms the basis of the system. Power is provided by silver-zinc cells and controlled by an 8-bit microprocessor. The control law is presented and the dynamical equations derived. Simulation results show that a payload with a roll MOI of 4.1 sl/sq ft and a transverse MOI of 20.3 sl/sq ft can typically be reoriented 90 degrees in 20-35 seconds, depending upon the initial body rates.

Ward, P. R.↗
NASA NTRS1991

Analysis of structural response data using discrete modal filters

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Freudinger, Lawrence C.↗
NASA NTRS1998

Bell-Curve Based Evolutionary Optimization Algorithm

The paper presents an optimization algorithm that falls in the category of genetic, or evolutionary algorithms. While the bit exchange is the basis of most of the Genetic Algorithms (GA) in research and applications in America, some alternatives, also in the category of evolutionary algorithms, but use a direct, geometrical approach have gained popularity in Europe and Asia. The Bell-Curve Based Evolutionary Algorithm (BCB) is in this alternative category and is distinguished by the use of a combination of n-dimensional geometry and the normal distribution, the bell-curve, in the generation of the offspring. The tool for creating a child is a geometrical construct comprising a line connecting two parents and a weighted point on that line. The point that defines the child deviates from the weighted point in two directions: parallel and orthogonal to the connecting line, the deviation in each direction obeying a probabilistic distribution. Tests showed satisfactory performance of BCB. The principal advantage of BCB is its controllability via the normal distribution parameters and the geometrical construct variables.

Sobieszczanski-Sobieski, J.↗
NASA NTRS2014

Creating a Test Validated Structural Dynamic Finite Element Model of the X-56A Aircraft

Small modeling errors in the finite element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of the Multi Utility Technology Test-bed, X-56A aircraft, is the flight demonstration of active flutter suppression, and therefore in this study, the identification of the primary and secondary modes for the structural model tuning based on the flutter analysis of the X-56A aircraft. The ground vibration test-validated structural dynamic finite element model of the X-56A aircraft is created in this study. The structural dynamic finite element model of the X-56A aircraft is improved using a model tuning tool. In this study, two different weight configurations of the X-56A aircraft have been improved in a single optimization run. Frequency and the cross-orthogonality (mode shape) matrix were the primary focus for improvement, while other properties such as center of gravity location, total weight, and offdiagonal terms of the mass orthogonality matrix were used as constraints. The end result was a more improved and desirable structural dynamic finite element model configuration for the X-56A aircraft. Improved frequencies and mode shapes in this study increased average flutter speeds of the X-56A aircraft by 7.6% compared to the baseline model.

ground vibration test↗
NASA NTRS2014

Creating a Test-Validated Finite-Element Model of the X-56A Aircraft Structure

Small modeling errors in a finite-element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of the X-56A Multi-Utility Technology Testbed aircraft is the flight demonstration of active flutter suppression and, therefore, in this study, the identification of the primary and secondary modes for the structural model tuning based on the flutter analysis of the X-56A aircraft. The ground-vibration test-validated structural dynamic finite-element model of the X-56A aircraft is created in this study. The structural dynamic finite-element model of the X-56A aircraft is improved using a model-tuning tool. In this study, two different weight configurations of the X-56A aircraft have been improved in a single optimization run. Frequency and the cross-orthogonality (mode shape) matrix were the primary focus for improvement, whereas other properties such as c.g. location, total weight, and off-diagonal terms of the mass orthogonality matrix were used as constraints. The end result was an improved structural dynamic finite-element model configuration for the X-56A aircraft. Improved frequencies and mode shapes in this study increased average flutter speeds of the X-56A aircraft by 7.6% compared to the baseline model.

ground vibration test↗
NASA NTRS2008

Ultra-Stable Beacon Source for Laboratory Testing of Optical Tracking

The ultra-stable beacon source (USBS) provides a laser-beam output with a very low angular jitter and can be used as an absolute angular reference to simulate a beacon in the laboratory. The laser is mounted on the top of a very short (approximately equal to 1 m) inverted pendulum (IP) with its optical axis parallel to the carbon fiber pendulum leg. The 85-cm, carbon fiber rods making up the leg are very lightweight and rigid, and are supported by a flex-joint at the bottom (see figure). The gimbal-mounted laser is a weight-adjustable load of about 1.5 kg with its center of rotation co-located with the center of percussion of the inverted pendulum. This reduces the coupling of transverse motion at the base of the pendulum to angular motion of the laser at the top. The inverted pendulum is mounted on a gimbal with its center of rotation coinciding with the pivot position of the inverted pendulum flexure joint. This reduces coupling of ground tilt at the inverted pendulum base to motion of the laser mounted at the top. The mass of the top gimbal is adjusted to give the pendulum a very low resonant frequency (approximately equal to 10 mHz) that filters transverse seismic disturbances from the ground where the base is attached. The motion of the IP is monitored by an optical-lever sensor. The laser light is reflected by the mirror on the IP, and then is detected by a quadrant photo-detector (QPD). The position of the beam spot on the QPD corresponds to the tilt of the IP. Damping of this motion is provided by two coil and magnet pairs. The bottom gimbal mount consists of two plates. The IP is mounted on the second plate. The first plate is supported by two posts through needles and can be rotated about the axis connecting the tips of the needles. The second plate hangs from the first plate and can be rotated about the axis perpendicular to the first plate. As a result, the second plate acts as a two-axis rotation stage. Its center of rotation is located at the effective bending point of the flex-joint. The second plate is pressed against two screw actuators by the weight of the IP. The screw actuators are orthogonal to each other and are used to adjust the inclination of the second plate. The actuators are driven by stepper motors. The whole IP system is housed in a box made of Lexan plastic plates to provide isolation from air currents and temperature variations. The signals from the sensors are processed and recorded with a PC using the xPC Target realtime environment of Math- Works. The control algorithms are written using the Simulink package from The MathWorks.

Aso, Yoichi↗
NASA NTRS1988

GENIE - Generation of computational geometry-grids for internal-external flow configurations

Progress realized in the development of a master geometry-grid generation code GENIE is presented. The grid refinement process is enhanced by developing strategies to utilize bezier curves/surfaces and splines along with weighted transfinite interpolation technique and by formulating new forcing function for the elliptic solver based on the minimization of a non-orthogonality functional. A two step grid adaptation procedure is developed by optimally blending adaptive weightings with weighted transfinite interpolation technique. Examples of 2D-3D grids are provided to illustrate the success of these methods.

Soni, B. K.↗
NASA NTRS1993

Polar decomposition for attitude determination from vector observations

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Bar-Itzhack, Itzhack Y.↗