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NASA NTRS1986

Robust detection, isolation and accommodation for sensor failures

The objective is to extend the recent advances in robust control system design of multivariable systems to sensor failure detection, isolation, and accommodation (DIA), and estimator design. This effort provides analysis tools to quantify the trade-off between performance robustness and DIA sensitivity, which are to be used to achieve higher levels of performance robustness for given levels of DIA sensitivity. An innovations-based DIA scheme is used. Estimators, which depend upon a model of the process and process inputs and outputs, are used to generate these innovations. Thresholds used to determine failure detection are computed based on bounds on modeling errors, noise properties, and the class of failures. The applicability of the newly developed tools are demonstrated on a multivariable aircraft turbojet engine example. A new concept call the threshold selector was developed. It represents a significant and innovative tool for the analysis and synthesis of DiA algorithms. The estimators were made robust by introduction of an internal model and by frequency shaping. The internal mode provides asymptotically unbiased filter estimates.The incorporation of frequency shaping of the Linear Quadratic Gaussian cost functional modifies the estimator design to make it suitable for sensor failure DIA. The results are compared with previous studies which used thresholds that were selcted empirically. Comparison of these two techniques on a nonlinear dynamic engine simulation shows improved performance of the new method compared to previous techniques

Emami-Naeini, A.↗
NASA NTRS1986

Aircraft control surface failure detection and isolation using the OSGLR test

The performance of the orthogonal series generalized likelihood ratio (OSGLR) test in detecting and isolating commercial aircraft control surface and actuator failures is evaluated. A modification to incorporate age-weighting which significantly reduces the sensitivity of the algorithm to modeling errors is presented. The steady-state implementation of the algorithm based on a single linear model valid for a cruise flight condition is tested using a nonlinear aircraft simulation. A number of off-nominal no-failure flight conditions including maneuvers, nonzero flap deflections, different turbulence levels and steady winds were tested. Based on the no-failure decision functions produced by off-nominal flight conditions, the failure detection and isolation performance at the nominal flight condition was determined. The extension of the algorithm to a wider flight envelope by scheduling on dynamic pressure and flap deflection is examined. Based on this testing, the OSGLR algorithm should be capable of detecting control surface failures that would affect the safe operation of a commercial aircraft. Isolation may be difficult if there are several surfaces which produce similar effects on the aircraft. Extending the algorithm over the entire operating envelope of a commercial aircraft appears feasible.

Bonnice, W. F.↗
NASA NTRS1988

Shuttle imaging radar A analysis of land use in Amazonia

Over large areas in the tropics, satellite imagery is the principal source of data on the area, current stature, and extent of disturbance of the forests. The information from imagery that covers large areas at low resolution is greatly enhanced when different types of imagery can be compared. The paper presents a comparison of data from Landsat MSS and from the Shuttle Imaging Radar (SIR-A) L band HH polarization data for sites in the Amazon Basin. Results indicate that SIR-A backscatter from the undisturbed forest was lower than that from some disturbed areas and from flooded forests and that SIR-A brightness, increases nonlinearly with the Landsat normalized difference vegetation index. It is hypothesized that the brightest radar returns in southern Amazonia are from newly cleared forests that are littered with standing and fallen tree boles that function as corner reflectors; and that backscatter will diminish from disturbed areas over time as fields are burned repeatedly.

Stone, Thomas A.↗
NASA NTRS1996

Modeling of Aircraft Unsteady Aerodynamic Characteristics/Part 3 - Parameters Estimated from Flight Data: Parameters Estimated from Flight Data - Part 3

A nonlinear least squares algorithm for aircraft parameter estimation from flight data was developed. The postulated model for the analysis represented longitudinal, short period motion of an aircraft. The corresponding aerodynamic model equations included indicial functions (unsteady terms) and conventional stability and control derivatives. The indicial functions were modeled as simple exponential functions. The estimation procedure was applied in five examples. Four of the examples used simulated and flight data from small amplitude maneuvers to the F-18 HARV and X-31A aircraft. In the fifth example a rapid, large amplitude maneuver of the X-31 drop model was analyzed. From data analysis of small amplitude maneuvers ft was found that the model with conventional stability and control derivatives was adequate. Also, parameter estimation from a rapid, large amplitude maneuver did not reveal any noticeable presence of unsteady aerodynamics.

