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NASA NTRS1976

The scattering of obliquely incident plane waves from a corrugated conducting surface

A physical optics solution is presented for the scattering of plane waves from a perfectly conducting corrugated surface in the case of waves incident from an arbitrary direction and for an observer far from the surface. This solution is used to compute the radar cross section of the surface in the case of backscatter from irregular (i.e., stochastic) corrugations. An interesting feature of the solution is the occurrence of singularities in the scattered fields. These singularities appear to be a manifestation of focusing by the surface at its 'stationary' points. Whether or not the singularities occur in the solution depends on the manner in which one restricts the analysis to the far-field.

Surface waves↗

NASA NTRS1992

Ionospheric gravity wave measurements with the USU dynasonde

A method for the measurement of ionospheric Gravity Wave (GW) using the USU Dynasonde is outlined. This method consists of a series of individual procedures, which includes functions for data acquisition, adaptive scaling, polarization discrimination, interpolation and extrapolation, digital filtering, windowing, spectrum analysis, GW detection, and graphics display. Concepts of system theory are applied to treat the ionosphere as a system. An adaptive ionogram scaling method was developed for automatically extracting ionogram echo traces from noisy raw sounding data. The method uses the well known Least Mean Square (LMS) algorithm to form a stochastic optimal estimate of the echo trace which is then used to control a moving window. The window tracks the echo trace, simultaneously eliminating the noise and interference. Experimental results show that the proposed method functions as designed. Case studies which extract GW from ionosonde measurements were carried out using the techniques described. Geophysically significant events were detected and the resultant processed results are illustrated graphically. This method was also developed for real time implementation in mind.

Berkey, Frank T.↗

NASA NTRS1990

Statistical analysis of near-wall structures in turbulent channel flow

The two-point correlation tensor is used to analyze near-wall structures in turbulent channel flow. Simulation results have been utilized to obtain the correlation tensor with sufficient spatial resolution to permit accurate differentiation for computing the vorticity correlation, and the resolution of sharp features such as the shear layer and its corresponding region of spanwise vorticity. Proper orthogonal decomposition and stochastic estimation were observed to yield similar results when appropriate conditions were employed for the estimation. Resulting structures were such that they would be detected by standard conditional sampling methods. The results of decomposing the vorticity field and the velocity field were significantly different, indicating that if a coherent structure is found that dominates the velocity fields, the curl of that velocity structure will not dominate the vorticity field.

Moser, Robert D.↗

NASA NTRS1998

Multi-Scale Fractal Analysis of Image Texture and Pattern

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as 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. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. 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. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and information content contained within these data. A software package known as the Image Characterization and Modeling System (ICAMS) was used to explore how fractal dimension is related to surface texture and pattern. The ICAMS software was verified using simulated images of ideal fractal surfaces with specified dimensions. The fractal dimension for areas of homogeneous land cover in the vicinity of Huntsville, Alabama was measured to investigate the relationship between texture and resolution for different land covers.

Emerson, Charles W.↗

NASA NTRS2021

The Stochastic X-ray Variability of the Accreting Millisecond Pulsar IGR J17062-6143

This work presents an investigation of the stochastic X-ray variability from the 164 Hz accreting millisecond pulsar IGR J17062–6143, based on regular observations collected with the Neutron Star Interior Composition Explorer between 2017 July and 2020 August. Over this period, the power density spectrum showed a stable morphology, with broad ∼ 25% rms band-limited noise below 16 Hz. Quasiperiodic oscillations (QPOs) were occasionally observed, with the most notably detections including a low-frequency QPO centered at 2.7 Hz and a sharp QPO centered at 115 Hz that may be a 2:3 resonance with the spin frequency. Further, the energy dependence of the band-limited noise is studied through a spectroscopic analysis of the complex covariance in two frequency intervals. It is found that the power law continuum is the primary driver for the observed variability, although the thermal (blackbody) emission also appears to be intrinsically variable in area (5% rms) and temperature (1% rms). Notably, the 1 keV emission feature seen in all X-ray spectra of IGR J17062–6143 varies with the same amplitude as the power law, but systematically lags behind that continuum emission. These results appear consistent with a scenario in which a time variable Compton-scattering corona is the primary source for the observed stochastic variability, with the variability observed in the emission feature and at the lowest photon energies being due to the disk reflection of the power law continuum.

Petrus Bult↗

NASA NTRS1986

Analysis of modeling errors in system identification

This paper is concerned with the identification of a system in the presence of several error sources. Following some basic definitions, the notion of 'near-equivalence in probability' is introduced using the concept of near-equivalence between a model and process. Necessary and sufficient conditions for the identifiability of system parameters are given. The effect of structural error on the parameter estimates for both deterministic and stochastic cases are considered.

