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NASA NTRS1994

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Enns, Dale F.↗

NASA NTRS1995

High Accuracy In-Flight Wavelength Calibration of Imaging Spectrometry Data

Accurate wavelength calibration of imaging spectrometer data is essential if proper atmospheric transmission corrections are to be made to obtain apparent surface reflectance. Accuracies of 0.1 nm are necessary for a 10 nm-sampling instrument in order to match the slopes of the deep atmospheric water vapor features that dominate the 0.7-2.3 micrometer regions. The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) is calibrated in the laboratory to determine the wavelength position and full-width-half-maximum (FWHM) response for each of the 224 channels. The accuracies are limited by the quality of the monochromator used as a source. The accuracies vary from plus or minus to plus or minus 1.5 nm depending on the wavelength region, in general decreasing with increasing wavelength. Green et al. make corrections to the wavelength calibrations by using the known positions of 14 atmospheric absorption features throughout the 0.4-2.5 micrometer wavelength region. These features, having varying width and intensity, were matched to the MODTRAN model with a non-linear least squares fitting algorithm. A complete calibration was developed for all 224 channels by interpolation. Instrument calibration cannot be assumed to be stable to 0.1 nm over a flight season given the rigors of thermal cycling and launch and landing loads. The upcoming sensor HYDICE will require a means for in-flight spectral calibration of each scene because the calibration is both temperature and pressure sensitive. In addition, any sensor using a two-dimensional array has the potential for systematic wavelength shifts as a function of cross-track position, commonly called 'smile'. Therefore, a rapid means for calibrating complete images will be required. The following describes a method for determining instrument wavelength calibration using atmospheric absorption features that is efficient enough to be used for entire images on workstations. This study shows the effect of the surface reflectance on the calibration accuracy and the calibration history for the AVIRIS B spectrometer over the 1992 flight season.

Goetz, Alexander F. H.↗

NASA NTRS1987

State-space self-tuning controllers for general multivariable stochastic systems

This paper presents a state-space approach for self-tuning control of a more general class of multivariable stochastic systems having a number of inputs equal or different from the number of outputs. The dynamic system is represented in the state-space innovation form with Luenberger's canonical structures. The model parameters and the Kalman gain are identified via either the extended least-squares algorithm or the least-squares ladder algorithm. The Kalman gain matrix and states can be estimated from the identified parameters without utilizing the standard state estimation algorithm. A long division method is introduced for finding the similarity transformation matrix.

Shieh, L. S.↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-851O network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS2001

Structural Damage Detection Using Virtual Passive Controllers

This paper presents novel approaches for structural damage detection which uses the virtual passive controllers attached to structures, where passive controllers are energy dissipative devices and thus guarantee the closed-loop stability. The use of the identified parameters of various closed-loop systems can solve the problem that reliable identified parameters, such as natural frequencies of the open-loop system may not provide enough information for damage detection. Only a small number of sensors are required for the proposed approaches. The identified natural frequencies, which are generally much less sensitive to noise and more reliable than the identified natural frequencies, are used for damage detection. Two damage detection techniques are presented. One technique is based on the structures with direct output feedback controllers while the other technique uses the second-order dynamic feedback controllers. A least-squares technique, which is based on the sensitivity of natural frequencies to damage variables, is used for accurately identifying the damage variables.

Lew, Jiann-Shiun↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the first two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-X510 network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS1987

State-space formulation of multi-shaker modal analysis

As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results have increased. This paper describes a new multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.

Craig, Roy R., Jr.↗

NASA NTRS1996

REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination

In order to find the attitude of a spacecraft with respect to a reference coordinate system, vector measurements are taken. The vectors are pairs of measurements of the same generalized vector, taken in the spacecraft body coordinates, as well as in the reference coordinate system. We are interested in finding the best estimate of the transformation between these coordinate system.s The algorithm called QUEST yields that estimate where attitude is expressed by a quarternion. Quest is an efficient algorithm which provides a least squares fit of the quaternion of rotation to the vector measurements. Quest however, is a single time point (single frame) batch algorithm, thus measurements that were taken at previous time points are discarded. The algorithm presented in this work provides a recursive routine which considers all past measurements. The algorithm is based on on the fact that the, so called, K matrix, one of whose eigenvectors is the sought quaternion, is linerly related to the measured pairs, and on the ability to propagate K. The extraction of the appropriate eigenvector is done according to the classical QUEST algorithm. This stage, however, can be eliminated, and the computation simplified, if a standard eigenvalue-eigenvector solver algorithm is used. The development of the recursive algorithm is presented and illustrated via a numerical example.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1987