Klein, Vladislav↗
NASA NTRS1995

A Simple Theory of Capillary-Gravity Wave Turbulence

Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

Glazman, Roman E.↗
NASA NTRS1997

Relative Concentration of He+ in the Inner Magnetosphere as Observed by the DE 1 Retarding Ion Mass Spectrometer

With Observations from the retarding ion mass spectrometer on the Dynamics Explorer I from 1981 through 1984, we examine the He(+) to H(+) density ratios as a function of altitude, latitude, season, local time, geomagnetic and solar activity. We find that the ratios are primarily a function of geocentric distance and the solar EUV input. The ratio of the densities, when plotted as a function of geocentric distance, decrease by an order of magnitude from 1 to 4.5 R(sub E). After the He(+) to H(+) density ratios are adjusted for the dependence on radial distance, they decrease nonlinearly by a factor of 5 as the solar EUV proxy varies from about 250 to about 70. When the mean variations with both these parameters are removed, the ratios appear to have no dependence on geomagnetic activity and weak dependence on local time or season, geomagnetic latitude, and L shell.

Craven, P. D.↗
NASA NTRS1996

A Simulated Spectrum of Convectively Generated Gravity Waves: Propagation from the Tropopause to the Mesopause and Effects on the Middle Atmosphere

This work evaluates the interaction of a simulated spectrum of convectively generated gravity waves with realistic middle atmosphere mean winds. The wave spectrum is derived from the nonlinear convection model described by Alexander et al. that simulated a two-dimensional midlatitude squall line. This spectrum becomes input to a linear ray tracing model for evaluation of wave propagation as a function of height through climatological background wind and buoyancy frequency profiles. The energy defined by the spectrum as a function of wavenumber and frequency is distributed spatially and temporally into wave packets for the purpose of estimating wave amplitudes at the lower boundary of the ray tracing model. A wavelet analysis provides an estimate of these wave packet widths in space and time. Without this redistribution of energies into wave packets the Fourier analysis alone inaccurately assumes the energy is evenly distributed throughout the storm model domain. The growth with height of wave amplitudes is derived from wave action flux conservation coupled to a convective instability saturation condition. Mean flow accelerations and wave energy dissipation profiles are derived from this analysis and compared to parameterized estimates of gravity wave forcing, providing a measure of the importance of the storm source to global gravity wave forcing. The results suggest that a single large convective storm system like the simulated squall line could provide a significant fraction of the zonal mean gravity wave forcing at some levels, particularly in the mesosphere. The vertical distributions of mean flow acceleration and energy dissipation do not much resemble the parameterized profiles in form because of the peculiarities of the spectral properties of the waves from the storm source. The ray tracing model developed herein provides a tool for examining the role of convectively generated waves in middle atmosphere physics.

Alexander, Joan↗
NASA NTRS2001

Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack

The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.

Pamadi, Bandu N.↗
NASA NTRS1993

Chirp Scaling Algorithms for SAR Processing

The chirp scaling SAR processing algorithm is both accurate and efficient. Successful implementation requires proper selection of the interval of output samples, which is a function of the chirp interval, signal sampling rate, and signal bandwidth. Analysis indicates that for both airborne and spaceborne SAR applications in the slant range domain a linear chirp scaling is sufficient. To perform nonlinear interpolation process such as to output ground range SAR images, one can use a nonlinear chirp scaling interpolator presented in this paper.

nonlinear chirp scaling.↗
NASA NTRS2005

Application of the Hilbert-Huang Transform to Financial Data

A paper discusses the application of the Hilbert-Huang transform (HHT) method to time-series financial-market data. The method was described, variously without and with the HHT name, in several prior NASA Tech Briefs articles and supporting documents. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear phenomena including physical phenomena and, in the present case, financial-market processes. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum. The instant paper begins with a discussion of prior approaches to quantification of market volatility, summarizes the HHT method, then describes the application of the method in performing time-frequency analysis of mortgage-market data from the years 1972 through 2000. Filtering by use of the EMD is shown to be useful for quantifying market volatility.

Huang, Norden↗
NASA NTRS2022

Advanced Statistical Methods in Spacecraft Flight Software Cost Estimation: Bayesian Regression and Nonlinear Principal Components Analysis to Support System Engineering in the Early Project Lifecycle

This paper provides an overview of the new features and model updates in the upcoming release of the NASA Analogy Software Cost Tool (ASCoT). ASCoT, hosted within the Online NASA Space Estimation Tools (ONSET) on the One NASA Cost Engineering (ONCE) Database, is a web-based tool that provides a suite of estimation tools to support early lifecycle NASA flight software cost analysis. In addition to the traditional parametric flight software costing method COCOMO II, ASCoT contains a Bayesian linear regression to predict total flight software development cost as a function of total spacecraft cost, as well as four analogic methods: k-Nearest Neighbors (kNN) and Clustering models to predict Effort (in work-months) and total source lines of code (SLOC). These methods are designed to work primarily with system-level inputs such as mission type (orbiter, lander, etc.), mission destination (Earth, Inner Planetary, etc.), and the number of instruments and deployables. Nonlinear principal components analysis (NLPCA) is performed to find the principal features of the data composed of both categorical and numerical variables and is necessary prior to defining our analogic methods. Sensitivity analyses and in- and out-of-sample model performance results are presented for the Bayesian CER and the analogic models.

