Results for “stochastic analysis” — Page 25

NASA NTRS2009

Stochastic Formal Correctness of Numerical Algorithms

We provide a framework to bound the probability that accumulated errors were never above a given threshold on numerical algorithms. Such algorithms are used for example in aircraft and nuclear power plants. This report contains simple formulas based on Levy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one out of a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.

Daumas, Marc↗

NASA NTRSDate not supplied

Computational Investigation of Oxidative Etch Pitting in FiberForm and Its Impact on Material Properties

Oxidation-driven carbon erosion does not occur uniformly but rather through the development of localized etch pits at active surface sites. These active sites form due to atomic defects on the carbon surface, making them significantly more reactive than the surrounding, non-defective areas. As a result, these sites are the first to react during ablation, leading to their removal. This process creates new defects in neighboring atoms, increasing their reactivity and causing localized carbon removal around these active sites. In this way, the highly reactive defective areas serve as nucleation points for the formation and growth of etch pits, which can have adverse effects on structural integrity of FiberForm. To better understand how these etch pits impact the material properties of carbon fiber microstructures, we have developed a new capability within the direct simulation Monte Carlo (DSMC) framework to capture the etch pit formation process. This capability, integrated into the DSMC code SPARTA (Stochastic Parallel Rarefied-gas Time-accurate Analyzer), models material removal in the presence of active sites, leading to the formation of etch pits. The current work focuses on studying the effects of these etch pits on the material properties of FiberForm, a widely used base material in thermal protection systems (TPS). The microstructure of virgin FiberForm, obtained via X-ray microtomography, is imported into SPARTA to generate the ablated geometries with etch pits. These modified microstructures are then analyzed using the Porous Microstructure Analysis (PuMA) software to compute various material properties, including elasticity, thermal conductivity, and permeability. We investigate the variation of these properties due to the complex surface topology changes caused by etch pit formation. Additionally, we compare the effects of pitting with the conventional model of shrinking fibers, traditionally used to simulate the ablation of carbon structures. Significant differences emerge between the two approaches. Consequently, this physically realistic model of material removal through etch pit formation offers improved accuracy in predicting the degradation of carbon-based TPS during oxidation. It also provides insights into other mechanisms, such as spallation, where chunks of material are removed into the flow due to etch pit growth. Ultimately, this model enhances our understanding of failure modes in these materials during ablation.

PuMA↗

NASA NTRS1977

Instantaneous and time-averaged dispersion and measurement models for estimation theory applications with elevated point source plumes

Estimation theory, which originated in guidance and control research, is applied to the analysis of air quality measurements and atmospheric dispersion models to provide reliable area-wide air quality estimates. A method for low dimensional modeling (in terms of the estimation state vector) of the instantaneous and time-average pollutant distributions is discussed. In particular, the fluctuating plume model of Gifford (1959) is extended to provide an expression for the instantaneous concentration due to an elevated point source. Individual models are also developed for all parameters in the instantaneous and the time-average plume equations, including the stochastic properties of the instantaneous fluctuating plume.

Diamante, J. M.↗

NASA NTRS1983

Approximation of the optimal compensator for a large space structure

This paper considers the approximation of the optimal compensator for a Large Space Structure. The compensator is based upon a solution to the Linear Stochastic Quadratic Regulator problem. Colocation of sensors and actuators is assumed. A small gain analytical solution for the optimal compensator is obtained for a single input/single output system, i.e., certain terms in the compensator can be neglected for sufficiently small gain. The compensator is calculated in terms of the kernel to a Volterra integral operator using a Neumann series. The calculation of the compensator is based upon the C sub 0 semigroup for the infinite dimensional system. A finite dimensional approximation of the compensator is, therefore, obtained through analysis of the infinite dimensional compensator which is a compact operator.

