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At least 127 records · Page 7

Influence of a fat layer on the near infrared spectra of human muscle: quantitative analysis based on two-layered Monte Carlo simulations and phantom experiments

The influence of fat thickness on the diffuse reflectance spectra of muscle in the near infrared (NIR) region is studied by Monte Carlo simulations of a two-layer structure and with phantom experiments. A polynomial relationship was established between the fat thickness and the detected diffuse reflectance. The influence of a range of optical coefficients (absorption and reduced scattering) for fat and muscle over the known range of human physiological values was also investigated. Subject-to-subject variation in the fat optical coefficients and thickness can be ignored if the fat thickness is less than 5 mm. A method was proposed to correct the fat thickness influence. c2005 Optical Society of America.

NASA Discipline Life Sciences Technologies↗

Pre-mare cratering and early solar system history

An evaluation of the application of the high extra-lunar flux in pre-mare times to more general problems of early solar system history is attempted by combining the results of dynamic studies with lunar chronological data. Dynamical studies permit separate evaluation of the possible sources for both the normal flux during the first 600 m.y. years of lunar history as well as the peak which apparently occurred 4.0 b.y. ago. Dynamical studies have been carried out in order to determine the extent to which a heliocentric flux could be confined to the Moon (and Earth). A Monte Carlo method has been used to calculate the relative impact rates of planet-crossing bodies with the moon and the terrestrial planets. It is concluded that the time-variation of the flux on these planets is closely related to that on the moon.

Wetherill, G. W.↗

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗

Thermal radiation model for solid rocket booster plumes

The Monte Carlo method is used to model the thermal radiation field of the plumes for the dual solid rocket boosters astride the Space Shuttle launch configuration. The model accounts for axial and radial variations in radiative properties of the plumes. The plumes are considered to be composed of a dispersion of aluminum oxide (Al2O3) particles immersed in the gaseous products of combustion. The principal emitting gases are taken to be CO, CO2, H2O, and HCl. The thermal model is based on local thermodynamic equilibrium. Scattering of radiant energy by Al2O3 particles may be treated as isotropic or anisotropic. Sample radiant heating rates to the base region of the Space Shuttle are shown. Space Shuttle geometries are simulated as combinations of quadric surfaces.

Watson, G. H.↗

A model for simulating random atmospheres as a function of latitude, season, and time

An empirical stochastic computer model was developed with the capability of generating random thermodynamic profiles of the atmosphere below an altitude of 99 km which are characteristic of any given season, latitude, and time of day. Samples of temperature, density, and pressure profiles generated by the model are statistically similar to measured profiles in a data base of over 6000 rocket and high-altitude atmospheric soundings; that is, means and standard deviations of modeled profiles and their vertical gradients are in close agreement with data. Model-generated samples can be used for Monte Carlo simulations of aircraft or spacecraft trajectories to predict or account for the effects on a vehicle's performance of atmospheric variability. Other potential uses for the model are in simulating pollutant dispersion patterns, variations in sound propagation, and other phenomena which are dependent on atmospheric properties, and in developing data-reduction software for satellite monitoring systems.

Campbell, J. W.↗

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗

Computation of flowfields for hypersonic flight at high altitudes

Recent direct simulation Monte Carlo methods are reviewed focusing on the nonequilibrium aspects of rarefied hypersonic flows typical of reentry conditions. The calculations identify the altitudes for which the onset of dissociation occurs, the magnitude of the surface temperature variations, the effect of the shock wave structure on the chemistry of a dissociating gas, and the radiation emisssion for reentry flowfields.

Moss, James N.↗

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗

Development of the X-33 Aerodynamic Uncertainty Model

An aerodynamic uncertainty model for the X-33 single-stage-to-orbit demonstrator aircraft has been developed at NASA Dryden Flight Research Center. The model is based on comparisons of historical flight test estimates to preflight wind-tunnel and analysis code predictions of vehicle aerodynamics documented during six lifting-body aircraft and the Space Shuttle Orbiter flight programs. The lifting-body and Orbiter data were used to define an appropriate uncertainty magnitude in the subsonic and supersonic flight regions, and the Orbiter data were used to extend the database to hypersonic Mach numbers. The uncertainty data consist of increments or percentage variations in the important aerodynamic coefficients and derivatives as a function of Mach number along a nominal trajectory. The uncertainty models will be used to perform linear analysis of the X-33 flight control system and Monte Carlo mission simulation studies. Because the X-33 aerodynamic uncertainty model was developed exclusively using historical data rather than X-33 specific characteristics, the model may be useful for other lifting-body studies.