Johnson, James K.↗
NASA NTRS1990

Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization

Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem.

Pototzky, Anthony S.↗
NASA NTRS1967

Subsonic and Supersonic Flutter Analysis of a Highly Tapered Swept-Wing Planform, Including Effects of Density Variation and Finite Wing Thickness, and Comparison with Experiments

The flutter characteristics of several wings with an aspect-ratio of 4.0, a taper ratio of 0.2, and a quarter-chord sweepback of 45 deg. have been investigated analytically for Mach numbers up to 2.0. The calculations were based on the modified-strip-analysis method, the subsonic-kernel-function method, piston theory, and quasi-steady second-order theory. Results of t h e analysis and comparisons with experiment indicated that: (1) Flutter speeds were accurately predicted by the modified strip analysis, although accuracy at t h e highest Mach numbers required the use of nonlinear aerodynamic theory (which accounts for effects of wing thickness) for the calculation of the aerodynamic parameters. (2) An abrupt increase of flutter-speed coefficient with increasing Mach number, observed experimentally in the transonic range, was also indicated by the modified strip analysis. (3) In the low supersonic range for some densities, a discontinuous variation of flutter frequency with Mach number was indicated by the modified strip analysis. An abrupt change of frequency appeared experimentally in the transonic range. (4) Differences in flutter-speed-coefficient levels obtained from tests at low supersonic Mach numbers in two wind tunnels were also predicted by the modified strip analysis and were shown to be caused primarily by differences in mass ratio. (5) Flutter speeds calculated by the subsonic-kernel-function method were in good agreement with experiment and with the results of the modified strip analysis. (6) Flutter speed obtained from piston theory and from quasi-steady second-order theory were higher than experimental values by at least 38 percent.

Yates, Carson, Jr.↗
NASA NTRS1979

Optimal estimator model for human spatial orientation

A model is being developed to predict pilot dynamic spatial orientation in response to multisensory stimuli. Motion stimuli are first processed by dynamic models of the visual, vestibular, tactile, and proprioceptive sensors. Central nervous system function is then modeled as a steady-state Kalman filter which blends information from the various sensors to form an estimate of spatial orientation. Where necessary, this linear central estimator has been augmented with nonlinear elements to reflect more accurately some highly nonlinear human response characteristics. Computer implementation of the model has shown agreement with several important qualitative characteristics of human spatial orientation, and it is felt that with further modification and additional experimental data the model can be improved and extended. Possible means are described for extending the model to better represent the active pilot with varying skill and work load levels.

Borah, J.↗
NASA NTRS1983

The physics of a single-event upset in integrated circuits: A review and critique of analytical models for charge collection

When an energetic particle (kinetic energy 0.5 MeV) originating from a radioactive decay or a cosmic ray transverse the active regions of semiconductor devices used in integrated circuit (IC) chips, it leaves along its track a high density electron hole plasma. The subsequent decay of this plasma by drift and diffusion leads to charge collection at the electrodes large enough in most cases to engender a false reading, hence the name single-event upset (SEU). The problem of SEU's is particularly severe within the harsh environment of Jupiter's radiation belts and constitutes therefore a matter of concern for the Galileo mission. The physics of an SEU event is analyzed in some detail. Owing to the predominance of nonlinear space charge effects and the fact that positive (holes) and negative (electrons) charges must be treated on an equal footing, analytical models for the ionized-charge collection and their corresponding currents as a function of time prove to be inadequate even in the simplest case of uniformly doped, abrupt p-n junctions in a one-dimensional geometry. The necessity for full-fledged computer simulation of the pertinent equations governing the electron-hole plasma therefore becomes imperative.

Vonroos, O.↗
NASA NTRS1986

Predicting the Dynamic Behavior of High-Speed Roller Bearings

Computer program developed for solving nonlinear differential equations of motion of high-speed, lightly loaded, cylindrical roller bearing. Program organized into three major parts: Main program, controls input and output; differential equation solver; and subroutines, used to evaluate vector function. Program has capability of performing either twodimensional or three-dimensional simulation.

Conry, T. F.↗
NASA NTRS1990

Estimating short-period dynamics using an extended Kalman filter

An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.

Bauer, Jeffrey E.↗
NASA NTRS1990

Nonlinear viscoelastic response of highly filled elastomers under multiaxial finite deformation

A biaxial tester was used to obtain precise biaxial stress responses of highly filled, high strain capability elastomers. Stress-relaxation experiments show that the time-dependent part of the relaxation response can be reasonably approximated by a function which is strain and biaxiality independent. Thus, isochronal data from the stress-relaxation curves can be used to determine the stored energy density function. The complex behavior of the elastomers under biaxial deformation may be caused by dewetting.

Peng, Steven T. J.↗