Robust eigensystem assignment for flexible structures

An improved method is developed for eigenvalues and eigenvectors placement of a closed-loop control system using either state or output feedback. The method basically consists of three steps. First, the singular value of QR decomposition is used to generate an orthonormal basis that spans admissible eigenvector space corresponding to each assigned eigenvalue. Secondly, given a unitary matrix, the eigenvector set which best approximates the given matrix in the least-square sense and still satisfy eigenvalue cosntraints is determined. Thirdly, a unitary matrix is sought to minimize the error between the unitary matrix and the assignable eigenvector matrix. For use as the desired eigenvector set, two matrices, namely, the open-loop eigenvector matrix and its closest unitary matrix are proposed. The latter matrix generally encourages both minimum conditioning and control gains. In addition, the algorithm is formulated in real arithmetic for efficient implementation. To illustrate the basic concepts, numerical examples are included.

Juang, Jer-Nan↗

NASA NTRS1993

The three-dimensional structure of cumulus clouds over the ocean. 1: Structural analysis

Thermal channel (channel 6, 10.4-12.5 micrometers) images of five Landsat thematic mapper cumulus scenes over the ocean are examined. These images are thresholded using the standard International Satellite Cloud Climatology Project (ISCCP) thermal threshold algorithm. The individual clouds in the cloud fields are segmented to obtain their structural statistics which include size distribution, orientation angle, horizontal aspect ratio, and perimeter-to-area (PtA) relationship. The cloud size distributions exhibit a double power law with the smaller clouds having a smaller absolute exponent. The cloud orientation angles, horizontal aspect ratios, and PtA exponents are found in good agreement with earlier studies. A technique also is developed to recognize individual cells within a cloud so that statistics of cloud cellular structure can be obtained. Cell structural statistics are computed for each cloud. Unicellular clouds are generally smaller (less than or equal to 1 km) and have smaller PtA exponents, while multicellular clouds are larger (greater than or equal to 1 km) and have larger PtA exponents. Cell structural statistics are similar to those of the smaller clouds. When each cell is approximated as a quadric surface using a linear least squares fit, most cells have the shape of a hyperboloid of one sheet, but about 15% of the cells are best modeled by a hyperboloid of two sheets. Less than 1% of the clouds are ellipsoidal. The number of cells in a cloud increases slightly faster than linearly with increasing cloud size. The mean nearest neighbor distance between cells in a cloud, however, appears to increase linearly with increasing cloud size and to reach a maximum when the cloud effective diameter is about 10 km; then it decreases with increasing cloud size. Sensitivity studies of threshold and lapse rate show that neither has a significant impact upon the results. A goodness-of-fit ratio is used to provide a quantitative measure of the individual cloud results. Significantly improved results are obtained after applying a smoothing operator, suggesting the eliminating subresolution scale variations with higher spatial resolution may yield even better shape analyses.

Kuo, Kwo-Sen↗

NASA NTRS1999

Adaptive Error Estimation in Linearized Ocean General Circulation Models

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Chechelnitsky, Michael Y.↗

NASA NTRS2015

Wing Shape Sensing from Measured Strain

A new two-step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations. In the first step, a measured strain is fitted using a piecewise least-squares curve fitting method together with the cubic spline technique. These fitted strains are integrated twice to obtain deflection data along the fibers. In the second step, computed deflection along the fibers are combined with a finite element model of the structure in order to interpolate and extrapolate the deflection and slope of the entire structure through the use of the System Equivalent Reduction and Expansion Process. The theory is first validated on a computational model, a cantilevered rectangular plate wing. The theory is then applied to test data from a cantilevered swept-plate wing model. Computed results are compared with finite element results, results using another strainbased method, and photogrammetry data. For the computational model under an aeroelastic load, maximum deflection errors in the fore and aft, lateral, and vertical directions are -3.2%, 0.28%, and 0.09%, respectively; and maximum slope errors in roll and pitch directions are 0.28% and -3.2%, respectively. For the experimental model, deflection results at the tip are shown to be accurate to within 3.8% of the photogrammetry data and are accurate to within 2.2% in most cases. In general, excellent matching between target and computed values are accomplished in this study. Future refinement of this theory will allow it to monitor the deflection and health of an entire aircraft in real time, allowing for aerodynamic load computation, active flexible motion control, and active induced drag reduction.

