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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Exit Presentation -- Maintaining Balance

This slide presentation reviews the projects which the author engaged in during an internship at Johnson Space Center. Project 1 was involved with Stochastic Resonance (SR). Stochastic resonance is a phenomenon in which the response of a non-linear system to a weak input signal is optimized by the presence of a particular non-zero level of noise. The goal of this project was to develop a countermeasure for sensorimotor disturbances that are experienced after long duration space flight. The second project was a pilot study that was to examine how adaptation to a novel functional task was affected by postural disturbance.

Heap, Erin↗
NASA NTRS1988

On-orbit parametric identification methodology

On-orbit system identification (ID) of large space systems is essential for various reasons. For example, the complex composite structure of such systems cannot be ground-tested; their structural dynamic characteristics must be known accurately in order to accomplish active control. Furthermore, such capability can be used to characterize/identify various disturbances. The identification process is consisted of four principal elements: (1) modeling, (2) the estimation algorithm, (3) input system, and (4) measurement system. These elements are highly correlated and all togerher determine the success of the identification problem. Accurate modeling of large space systems is the most important element of the identification process. Large flexible structures are non-linear and infinite dimensional systems with highly coupled parameters and low frequency packed modes. In addition, these systems are subject to stochastic and time-varying disturbances, they have structural parameters which can vary due to on-orbit assembly deployment, and operations. These systems are generally; however, represented by constant coefficient, finite order differential equations. The non-linearities, coupling and noise effects are also often neglected. Moreover, identification experiment designs which lead to highly complex optimization problems usually require the simultaneous choice of ID algorithm, sensor, and actuator type and placement. On-orbit bandwidth and power restrictions on excitation, limited data window, and restrictions on sensor/actuator type, placement and number, has led to practical questions of implementations.

Hadaegh, Fred Y.↗
NASA NTRS1984

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗
NASA NTRS2003

Stochastic Control Synthesis of Systems with Structured Uncertainty

This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.

Padula, Sharon L.↗
NASA NTRS2004

Fossil Signatures Using Elemental Abundance Distributions and Bayesian Probabilistic Classification

Elemental abundances (C6, N7, O8, Na11, Mg12, Al3, P15, S16, Cl17, K19, Ca20, Ti22, Mn25, Fe26, and Ni28) were obtained for a set of terrestrial fossils and the rock matrix surrounding them. Principal Component Analysis extracted five factors accounting for the 92.5% of the data variance, i.e. information content, of the elemental abundance data. Hierarchical Cluster Analysis provided unsupervised sample classification distinguishing fossil from matrix samples on the basis of either raw abundances or PCA input that agreed strongly with visual classification. A stochastic, non-linear Artificial Neural Network produced a Bayesian probability of correct sample classification. The results provide a quantitative probabilistic methodology for discriminating terrestrial fossils from the surrounding rock matrix using chemical information. To demonstrate the applicability of these techniques to the assessment of meteoritic samples or in situ extraterrestrial exploration, we present preliminary data on samples of the Orgueil meteorite. In both systems an elemental signature produces target classification decisions remarkably consistent with morphological classification by a human expert using only structural (visual) information. We discuss the possibility of implementing a complexity analysis metric capable of automating certain image analysis and pattern recognition abilities of the human eye using low magnification optical microscopy images and discuss the extension of this technique across multiple scales.

Hoover, Richard B.↗
NASA NTRS2010

Extracting Independent Local Oscillatory Geophysical Signals by Geodetic Tropospheric Delay

Zenith Tropospheric Delay (ZTD) due to water vapor derived from space geodetic techniques and numerical weather prediction simulated-reanalysis data exhibits non-linear and non-stationary properties akin to those in the crucial geophysical signals of interest to the research community. These time series, once decomposed into additive (and stochastic) components, have information about the long term global change (the trend) and other interpretable (quasi-) periodic components such as seasonal cycles and noise. Such stochastic component(s) could be a function that exhibits at most one extremum within a data span or a monotonic function within a certain temporal span. In this contribution, we examine the use of the combined Ensemble Empirical Mode Decomposition (EEMD) and Independent Component Analysis (ICA): the EEMD-ICA algorithm to extract the independent local oscillatory stochastic components in the tropospheric delay derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) over six geodetic sites (HartRAO, Hobart26, Wettzell, Gilcreek, Westford, and Tsukub32). The proposed methodology allows independent geophysical processes to be extracted and assessed. Analysis of the quality index of the Independent Components (ICs) derived for each cluster of local oscillatory components (also called the Intrinsic Mode Functions (IMFs)) for all the geodetic stations considered in the study demonstrate that they are strongly site dependent. Such strong dependency seems to suggest that the localized geophysical signals embedded in the ZTD over the geodetic sites are not correlated. Further, from the viewpoint of non-linear dynamical systems, four geophysical signals the Quasi-Biennial Oscillation (QBO) index derived from the NCEP/NCAR reanalysis, the Southern Oscillation Index (SOI) anomaly from NCEP, the SIDC monthly Sun Spot Number (SSN), and the Length of Day (LoD) are linked to the extracted signal components from ZTD. Results from the synchronization analysis show that ZTD and the geophysical signals exhibit (albeit subtle) site dependent phase synchronization index.