Hadaegh, F. Y.↗

NASA NTRS1988

Statistical analysis of SSME system data

A statistical methodology to enhance the Space Shuttle Main Engine (SSME) performance prediction accuracy is proposed. This methodology was to be used in conjunction with existing SSME performance prediction computer codes to improve parameter prediction accuracy and to quantify that accuracy. However, after a review of related literature, researchers concluded that the proposed problem required a coverage of areas such as linear and nonlinear system theory, measurement theory, statistics, and stochastic estimation. Since state space theory is the foundation for a more complete study of each of the before mentioned areas, these researchers chose to refocus emphasis to cover the more specialized topic of state vector estimation procedures. State vector estimation was also selected because of current and future concerns by NASA for SSME performance evaluation; i.e., there is a current interest in an improved evaluation procedure for actual SSME post flight performance as well as for post static test performance of a single SSME. A current investigation of analytical methods may be used to improve test stand failure detection. This paper considers the issue of post flight/test state variable reconstruction through the application of observations made on the output of the Space Shuttle propulsion system. Rogers used the Kalman filtering procedure to reconstruct the state variables of the Space Shuttle propulsion system. An objective of this paper is to give the general setup of the Kalman filter and its connection to linear regression. A second objective is to examine the reconstruction methodology for application to the reconstruction of the state vector of a single Space Shuttle Main Engine (SSME) by using static test firing data.

Temple, Enoch C.↗

NASA NTRS1976

Buckling of structures; Proceedings of the Symposium, Harvard University, Cambridge, Mass., June 17-21, 1974

The papers deal with such topics as the buckling and post-buckling behavior of plates and shells; methods of calculating critical buckling and collapse loads; finite element representations for thin-shell instability analysis; theory and experiment in the creep buckling of plates and shells; creep instability of thick shell structures; analytical and numerical studies of the influence of initial imperfections on the elastic buckling of columns; mode interaction in stiffened panels under compression; imperfection-sensitivity in the interactive buckling of stiffened plates; buckling of stochastically imperfect structures; and the Liapunov stability of elastic dynamic systems. A special chapter is devoted to design problems, including the design of a Mars entry 'aeroshell', and buckling design in vehicle structures. Individual items are announced in this issue.

Budiansky, B.↗

NASA NTRS1994

A probabilistic fatigue analysis of multiple site damage

The variability in initial crack size and fatigue crack growth is incorporated in a probabilistic model that is used to predict the fatigue lives for unstiffened aluminum alloy panels containing multiple site damage (MSD). The uncertainty of the damage in the MSD panel is represented by a distribution of fatigue crack lengths that are analytically derived from equivalent initial flaw sizes. The variability in fatigue crack growth rate is characterized by stochastic descriptions of crack growth parameters for a modified Paris crack growth law. A Monte-Carlo simulation explicitly describes the MSD panel by randomly selecting values from the stochastic variables and then grows the MSD cracks with a deterministic fatigue model until the panel fails. Different simulations investigate the influences of the fatigue variability on the distributions of remaining fatigue lives. Six cases that consider fixed and variable conditions of initial crack size and fatigue crack growth rate are examined. The crack size distribution exhibited a dominant effect on the remaining fatigue life distribution, and the variable crack growth rate exhibited a lesser effect on the distribution. In addition, the probabilistic model predicted that only a small percentage of the life remains after a lead crack develops in the MSD panel.

Rohrbaugh, S. M.↗

NASA NTRS1984

Doppler lidar results from the San Gorgonio Pass experiments

During FY-84, the Doppler Lidar data from the San Gorgonio Pass experiments were analyzed, evaluated, and interpreted with regard to signal strength, signal width, magnitude and direction of velocity component and a goodness parameter associated with the expected noise level of the signal. From these parameters, a screening criteria was developed to eliminate questionable data. For the most part analysis supports the validity of Doppler Lidar data obtained at San Gorgonio Pass with respect to the mean velocity magnitude and direction. The question as to whether the Doppler width could be interpreted as a measure of the variance of the turbulence within the Doppler Lidar System (DLS) focal volume was not resolved. The stochastic nature of the Doppler broadening from finite residence time of the particles in the beam as well as other Doppler broadening phenomenon tend to mask the Doppler spread associated with small scale turbulence. Future tests with longer pulses may assist in better understanding.

Cliff, W. C.↗

NASA NTRS1991

A statistical approach to the brittle fracture of a multi-phase solid

A stochastic damage model is proposed to quantify the inherent statistical distribution of the fracture toughness of a brittle, multi-phase solid. The model, based on the macrocrack-microcrack interaction, incorporates uncertainties in locations and orientations of microcracks. Due to the high concentration of microcracks near the macro-tip, a higher order analysis based on traction boundary integral equations is formulated first for an arbitrary array of cracks. The effects of uncertainties in locations and orientations of microcracks at a macro-tip are analyzed quantitatively by using the boundary integral equations method in conjunction with the computer simulation of the random microcrack array. The short range interactions resulting from surrounding microcracks closet to the main crack tip are investigated. The effects of microcrack density parameter are also explored in the present study. The validity of the present model is demonstrated by comparing its statistical output with the Neville distribution function, which gives correct fits to sets of experimental data from multi-phase solids.

