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NASA NTRS1990

Estimation of subpixel vegetation cover using red-infrared scattergrams

The bulk properties of discontinuous vegetation canopies are estimated at subpixel scales by applying the method of moments to a linear stochastic geometric model of canopy-soil reflectance and one set of multispectral observations without ground truth. The procedure involves the formulation of conditional moments for subsets of pixels that possess similar properties and can be identified through their common orientation in red-infrared scattergrams. The analysis is facilitated by assuming geometric similarity among the canopy elements and by formulating a sampling scale ratio in terms of the bulk geometric scales of the canopy and the pixel. Three versions of the method are demonstrated using two simulated scenes and an actual forested watershed for which aerial radiometric data and corresponding ground truth were obtained.

Jasinski, Michael F.↗

NASA NTRS1990

Randomly Sampled-Data Control Systems

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

Han, Kuoruey↗

NASA NTRS1990

Electron acceleration by magnetosonic waves in solar flares

Results of a simulation of electron acceleration by magnetosonic waves in a solar coronal loop are presented. The dependence of the energization rate on the strength and shape of the wave spectrum is discussed. Comparisons are made with the predictions of quasilinear theory and of a model describing stochastic acceleration by waves as isotropic diffusion in momentum space.

Zweibel, Ellen G.↗

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 NTRS1990

Comparison of effects of copropagated and precomputed atmosphere profiles on Monte Carlo trajectory simulation

A realization of a stochastic atmosphere model for use in simulations is presented. The model provides pressure, density, temperature, and wind velocity as a function of latitude, longitude, and altitude, and is implemented in a three degree of freedom simulation package. This implementation is used in the Monte Carlo simulation of an aeroassisted orbital transfer maneuver and results are compared to those of a more traditional approach.

Queen, Eric M.↗

NASA NTRS1992

Response of Thematic Mapper bands to plant water stress

Changes in leaf reflectance as water content decreases have been hypothesized to occur in the 1.55-1.75 and 2.08-2.35 micron wavelength regions. To evaluate this hypothesis, studies were conducted on ryegrass (Lolium multiflorum Lam.) and oats (Avena sativa L.), which were grown in a controlled, outdoor situation. Both fully-watered control beds and water-stressed beds were periodically examined with a spectroradiometer calibrated against a reflectance reference of polytetrafluoroethylene. The observed changes correspond to those predicted by stochastic leaf models employed by other investigators (leaf reflection increases in the 1.55-1.75 micron region as leaf water content decreases). Although the percentage changes in TM bands 1-3 are nearly as great as those found in TM bands 5 and 7, the absolute values of reflectance change are much lower. It is believed that these patterns are probably characteristic of a broad range of vegetation types. In terms of phenomena detection, these patterns should be considered in any practical remote sensing sensor scenario.

Cibula, W. G.↗

NASA NTRS1992

Robustness of solutions to a benchmark control problem

The robustness of 10 solutions to a benchmark control design problem presented at the 1990 American Control Conference has been evaluated. The 10 controllers have second-to-eighth-order transfer functions and have been designed using several different methods, including H-infinity optimization, loop-transfer recovery, imaginary-axis shifting, constrained optimization, structured covariance, game theory, and the internal model principle. Stochastic robustness analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights into system response that are not readily derived from other robustness criteria and provides a common ground for judging controllers produced by alternative methods. One important conclusion is that gain and phase margins are not reliable indicators of the probability of instability. Furthermore, parameter variations actually may improve the likelihood of achieving selected performance metrics, as demonstrated by results for the probability of settling-time exceedance.

Stengel, Robert F.↗

NASA NTRS1993

A coupled multi-block solution procedure for spray combustion in complex geometries

Turbulent spray-combusting flow in complex geometries is presently treated by a coupled implicit procedure that employs finite-rate chemistry and real gas properties for combustion, as well as the stochastic separated model for spray and a multiblock treatment for complex geometries. Illustrative numerical tests conducted encompass a steady-state nonreacting backward-facing step flow, a premixed single-phase combustion flow, and spray combustion flow in a gas turbine combustor.

Chen, Kuo-Huey↗

NASA NTRS1992

An information theory approach for evaluating earth radiation budget (ERB) measurements - Nonuniform sampling of reflected shortwave radiation

An information theory approach to examine the temporal nonuniform sampling characteristics of shortwave (SW) flux for earth radiation budget (ERB) measurements is suggested. The information gain is computed by computing the information content before and after the measurements. A stochastic diurnal model for the SW flux is developed, and measurements for different orbital parameters are examined. The methodology is applied to specific NASA Polar platform and Tropical Rainfall Measuring Mission (TRMM) orbital parameters. The information theory approach, coupled with the developed SW diurnal model, is found to be promising for measurements involving nonuniform orbital sampling characteristics.

Barkstrom, Bruce R.↗

NASA NTRS1994

Turbulent mixing noise from supersonic jets

There is now a substantial body of theoretical and experimental evidence that the dominant part of the turbulent noise of supersonic jets is generated directly by the large turbulence structures/instability waves of the jet flow. Earlier, Tam and Burton provided a description of the physical mechanism by which supersonically traveling instability waves can generate sound efficiently. They used the method of matched asymptotic expansions to construct an instability wave solution which is valid in the far field. The present work is an extension of the theory of Tam and Burton. It is argued that the instability wave spectrum of the jet may be regarded as generated by stochastic white noise excitation at the nozzle lip region. The reason why the excitation has white noise characteristics is that near the nozzle lip region the flow in the jet mixing layer has no intrinsic length and time scales. The present stochastic wave model theory of supersonic jet noise contains a single unknown multiplicative constant. Comparisons between the calculated noise directivities at selected Strouhal numbers and experimental measurements of a Mach 2 jet at different jet temperatures have been carried out. Favorable agreements are found.