Botai, O. J.↗
NASA NTRS2016

The Impact of Crosstalk in the X-IFU Instrument on Athena Science Cases

In this paper we present a first assessment of the impact of various forms of instrumental crosstalk on the science performance of the X-ray Integral Field Unit (X-IFU) on the Athena X-ray mission. This assessment is made using the SIXTE end-to-end simulator in the context of one of the more technically challenging science cases for the XIFU instrument. Crosstalk considerations may influence or drive various aspects of the design of the array of high-count-rate Transition Edge Sensor (TES) detectors and its Frequency Domain Multiplexed (FDM) readout architecture. The Athena X-ray mission was selected as the second L-class mission in ESA's Cosmic Vision 2015–25 plan, with alaunch foreseen in 2028, to address the theme ''Hot and Energetic Universe"1. One of the two instruments on boardAthena is the X-ray Integral Field Unit2 (X-IFU) which is based on an array of ~3800 Transition Edge Sensors (TES's)operated at a temperature of ~90 mK. The science cases pose an interesting challenge for this instrument, as they requirea combination of high energy resolution (2.5 eV FWHM or better), high spatial resolution (5 arcsec or better) and highcount rate capability (several tens of counts per second per detector for point sources as bright as 10 mCrab).The performance at the single sensor level has been demonstrated3, but the operation of such detectors in an array, usingmultiplexed readout, brings additional challenges, both for the design of the array in which the sensors are placed and forthe readout of the sensors. The readout of the detector array will be based on Frequency Domain Multiplexing (FDM)4.In this system of detectors and readout, crosstalk can arise through various mechanisms: on the TES array, neighboringsensors can couple through thermal crosstalk. Detectors adjacent in carrier frequency may suffer from electrical crosstalkdue to the finite width of the bandpass filters, and shared sources of impedance in their signal lines. The signals from theindividual detectors are summed and then amplified by a pair of SQUID amplifiers before being sent to warm front-endelectronics. The transfer function of the SQUID amplifiers is non-linear, which will give rise to higher harmonics ofcarriers and intermodulation products when multiple signal pulses are simultaneously present in the SQUID. Under highcount rate conditions this is another source of crosstalk. The effect of all these crosstalk sources is that parasitic pulseswill appear in the record of a signal pulse which will create a stochastic offset of the measured energy and thus adegradation of the energy resolution.

SIXTE↗
NASA NTRS1995

Expendable launch vehicle studies

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Bainum, Peter M.↗
NASA NTRS2000

Applications of Fractal Analytical Techniques in the Estimation of Operational Scale

The observational scale and the resolution of remotely sensed imagery are essential considerations in the interpretation process. Many atmospheric, hydrologic, and other natural and human-influenced spatial phenomena are inherently scale dependent and are governed by different physical processes at different spatial domains. This spatial and operational heterogeneity constrains the ability to compare interpretations of phenomena and processes observed in higher spatial resolution imagery to similar interpretations obtained from lower resolution imagery. This is a particularly acute problem, since longterm global change investigations will require high spatial resolution Earth Observing System (EOS), Landsat 7, or commercial satellite data to be combined with lower resolution imagery from older sensors such as Landsat TM and MSS. Fractal analysis is a useful technique for identifying the effects of scale changes on remotely sensed imagery. The fractal dimension of an image is a non-integer value between two and three which indicates the degree of complexity in the texture and shapes depicted in the image. A true fractal surface exhibits self-similarity, a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution, and the slope of the fractal dimension-resolution relationship would be zero. Most geographical phenomena, however, are not self-similar at all scales, but they can be modeled by a stochastic fractal in which the scaling properties of the image exhibit patterns that can be described by statistics such as area-perimeter ratios and autocovariances. Stochastic fractal sets relax the self-similarity assumption and measure many scales and resolutions to represent the varying form of a phenomenon as the pixel size is increased in a convolution process. We have observed that for images of homogeneous land covers, the fractal dimension varies linearly with changes in resolution or pixel size over the range of past, current, and planned space-borne sensors. This relationship differs significantly in images of agricultural, urban, and forest land covers, with urban areas retaining the same level of complexity, forested areas growing smoother, and agricultural areas growing more complex as small pixels are aggregated into larger, mixed pixels. Images of scenes having a mixture of land covers have fractal dimensions that exhibit a non-linear, complex relationship to pixel size. Measuring the fractal dimension of a difference image derived from two images of the same area obtained on different dates showed that the fractal dimension increased steadily, then exhibited a sharp decrease at increasing levels of pixel aggregation. This breakpoint of the fractal dimension/resolution plot is related to the spatial domain or operational scale of the phenomenon exhibiting the predominant visible difference between the two images (in this case, mountain snow cover). The degree to which an image departs from a theoretical ideal fractal surface provides clues as to how much information is altered or lost in the processes of rescaling and rectification. The measured fractal dimension of complex, composite land covers such as urban areas also provides a useful textural index that can assist image classification of complex scenes.

Emerson, Charles W.↗
NASA NTRS2004

Fleet Assignment Using Collective Intelligence

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Antoine, Nicolas E.↗
NASA NTRS2019

A Communication Channel Density Estimating Generative Adversarial Network

Autoencoder-based communication systems use neural network channel models to backwardly propagate message reconstruction error gradients across an approximation of the physical communication channel. In this work, we develop and test a new generative adversarial network (GAN) architecture for the purpose of training a stochastic channel approximating neural network. In previous research, investigators have focused on additive white Gaussian noise (AWGN) channels and/or simplified Rayleigh fading channels, both of which are linear and have well defined analytic solutions. Given that training a neural network is computationally expensive, channel approximation networks— and more generally the autoencoder systems—should be evaluated in communication environments that are traditionally difficult. To that end, our investigation focuses on channels that contain a combination of non-linear amplifier distortion, pulse shape filtering, intersymbol interference, frequency-dependent group delay, multipath, and non-Gaussian statistics. Each of our models are trained without any prior knowledge of the channel. We show that the trained models have learned to generalize over an arbitrary amplifier drive level and constellation alphabet. We demonstrate the versatility of our GAN architecture by comparing the marginal probability density function of several channel simulations with that of their corresponding neural network approximations

Smith, Aaron↗