Cobleigh, Brent R.↗

Uncertainty Analysis of the NASA Glenn 8x6 Supersonic Wind Tunnel

This paper presents methods and results of a detailed measurement uncertainty analysis that was performed for the 8- by 6-foot Supersonic Wind Tunnel located at the NASA Glenn Research Center. The statistical methods and engineering judgments used to estimate elemental uncertainties are described. The Monte Carlo method of propagating uncertainty was selected to determine the uncertainty of calculated variables of interest. A detailed description of the Monte Carlo method as applied for this analysis is provided. Detailed uncertainty results for the uncertainty in average free stream Mach number as well as other variables of interest are provided. All results are presented as random (variation in observed values about a true value), systematic (potential offset between observed and true value), and total (random and systematic combined) uncertainty. The largest sources contributing to uncertainty are determined and potential improvement opportunities for the facility are investigated.

Error↗

A Comparison of Bank Control and Direct Force Control for Aerocapture at Uranus

We compare bank angle control and direct force control for aerocapture at Uranus. We utilize the Fully Numerical Predictor-corrector Aerocapture Guidance for both configurations and discuss modifications to the direct force control corrector to handle multiple roots. Using the Genesis flight mechanics simulation, we analyze both nominal and dispersed three-degree-of-freedom trajectories with perfect navigation and control. We present Monte Carlo results and discuss differences between the performance of the two control approaches. We find that increased bank angle rate and acceleration limits do not increase the performance of the bank control configuration. We analyze a variation with tighter angle of attack bounds and find that the tuning and performance of the two configurations converges, because direct force control is less able to modulate drag.

Sergio A Sandoval↗

Investigation of Magmatic Activities on Early Mars Using Igneous Mineral Chemistry in Gale Crater, Mars