Mackay, M. K.↗

NASA NTRS1999

Tropical Intraseasonal Air-Sea Exchanges during the 1997 Pacific Warming

The Madden Julian Oscillations (MJO) and associated westerly wind (WW) events account for much of the tropical intraseasonal variability (TISV). The TISV has been suggested as an important stochastic forcing that may be one of the underlying causes for the observed irregularities of the El Nino-Southern Oscillation (ENSO). Recent observational studies and theories of interannual to interdecadal-scale variability suggest that ENSO may arise from different mechanisms depending on the basic states. The Pacific warming event of 1997, being associated with a period of strong MJO and WW events, serves as a natural experiment for studying the possible role of TISV in triggering an ENSO event. We have performed a combined statistical and composite analysis of surface WW events based on the assimilated surface wind and sea level pressure for the period of 1980-1993, the SSM/I wind for the period of 1988-1997, and OLR. Results indicates that extratropical forcing contribute significantly to the evolution of MJO and establishment of WW events over the Pacific warm pool. Following the major WW events, there appeared an eastward extension of equatorial warm SST anomalies from the western Pacific warm pool. Such tropical-extratropical interaction is particularly clear in the winter of 96-97 that leads to the recent warming event in 1997/98. From the above discussion, our current study on this subject is based on the hypothesis that 1) there is an enhanced air-sea interaction associated with TISV and the northerly surges from the extratropics in the initial phase of the 97/98 warming event, and 2) the relevant mechanisms are functions of the basic state of the coupled system (in terms of SST distribution and atmospheric mean circulation) that varies at the interannual and interdecadal time scale. We are analyzing the space-time structure of the northerly surges, their association with air-sea fluxes and upper ocean responses during the period of September 1996 to June 1997. The estimate of daily values of latent heat fluxes is based on NSCAT wind, SST, and ECMWF surface air temperature and SSM/I water vapor data (Chou et al. 1997). To understand the relevant mechanisms, we will analyze the origin of the northerly surges in terms of atmospheric instability associated with the extratropical circulation, and the mutual influence between the tropical heating and the extratropical circulation. In this meeting, we will report the analysis addressing the first part of the above hypothesis.

Sui, C.-H.↗

NASA NTRS1981

Data acquisition and analysis of range-finding systems for spacing construction

For space missions of future, completely autonomous robotic machines will be required to free astronauts from routine chores of equipment maintenance, servicing of faulty systems, etc. and to extend human capabilities in hazardous environments full of cosmic and other harmful radiations. In places of high radiation and uncontrollable ambient illuminations, T.V. camera based vision systems cannot work effectively. However, a vision system utilizing directly measured range information with a time of flight laser rangefinder, can successfully operate under these environments. Such a system will be independent of proper illumination conditions and the interfering effects of intense radiation of all kinds will be eliminated by the tuned input of the laser instrument. Processing the range data according to certain decision, stochastic estimation and heuristic schemes, the laser based vision system will recognize known objects and thus provide sufficient information to the robot's control system which can develop strategies for various objectives.

Shen, C. N.↗

NASA NTRSDate not supplied

Some Unexpected Risks from Lunar Ejecta

Human or robotic operations on the lunar surface or other airless bodies are vulnerable not just to direct impacts from meteoroids, but by impacts of meteoroids or asteroids elsewhere on the planetary surface excavating a large mass of high-speed ejecta that may in turn impact the asset. While this ejecta environment has been known since Apollo days, recent analysis of this risk has uncovered some interesting and unexpected properties of the ejecta environment. This includes a non-trivial contribution from nearby primary impacts (within a few tens of meters) where the ejecta impact the asset while still ascending from the planetary surface, over and above the more “traditional” ejecta component that descends from above. In addition, the outsized contribution to the ejecta risk from nearby primary impacts (within a few tens of kilometers) relative to impacts far away means that the flux on an asset will show considerable stochastic variability, such that a simple average flux may not reveal the full impact risk to a mission. This presentation will describe some of these phenomena and offer suggestions for how these risks can be better calculated to ensure mission safety.

Mark Matney↗

NASA NTRSDate not supplied

Computational Study of Oxidative Etch Pitting in FiberForm and the Effect on Its Material Properties

Erosion of carbon due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface, and have much higher reactivity compared to average non-defective sites. Thus, these active sites are first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these “active” sites. In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, a commonly used base material within many thermal protection system materials (TPS). The microstructure of virgin FiberForm obtained directly from X-ray microtomography experiments is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported within the Porous Microstructure Analysis (PuMA) software and various material properties such as elasticity, thermal conductivity, and permeability are computed. The variation of these properties as a result of the complex evolution of the surface topology due to etch pit formation is studied and analyzed. Furthermore, the effect of pitting is compared to the case of shrinking fibers, which has been the standard for modelling ablation of carbon structures; and significant differences are observed. Thus, such a physically realistic modeling of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to etch pit growth. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

Carbon Ablators↗

NASA NTRSDate not supplied

Computational Study of Oxidative Etch Pitting in FiberForm and the Effect on Its Material Properties