shape sensing↗

NASA NTRS1992

Development of a four-dimensional variational analysis system using the adjoint method at GLA. I - Dynamics

Recent developments in the field of data assimilation have pointed to variational analysis (essentially least-squares fitting of a model solution to observed data) using the adjoint method as a new direction that holds the potential of major improvements over the current optimal interpolation method. This paper describes the initial effort in the development of a 4D variational analysis system. Although the development is based on the Goddard Laboratory for Atmospheres General Circulation Model (GCM), the methods and procedures described in this paper can be applied to any model. The adjoint code that computes the gradients needed in the analysis can be written directly from the GCM code. An easy error-detection technique was devised in the construction of the adjoint model. Also, a method of determining the weights and the preconditioning scales for the cases where model-generated data, which are error free, are used as observation is proposed. Two test experiments show that the dynamics part of the system has been successfully completed.

Chao, Winston C.↗

NASA NTRSDate not supplied

Using Distributed Fiber-Optic Strain Sensing to Estimate Modal Generalized Modal Coordinates from Flight-Test Data

Background and Motivation - Problem - Contemporary aircraft carry around structural mass so that the flutter instabilities lie well outside of the operational envelope. - Better methods of measuring the structural state could allow reduction of the extra structural weight. - Modal filtering - Standard method in structural analysis - Deformations are a combination of mode shapes - Modal filtering is estimating these modal coordinates from data - Often ordinary least squares methods - Often applied to simpler test articles - Factor Analysis - Classic (in psychology) analysis method - Measurements are a combination of small number of unmeasurable variables - Lessons from this factor can be adapted to improve the modal filtering methods

Jeffrey Ouellette↗

NASA NTRSDate not supplied

Using Distributed Fiber-optic Strain Sensing to Estimate Generalized Modal Coordinates from Flight-test Data

Background and Motivation - Problem - Contemporary aircraft carry around structural mass so that the flutter instabilities lie well outside of the operational envelope. - Better methods of measuring the structural state could allow reduction of the extra structural weight - Modal filtering - Standard method in structural analysis - Deformations are a combination of mode shapes - Modal filtering is estimating these modal coordinates from data - Often ordinary least squares methods - Often applied to simpler test articles - Factor Analysis - Analysis method from psychology - Measurements are a combination of small number of unmeasurable variables. - Lessons from factor analysis can be adapted to improve the modal filtering methods

Jeffrey Ouellette↗

NASA NTRS1981

Investigation of antarctic crust and upper mantle using MAGSAT and other geophysical data

The isolation of the crustal magnetic anomaly field is discussed. Slowly spatially varying ring current fields were modeled as a least squares fit to each MAGSAT pass over Antarctica. Selection criteria were applied to data from 3000 MAGSAT passes to remove field aligned currents, yielding 87 data sets used to construct a scalar magnetic anomaly map for regions south of 55 S latitude. Internal tests performed on MAGSAT data and comparisons with the POGO map indicated that the general anomaly features are of crustal origin. The sources of anomalies generated in continental and in oceanic regions are discussed. Correlations were found between crustal magnetic anomalies and known geologic features over West and East Antarctica and over the surrounding oceanic regions.

Bentley, C. R.↗

NASA NTRS1992

Interactive Spectral Analysis and Computation (ISAAC)

Isaac is a task in the NSO external package for IRAF. A descendant of a FORTRAN program written to analyze data from a Fourier transform spectrometer, the current implementation has been generalized sufficiently to make it useful for general spectral analysis and other one dimensional data analysis tasks. The user interface for Isaac is implemented as an interpreted mini-language containing a powerful, programmable vector calculator. Built-in commands provide much of the functionality needed to produce accurate line lists from input spectra. These built-in functions include automated spectral line finding, least squares fitting of Voigt profiles to spectral lines including equality constraints, various filters including an optimal filter construction tool, continuum fitting, and various I/O functions.

Lytle, D. M.↗

NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Liu, Yen↗