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NASA NTRS2002

Multi-wavelength Luminosity Functions of Galaxies

Multivariate or multi-wavelength luminosity functions will reveal the interplay between star formation, chemical evolution, and absorption and re-emission of dust within evolving galaxy populations. By using principal component analysis to reduce the dimensionality of the problem, we optimally extract the relevant photometric information from large galaxy catalogs. As a demonstration of the technique, we derive the multi-wavelength luminosity function for the galaxies in the released SDSS catalog, and compare the results with those obtained by traditional methods. This technique will be applicable to catalogs of galaxies from datasets obtained by 2MASS, and the SIRTF and GALEX missions.

Gardner, J. P.↗

NASA NTRS2002

Multi-Wavelength Luminosity Functions of Galaxies

Multivariate or multi-wavelength luminosity functions will reveal the interplay between star formation, chemical evolution, and ab- sorption and re-emission of dust within evolving galaxy populations. By using principal component analysis to reduce the dimensionality of the problem, I optimally extract the relevant photometric information from large galaxy catalogs. As a demonstration of the technique, I derive the multi-wavelength luminosity function for the galaxies in the released SDSS catalog, and compare the results with those obtained by traditional methods. This technique will be applicable to catalogs of galaxies from datasets obtained by 2MASS, and the SIRTF and GALEX missions.

Gardner, Jonathan P.↗

NASA NTRS1998

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

NASA Discipline Neuroscience↗

NASA NTRS1992

Astronomical data analysis software and systems I; Proceedings of the 1st Annual Conference, Tucson, AZ, Nov. 6-8, 1991

Consideration is given to a definition of a distribution format for X-ray data, the Einstein on-line system, the NASA/IPAC extragalactic database, COBE astronomical databases, Cosmic Background Explorer astronomical databases, the ADAM software environment, the Groningen Image Processing System, search for a common data model for astronomical data analysis systems, deconvolution for real and synthetic apertures, pitfalls in image reconstruction, a direct method for spectral and image restoration, and a discription of a Poisson imagery super resolution algorithm. Also discussed are multivariate statistics on HI and IRAS images, a faint object classification using neural networks, a matched filter for improving SNR of radio maps, automated aperture photometry of CCD images, interactive graphics interpreter, the ROSAT extreme ultra-violet sky survey, a quantitative study of optimal extraction, an automated analysis of spectra, applications of synthetic photometry, an algorithm for extra-solar planet system detection and data reduction facilities for the William Herschel telescope.

Worrall, Diana M.↗

NASA NTRS1996

Software For Multivariate Bayesian Classification

PHD general-purpose classifier computer program. Uses Bayesian methods to classify vectors of real numbers, based on combination of statistical techniques that include multivariate density estimation, Parzen density kernels, and EM (Expectation Maximization) algorithm. By means of simple graphical interface, user trains classifier to recognize two or more classes of data and then use it to identify new data. Written in ANSI C for Unix systems and optimized for online classification applications. Embedded in another program, or runs by itself using simple graphical-user-interface. Online help files makes program easy to use.

Saul, Ronald↗

NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed in 2011 that may be used to analyze both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The new algorithm is a simplified version of a more complex search algorithm that was originally developed at the NASA Ames Balance Calibration Laboratory. The new algorithm has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression models. Therefore, the simplified search algorithm is not intended to replace the original search algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm either fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new regression model search algorithm.

multivariate experimental data↗

NASA NTRS1993

A numerical approach to controller design for the ACES facility

In recent years the employment of active control techniques for improving the performance of systems involving highly flexible structures has become a topic of considerable research interest. Most of these systems are quite complicated, using multiple actuators and sensors, and possessing high order models. The majority of analytical controller synthesis procedures capable of handling multivariable systems in a systematic way require considerable insight into the underlying mathematical theory to achieve a successful design. This insight is needed in selecting the proper weighting matrices or weighting functions to cast what is naturally a multiple constraint satisfaction problem into an unconstrained optimization problem. Although designers possessing considerable experience with these techniques have a feel for the proper choice of weights, others may spend a significant amount of time attempting to find an acceptable solution. Another disadvantage of such procedures is that the resulting controller has an order greater than or equal to that of the model used for the design. Of course, the order of these controllers can often be reduced, but again this requires a good understanding of the theory involved.