Erosion of carbon due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface, and have much higher reactivity compared to average non-defective sites. Thus, these active sites are first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these “active” sites. In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, a commonly used base material within many thermal protection system materials (TPS). The microstructure of virgin FiberForm obtained directly from X-ray microtomography experiments is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported within the Porous Microstructure Analysis (PuMA) software and various material properties such as elasticity, thermal conductivity, and permeability are computed. The variation of these properties as a result of the complex evolution of the surface topology due to etch pit formation is studied and analyzed. Furthermore, the effect of pitting is compared to the case of shrinking fibers, which has been the standard for modelling ablation of carbon structures; and significant differences are observed. Thus, such a physically realistic modeling of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to etch pit growth. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

Carbon Ablators↗

NASA NTRSDate not supplied

Simulation of Oxidative Etch Pit Formation and Growth on FiberForm

Erosion of carbon surfaces due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface and have much higher reactivity compared to average non-defective sites. Thus, these active sites are the first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective, and increasing their reactivity, thus leading to localized carbon removal around these “active” sites. In this manner, these highly reactive defects serve as nucleation sites for the formation and growth of etch pits, with detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in the presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, the precursor substrate of the PICA Thermal Protection System (TPS) material. The microstructure of virgin FiberForm obtained directly from X-ray microtomography scans is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported into the Porous Microstructure Analysis (PuMA) software and various material properties such as thermal conductivity, elasticity, and permeability are computed. The variation of these properties because of the complex evolution of the surface topology due to the formation of etch pits is studied and analyzed. Furthermore, the effect of pitting is compared to the case of uniform radial shrinking of fibers, which has been the standard for modelling ablation of carbon structures, and significant differences are observed. Thus, a physically realistic model of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to the growth of etch pits. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

DSMC↗

NASA NTRSDate not supplied

Simulation of Oxidative Etch Pit Formation and Growth on FiberForm

Erosion of carbon surfaces due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface and have much higher reactivity compared to average non-defective sites. Thus, these active sites are the first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective, and increasing their reactivity, thus leading to localized carbon removal around these “active” sites. In this manner, these highly reactive defects serve as nucleation sites for the formation and growth of etch pits, with detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in the presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, the precursor substrate of the PICA Thermal Protection System (TPS) material. The microstructure of virgin FiberForm obtained directly from X-ray microtomography scans is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported into the Porous Microstructure Analysis (PuMA) software and various material properties such as thermal conductivity, elasticity, and permeability are computed. The variation of these properties because of the complex evolution of the surface topology due to the formation of etch pits is studied and analyzed. Furthermore, the effect of pitting is compared to the case of uniform radial shrinking of fibers, which has been the standard for modelling ablation of carbon structures, and significant differences are observed. Thus, a physically realistic model of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to the growth of etch pits. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

DSMC↗

NASA NTRS1979

Modeling of terrain gradient for stochastically spaced rows of a measurement matrix

Terrain gradients are employed to evaluate passable regions for unmanned martian roving vehicle. Range data matrix is displaced randomly row wise at the shallow elevation angles near the skyline. The magnitude of the measurement noise in the elevation angles can approach that of the spacing of the same angle. By using a variable incremental data spacing scanning scheme, one can estimate this signal noise ratio. It is found that the error in slope estimate at far distance becomes large for a given elevation angle error. Evaluation of the in-path slopes can be expressed in terms of the inverse of the range slopes. This is because of the fact that the elevation angle is considered as a random variable while the range data are relatively less noisy. An error analysis is performed and it is found that the change of slope is a nonlinear function of the error in elevation angle.

Mediavilla, R.↗

NASA NTRS1986

Control design for robust stability in linear regulators: Application to aerospace flight control

Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.

Yedavalli, R. K.↗

NASA NTRS2013

Unit-Sphere Multiaxial Stochastic-Strength Model Applied to Anisotropic and Composite Materials

Models that predict the failure probability of brittle materials under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This methodology has been extended to predict the multiaxial strength response of transversely isotropic brittle materials, including polymer matrix composites (PMCs), by considering (1) flaw-orientation anisotropy, whereby a preexisting microcrack has a higher likelihood of being oriented in one direction over another direction, and (2) critical strength, or K (sub Ic) orientation anisotropy, whereby the level of critical strength or fracture toughness for mode I crack propagation, K (sub Ic), changes with regard to the orientation of the microstructure. In this report, results from finite element analysis of a fiber-reinforced-matrix unit cell were used with the unit-sphere model to predict the biaxial strength response of a unidirectional PMC previously reported from the World-Wide Failure Exercise. Results for nuclear-grade graphite materials under biaxial loading are also shown for comparison. This effort was successful in predicting the multiaxial strength response for the chosen problems. Findings regarding stress-state interactions and failure modes also are provided.