Liu, W. K.↗

NASA NTRS2001

A stochastic differential equation model of diurnal cortisol patterns

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

NASA Discipline Space Human Factors↗

NASA NTRS2003

Development of Probabilistic Life Prediction Methodologies and Testing Strategies for MEMS and CMC's

This effort is to investigate probabilistic life prediction methodologies for ceramic matrix composites and MicroElectroMechanical Systems (MEMS) and to analyze designs that determine stochastic properties of MEMS. For CMC's this includes a brief literature survey regarding lifing methodologies. Also of interest for MEMS is the design of a proper test for the Weibull size effect in thin film (bulge test) specimens. The Weibull size effect is a consequence of a stochastic strength response predicted from the Weibull distribution. Confirming that MEMS strength is controlled by the Weibull distribution will enable the development of a probabilistic design methodology for MEMS - similar to the GRC developed CARES/Life program for bulk ceramics. A main objective of this effort is to further develop and verify the ability of the Ceramics Analysis and Reliability Evaluation of Structures/Life (CARES/Life) code to predict the time-dependent reliability of MEMS structures subjected to multiple transient loads. A second set of objectives is to determine the applicability/suitability of the CARES/Life methodology for CMC analysis, what changes would be needed to the methodology and software, and if feasible, run a demonstration problem. Also important is an evaluation of CARES/Life coupled to the ANSYS Probabilistic Design System (PDS) and the potential of coupling transient reliability analysis to the ANSYS PDS.

Jadaan, Osama↗

NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗

NASA NTRS2009

The Status of the Mock LISA Data Challenges

For the last four years, many gravitational-wave researchers around the world have participated in the Mock LISA Data Challenges (MLDCs), a program to demonstrate and encourage the development of LISA data-analysis capabilities, tools and techniques. In this poster, we present a summary of the results of MLDC 3, which was completed in 2009. During MLDC 3, 27 participants from 15 institutions successfully analyzed data sets that included Galactic binaries, coalescing spinning massive black holes, extreme-mass-ratio inspirals, cosmic-string cusp bursts and a stochastic gravitational-wave background. We also describe the technical and scientific challenges that will be addressed by future MLI)Cs, starting with MLDC 4, which is currently in progress.

Baker, John↗

NASA NTRS2010

An Aircraft Separation Algorithm with Feedback and Perturbation

A separation algorithm is a set of rules that tell aircraft how to maneuver in order to maintain a minimum distance between them. This paper investigates demonstrating that separation algorithms satisfy the FAA requirement for the occurrence of incidents by means of simulation. Any demonstration that a separation algorithm, or any other aspect of flight, satisfies the FAA requirement is a challenge because of the stringent nature of the requirement and the complexity of airspace operations. The paper begins with a probability and statistical analysis of both the FAA requirement and demonstrating meeting it by a Monte Carlo approach. It considers the geometry of maintaining separation when one plane must change its flight path. It then develops a simple feedback control law that guides the planes on their paths. The presence of feedback control permits the introduction of perturbations, and the stochastic nature of the chosen perturbation is examined. The simulation program is described. This paper is an early effort in the realistic demonstration of a stringent requirement. Much remains to be done.

White, Allan L.↗

NASA NTRS1972

Sequence data - Magnitude and implications of some ambiguities.

A stochastic model is applied to the divergence of the horse-pig lineage from a common ansestor in terms of the alpha and beta chains of hemoglobin and fibrinopeptides. The results are compared with those based on the minimum mutation distance model of Fitch (1972). Buckwheat and cauliflower cytochrome c sequences are analyzed to demonstrate their ambiguities. A comparative analysis of evolutionary rates for various proteins of horses and pigs shows that errors of considerable magnitude are introduced by Glx and Asx ambiguities into evolutionary conclusions drawn from sequences of incompletely analyzed proteins.

Holmquist, R.↗

NASA NTRS1976

Linear and nonlinear analysis of orbital telescope/space shuttle dynamics and control

Work completed on the design and study of an annular suspension and pointing (ASP) system for the space shuttle was presented. This system makes use of a magnetically suspended vernier pointing assembly. The following objectives were pursued in this study: (1) development of a detailed mathematical model of the Space Shuttle/ASP system, (2) design of control laws in order to obtain the desired pointing performance, and (3) prediction of the statistical pointing accuracies in the presence of stochastic disturbances such as crew-motion, and sensor and actuator noise. The first two of these objectives are documented in this report.

Roberts, A. S., Jr.↗