Frazier, W. Garth↗

NASA NTRS1992

Multivariable frequency domain identification via 2-norm minimization

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Bayard, David S.↗

NASA NTRS1988

Effect of model uncertainty on failure detection - The threshold selector

The performance of all failure detection, isolation, and accomodation (DIA) algorithms is influenced by the presence of model uncertainty. A unique framework is presented to incorporate a knowledge of modeling error in the analysis and design of failure detection systems. The tools being used are very similar to those in robust control theory. A concept is introduced called the threshold selector, which is a nonlinear inequality whose solution defines the set of detectable sensor failure signals. The threshold selector represents an innovative tool for analysis and synthesis of DIA algorithms. It identifies the optimal threshold to be used in innovations-based DIA algorithms. The optimal threshold is shown to be a function of the bound on modeling errors, the noise properties, the speed of DIA filters, and the classes of reference and failure signals. The size of the smallest detectable failure is also determined. The results are applied to a multivariable turbofan jet engine example, which demonstrates improvements compared to previous studies.

Emami-Naeini, Abbas↗

NASA NTRS1985

Proceedings of the Third Annual Symposium on Mathematical Pattern Recognition and Image Analysis

Topics addressed include: multivariate spline method; normal mixture analysis applied to remote sensing; image data analysis; classifications in spatially correlated environments; probability density functions; graphical nonparametric methods; subpixel registration analysis; hypothesis integration in image understanding systems; rectification of satellite scanner imagery; spatial variation in remotely sensed images; smooth multidimensional interpolation; and optimal frequency domain textural edge detection filters.

Guseman, L. F., Jr.↗

NASA NTRS1981

Multivariable closed loop control analysis and synthesis for complex flight systems

A flight control system analysis and synthesis method is presented that is intended to be especially suitable for application to vehicles exhibiting complex dynamic characteristics. For such vehicles quantitative handling qualities specifications are not usually available. Howver, handling qualities objectives are specifically introduced in this method via the hypothesis of correlation between pilot ratings and the objective function of an optimal control model of the human pilot. Further, since augmentation and pilot operate in parallel, simultaneous determination of the augmentation and pilot model gains is required. Desirable augmented dynamics are obtained for a variety of complex systems and the method is experimentally verified in the case of simple pilot damper gain selection for optimum pitch tracking performance.

Schmidt, D. K.↗

NASA NTRS1979

Multivariate approximation methods and applications to geophysics and geodesy

The first report in a series is presented which is intended to be written by the author with the purpose of treating a class of approximation methods of functions in one and several variables and ways of applying them to geophysics and geodesy. The first report is divided in three parts and is devoted to the presentation of the mathematical theory and formulas. Various optimal ways of representing functions in one and several variables and the associated error when information is had about the function such as satellite data of different kinds are discussed. The framework chosen is Hilbert spaces. Experiments were performed on satellite altimeter data and on satellite to satellite tracking data.

Munteanu, M. J.↗

NASA NTRS1989

Application of precomputed control laws in a reconfigurable aircraft flight control system

A self-repairing flight control system concept in which the control law is reconfigured after actuator and/or control surface damage to preserve stability and pilot command tracking is described. A key feature of the controller is reconfigurable multivariable feedback. The feedback gains are designed off-line and scheduled as a function of the aircraft control impairment status so that reconfiguration is performed simply by updating the gain schedule after detection of an impairment. A novel aspect of the gain schedule design procedure is that the schedule is calculated using a linear quadratic optimization-based simultaneous stabilization algorithm in which the scheduled gain is constrained to stabilize a collection of plant models representing the aircraft in various control failure modes. A description and numerical evaluation of a controller design for a model of a statically unstable high-performance aircraft are given.