Nemeth, Noel, N.↗

NASA NTRSDate not supplied

Uniform Dust Deposition System for Dust Tolerance Studies

Future missions to the Moon will require mechanisms and materials to effectively and reliably operate in the presences of lunar regolith. One of the challenges of developing such technologies is terrestrial testing with lunar dust simulants. Dust has a stochastic nature of depositing and it can be difficult to accurately apply it to surfaces of interest. Deposition density, particles size distribution, and percent coverage are all factors that affect the quality of dust mitigation testing. Therefore, to enable such testing the dust mitigation and seals teams at NASA Glenn Research Center (GRC) have developed a system that can uniformly and repeatably deposit lunar simulants on a range of surfaces. Testing of the Dust Deposition System (DDS) and an associatedsimulant preparation methodology have quantified the levels of uniformity and precision for this system. Furthermore, the deposition system has been paired with automated micrograph capturing and machine learning image analysis to correlate the images of dust on a surface to deposition density (in g/cm2). This correlation alleviates the need for tested samples to be accurately weighed with milligram precision and may be a useful tool for in-situ contamination evaluation on the Moon. This paper covers the design and validation testing for the DDS.

Stephen Gerdts↗

NASA NTRSDate not supplied

Uniform Dust Deposition System for Dust Tolerance Studies

Future missions to the Moon will require mechanisms and materials to effectively and reliably operate in the presences of lunar regolith. One of the challenges of developing such technologies is terrestrial testing with lunar dust simulants. Dust has a stochastic nature of depositing and it can be difficult to accurately apply it to surfaces of interest. Deposition density, particles size distribution, and percent coverage are all factors that affect the quality of dust mitigation testing. Therefore, to enable such testing the dust mitigation and seals teams at NASA Glenn Research Center (GRC) have developed a system that can uniformly and repeatably deposit lunar simulants on a range of surfaces. Testing of the Dust Deposition System (DDS) and an associated simulant preparation methodology have quantified the levels of uniformity and precision for this system. Furthermore, the deposition system has been paired with automated micrograph capturing and machine learning image analysis to correlate the images of dust on a surface to deposition density (in g/cm2). This correlation alleviates the need for tested samples to be accurately weighed with milligram precision and may be a useful tool for in-situ contamination evaluation on the Moon. This paper covers the design and validation testing for the DDS.

Dust↗

NASA NTRS1994

Micromechanics of fatigue in woven and stitched composites

The goals of this research program were to: (1) determine how microstructural factors, especially the architecture of reinforcing fibers, control stiffness, strength, and fatigue life in 3D woven composites; (2) identify mechanisms of failure; (3) model composite stiffness; (4) model notched and unnotched strength; and (5) model fatigue life. We have examined a total of eleven different angle and orthogonal interlock woven composites. Extensive testing has revealed that these 3D woven composites possess an extraordinary combination of strength, damage tolerance, and notch insensitivity in compression and tension and in monotonic and cyclic loading. In many important regards, 3D woven composites far outstrip conventional 2D laminates or stitched laminates. Detailed microscopic analysis of damage has led to a comprehensive picture of the essential mechanisms of failure and how they are related to the reinforcement geometry. The critical characteristics of the weave architecture that promote favorable properties have been identified. Key parameters are tow size and the distributions in space and strength of geometrical flaws. The geometrical flaws should be regarded as controllable characteristics of the weave in design and manufacture. In addressing our goals, the simplest possible models of properties were always sought, in a blend of old and new modeling concepts. Nevertheless, certain properties, especially regarding damage tolerance, ultimate failure, and the detailed effects of weave architecture, require computationally intensive stochastic modeling. We have developed a new model, the 'binary model,' to carry out such tasks in the most efficient manner and with faithful representation of crucial mechanisms. This is the final report for contract NAS1-18840. It covers all work from April 1989 up to the conclusion of the program in January 1993.

Cox, B. N.↗

NASA NTRS2008

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Cohn, Stephen E.↗