Tam, Christopher K. W.↗

NASA NTRS1993

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that the authors' techniques allow more accurate estimation of the global system loading, resulting in fewer object migrations than local methods. The authors' method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive load-balancing methods. Results from a preliminary analysis of another system and from simulation with a synthetic load provide some evidence of more general applicability.

LOAD CONTROL↗

NASA NTRS1997

Computation of Reacting Flows in Combustion Processes

The main objective of this research was to develop an efficient three-dimensional computer code for chemically reacting flows. The main computer code developed is ALLSPD-3D. The ALLSPD-3D computer program is developed for the calculation of three-dimensional, chemically reacting flows with sprays. The ALL-SPD code employs a coupled, strongly implicit solution procedure for turbulent spray combustion flows. A stochastic droplet model and an efficient method for treatment of the spray source terms in the gas-phase equations are used to calculate the evaporating liquid sprays. The chemistry treatment in the code is general enough that an arbitrary number of reaction and species can be defined by the users. Also, it is written in generalized curvilinear coordinates with both multi-block and flexible internal blockage capabilities to handle complex geometries. In addition, for general industrial combustion applications, the code provides both dilution and transpiration cooling capabilities. The ALLSPD algorithm, which employs the preconditioning and eigenvalue rescaling techniques, is capable of providing efficient solution for flows with a wide range of Mach numbers. Although written for three-dimensional flows in general, the code can be used for two-dimensional and axisymmetric flow computations as well. The code is written in such a way that it can be run in various computer platforms (supercomputers, workstations and parallel processors) and the GUI (Graphical User Interface) should provide a user-friendly tool in setting up and running the code.

Keith, Theo G., Jr.↗

NASA NTRS1993

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that our techniques allow more accurate estimation of the global system load ing, resulting in fewer object migration than local methods. Our method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive methods.

REAL TIME↗

NASA NTRS1998

Spatial Aspects of Interspecific Competition

Using several variants of a stochastic spatial model introduced by Silvertown et al., we investigate the effect of spatial distribution of individuals on the outcome of competition. First, we prove rigorously that if one species has a competitive advantage over each of the others, then eventually it takes over all the sites in the system. Second, we examine tradeoffs between competition and dispersal distance in a two-species system. Third, we consider a cyclic competitive relationship between three types. In this case, a nonspatial treatment leads to densities that follow neutrally stable cycles or even unstable spiral solutions, while a spatial model yields a stationary distribution with an interesting spatial structure.

Durrett, Rick↗

NASA NTRS1998

Modeling the Variability of the BL Lacertae Object PKS 2155-304

The bright X-ray-selected BL Lacertae object PKS 2155-304 has been the target of two intense multi-wavelength campaigns in 1991 November and in 1994 May. Although the spectral energy distributions at both epochs were quite similar, the source exhibited two very distinct variability patterns that cannot be easily reconciled with homogeneous one-zone C7 jet models. During the first epoch the variability was almost achromatic in amplitude, with a time lag between X-rays and ultraviolet radiation (UV) of approximately three hours, while during the second epoch the variability amplitude increased as a function of wavelength with the EUV flare peaking approximately one day after the X-ray flare. We model the source using a time-dependent inhomogeneous accelerating jet model. We reproduce the general characteristics of the different variability signatures by assuming that plasma disturbances with different physical properties propagate downstream in an underlying jet characterized by the same set of physical parameters at both epochs. A time delay of approximately one day between the hardening of the UV spectral index and the UV flux present at both epochs is modeled with stochastic fluctuations in the particle acceleration manifested through small variations of the maximum energy of the injected electrons. We predict that similar time delays will be present in future observations even in the absence of strong variability event. We stress the importance of observations at neighboring frequencies as a diagnostic tool for the structure of the quiescent jet in blazars especially in the seemingly dull case in which strong variability is absent.

Georganopuolos, Markos↗

NASA NTRS2006

What does reflection from cloud sides tell us about vertical distribution of cloud droplets?

In order to accurately measure the interaction of clouds with aerosols, we have to resolve the vertical distribution of cloud droplet sizes and determine the temperature of glaciation for clean and polluted clouds. Knowledge of the droplet vertical profile is also essential for understanding precipitation. So far, all existing satellites either measure cloud microphysics only at cloud top (e.g., MODIS) or give a vertical profile of precipitation sized droplets (e.g., Cloudsat). What if one measures cloud microphysical properties in the vertical by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides? This was the idea behind CLAIM-3D (A 3D - cloud aerosol interaction mission) recently proposed by NASA GSFC. This presentation will focus on the interpretation of the radiation reflected from cloud sides. In contrast to plane-parallel approximation, a conventional approach to all current operational retrievals, 3D radiative transfer will be used for interpreting the observed reflectances. As a proof of concept, we will show a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with prescribed microphysics. Instead of fixed values of the retrieved effective radii, the probability density functions of droplet size distributions will serve as possible retrievals.

Marshak, A.↗

NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗

NASA NTRS2006

What does Reflection from Cloud Sides tell us about Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from CloudSat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3-D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimentional(3-D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 microns) and one with liquid water efficient absorption of solar radiation (2.1 microns). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3-D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, A.↗