Moerder, Daniel D.↗

NASA NTRS1982

Lateral control system design for VTOL landing on a DD963 in high sea states

The problem of designing lateral control systems for the safe landing of VTOL aircraft on small ships is addressed. A ship model is derived. The issues of estimation and prediction of ship motions are discussed, using optimal linear linear estimation techniques. The roll motion is the most important of the lateral motions, and it is found that it can be predicted for up to 10 seconds in perfect conditions. The automatic landing of the VTOL aircraft is considered, and a lateral controller, defined as a ship motion tracker, is designed, using optimal control techniqes. The tradeoffs between the tracking errors and the control authority are obtained. The important couplings between the lateral motions and controls are demonstrated, and it is shown that the adverse couplings between the sway and the roll motion at the landing pad are significant constraints in the tracking of the lateral ship motions. The robustness of the control system, including the optimal estimator, is studied, using the singular values analysis. Through a robustification procedure, a robust control system is obtained, and the usefulness of the singular values to define stability margins that take into account general types of unstructured modelling errors is demonstrated. The minimal destabilizing perturbations indicated by the singular values analysis are interpreted and related to the multivariable Nyquist diagrams.

Bodson, M.↗

NASA NTRS2024

Quantifying Caloric Expenditure During Zero-G Exercise

BACKGROUND: Exercise is a fundamental component of maintaining astronaut health on long-duration space missions, where the microgravity environment poses unique challenges to physiological homeostasis. Accurate quantification of energy expenditure during such exercises is crucial for optimizing nutritional and physical health strategies for spacefarers. OBJECTIVE: This study aims to develop a comprehensive model to estimate caloric expenditure during exercise in a microgravity environment, employing a combination of spirometry, heart rate data, and other relevant parameters. By assessing energy utilization under these conditions, we seek to facilitate enhanced health management protocols for astronauts in space. METHODS & OUTCOMES: A multivariate predictive model will be constructed, utilizing spirometry and heart rate data, coupled with additional physiological and environmental parameters. A systematic approach will be applied to analyze the relationship between these variables and energy expenditure during various exercises. The proposed model will subsequently undergo rigorous validation to ensure accuracy and reliability. This research is expected to yield a precise and reliable predictive model, contributing to improved strategies for exercise prescription and nutritional intake, addressing the unique challenges presented by microgravity environments. We anticipate that our findings will support the development of more effective health maintenance protocols for astronauts during extended space missions, mitigating the adverse effects of space travel on the human body. SIGNIFICANCE: The development of an accurate and adaptable model to quantify caloric expenditure during exercise in space represents a pivotal advancement in space medicine. The insights gained from this study have the potential to inform the design of enhanced health and wellness strategies, ensuring the well-being and operational effectiveness of astronauts in long-duration space missions.

Calorie↗

NASA NTRS1995

An Optimized Integrator Windup Protection Technique Applied to a Turbofan Engine Control

This paper introduces a new technique for providing memoryless integrator windup protection which utilizes readily available optimization software tools. This integrator windup protection synthesis provides a concise methodology for creating integrator windup protection for each actuation system loop independently while assuring both controller and closed loop system stability. The individual actuation system loops' integrator windup protection can then be combined to provide integrator windup protection for the entire system. This technique is applied to an H(exp infinity) based multivariable control designed for a linear model of an advanced afterburning turbofan engine. The resulting transient characteristics are examined for the integrated system while encountering single and multiple actuation limits.

Watts, Stephen R.↗

NASA NTRS1981

Considerations of open-loop, closed-loop, and adaptive multicyclic control systems

Four different types of self-tuning regulators were studied for multicyclic control of helicopter vibration. A numerical simulation of the helicopter is made, using a multivariable frequency-domain model, in terms of transfer function with six input control harmonics and six output harmonics. The model characteristics vary with flight speed. An off-line identification of model characteristics is made, using the least-squared-error method and using a succession of input and output measurements. The on-line identification of model characteristics is made using the Kalman filter solution. The optimal controls are calculated from the minimization of quadratic performance function based on response and multicyclic inputs. The performance of various regulators or controllers is judged from the stability, transient response, convergence time, and amplitude of the steady state.

Chopra, I.↗

NASA NTRS1984

Crewstation design and validation

The central problem in crewstation design, that of optimizing the exchange of information between the human and machine components of a system is addressed. The CAR, CUBITS, GROUP, ABBREV, VRAS, and HOS programs, products of the Navy's Human Factors Engineering Technology Development program are all discussed. They are representative to the type of technology which was previously indicated as necessary to move crewstation design and validation to a higher lever of maturity, one which takes cognizance of the multivariate nature of the problems faced by the crewstation designer and has a far less dependence of the whims of personal or subjective opinion.

Wherry, R. J., Jr.↗