One objective of rover missions is exploring the geological context of the surroundings. Over the years, igneous petrology and sedimentology have been disconnected, the first investigating magmatic processes and volcanic activities, and the second seeking environmental conditions in the past and assessing the habitability of the planet. Although different, one is related to the other: igneous rocks are altered and broken down, leading to the formation of sedimentary rocks, which can in turn be used to back out the nature of their magmatic source. The Curiosity rover that landed in the 3.7 Gyr old impact crater Gale is traveling through sedimentary rocks. About fifty float rocks have been observed, and several of them with ambiguous texture and composition have been classified as igneous or sedimentary depending on studies such as Jake_M. The composition of several unambiguous igneous rocks has been analyzed [4- 6] but their heterogeneity at a larger instrumental (measurement size < 2 cm) scale prevents the measurement of a bulk composition as performed on Earth. An original approach avoiding these two last issues is to consider igneous mineral chemistry analyzed within igneous and sedimentary rocks to assess magmatic processes that could have formed them. Most Curiosity data are used to explore ancient environmental conditions, and a significant number of compositional analyses are under-explored for constraining magmatic activities. We will present how we can make use of sedimentary data for investigating igneous processes in the vicinity of Gale crater. Geological Context: We focus on the first 750 martian days, corresponding to measurements in a coherent lacustrine sedimentary unit called Bradbury, because all sedimentary rocks were sourced from the same watershed and appear to have a consistent source with minimal alteration [2-3]. Igneous detrital minerals including feldspar and pyroxene, are observed in sedimentary rocks. Monte Carlo models showed that minimal cation loss is observed based on the composition of all Bradbury rocks, implying negligible weathering [3]. Although clay minerals are detected in few rocks [7], chemical compositions of rocks can be explained by a mixture of primary igneous minerals [3]. Variation of composition within Bradbury rocks can be explained by mineral sorting and one distinct source component. While a common magmatic source is suggested, Bradbury sediments likely come from several volcanic eruptions from a single magmatic chamber [9- 10]. The occurrence of alkali minerals like sanidine and K-rich rocks throughout Bradbury supports the presence of a potassic component, likely trachytic, while plagioclase and a mafic composition suggest a basaltic component [8-9]. Instruments: Mineral chemistry can be estimated by three instruments onboard Curiosity. The CheMin instrument enables detection of mineral assemblages using X-ray diffraction (XRD). Using Rietveld refinement, each mineral is identified according to their 1D XRD pattern [11]. Note that distinction between pyroxene minerals is challenging with the CheMin instrument due to overlapping peaks on XRD patterns and low angular resolution of the instrument [12]. Then, using least square regression and optimization algorithms based on unit-cell parameters, mineral chemistry has been estimated by [11]. Plagioclase composition has been estimated using the NaAlSi3O8- CaAl2Si2O8 system and alkali feldspar is based on the NaAlSi3O8-KAlSi3O8 system (stars in Fig.1). Two mudstone samples (John Klein and Cumberland) and one sandstone sample (Windjana) were analyzed by CheMin at Yellowknife Bay and Kimberley, respectively. Figure 1. Ternary diagrams of feldspars (top) and pyroxene (bottom) quadrilateral. Stars correspond to CheMin composition and the gray patches to ChemCam composition. The colored dots are the composition of feldspar and pyroxene that crystallized during fractional crystallization at FMQ+1 of a melt extracted at distinct melting degree during the adiabatic ascent of a primitive mantle composition, without any water (left panels) and with 0.5 wt.% of water (right panels) at distinct pressure. The ChemCam instrument enables the analysis of the chemical compositions of rocks at hundreds of micrometer scale (350-550 μm) using laser induced breakdown spectroscopy (LIBS), which may provide the composition of minerals when they are larger than the beam spot (>550 μm) [13]. Within >5000 LIBS points, we performed a typical stoichiometric filtering allowing us to distinguish 56 feldspar and 10 pyroxene mineral compositions (grey patches in Fig. 1). Finally, the Alpha Particle X-ray Spectrometer (APXS) analyzes the composition of rocks with a 1.6 cm diameter spot size. Monte Carlo mass balance modeling allowed [3] to decipher a feldspar range varying between An30 and An40 (Fig. 1). Discussion: Although there could be a more complex history and other ways to form the whole compositional range of igneous minerals analyzed within the Bradbury formation, we are presenting here simple magmatic pathways commonly occurring on Earth using the thermodynamical softwares pMELTS and rhyoliteMELTS [14]. The objective is to find reasonable igneous processes that produce minerals that parallel the compositions of feldspar and pyroxene analyzed by the Curiosity rover. As commonly observed for mid-ocean ridge basalts, the adiabatic ascent of a primitive mantle composition [15] partially melting at 2 GPa has been modeled, followed by the extraction of a liquid at distinct degrees of partial melting, which undergoes fractional crystallization at an oxygen fugacity +1 log unit above the fayalite-magnetite-quartz (FMQ) buffer within the crust (0.02-0.4 GPa) with H2O = 0- 0.5 wt. %. These latter conditions correspond to those recorded within igneous clasts from the Noachian martian breccia NWA 7034 and paired and within Gale igneous rocks (colored dots in Fig. 1) [16-17]. To check the reliability of these 2-step models, we also tested fractional crystallization at similar conditions (FMQ+1; P=0.02-0.4 GPa; H2O = 0-0.5 wt. %) of starting compositions corresponding to that of magmas with distinct melting degrees obtained from isobaric experiments at 2 GPa [18]. Mineral compositions obtained from both models are similar. As shown on Fig. 1, the whole range of observed feldspar compositions cannot be reproduced by fractionation of one magma only. Indeed, while alkali feldspar and Na-plagioclase likely crystallized from fractional crystallization of a low-degree melt (here <15%), plagioclase and pyroxene can only be formed by fractional crystallization of a higher degree melt (here >19%). The corresponding liquid descent lines are broadly in agreement with compositions estimated by ChemCam corresponding to float igneous rocks (Fig. 2) [4-6]. Figure 2. Silica versus alkali content. Lines show the liquid lines of descent from magmas with distinct degrees of melting. Gray patches represents the composition of Gale igneous rocks [4-6]. Trachytic to rhyolitic magmas crystallize alkali feldspar, and andesite to dacite magmas likely form plagioclase. Therefore, at least two starting magmas at distinct melting degrees, which could easily come from a single mantle source, are necessary to explain the whole compositional range of feldspar and pyroxene analyzed within Bradbury rocks. Conclusion: Because rocks from the Bradbury formation are likely originating from the same magmatic source with minimal weathering as supported by several studies using different approaches, igneous mineral chemistry analyzed by CheMin and ChemCam allows us to back out reasonable magmatic pathways that could have crystallized them. Fractional crystallization of at least two starting magmas originating from distinct melting degrees of a single mantle source can explain the whole range of feldspar and pyroxene composition. Both alkaline and sub-alkaline liquids can be produced, with compositions corresponding to those of the igneous rocks analyzed by ChemCam within the Bradbury formation, highlighting the complexity of Mars magmatism.

Payre, V.↗

Degree and direction of polarization of multiple scattered light. I - Homogeneous cloud layers.

It is shown that the Monte Carlo method can provide useful information on the polarization and its direction for homogeneous layers corresponding to the haze C, nimbostratus, and ice crystals models. Results for various optical thicknesses and two solar zenith angles show the variation with these parameters. In most cases the direction of polarization with respect to the meridian plane (which contains the outgoing photon) does not change appreciably with the optical thickness of the scattering layer, so that the conclusion that the direction of polarization is determined mainly by the direction of the incident and scattered photons, obtained for single scattering, should apply approximately when multiple scattering is taken into account.

Kattawar, G. W.↗

Development and computer implementation of design/analysis techniques for multilayered composite structures. Probabilistic fiber composite micromechanics

Probabilistic composite micromechanics methods are developed that simulate expected uncertainties in unidirectional fiber composite properties. These methods are in the form of computational procedures using Monte Carlo simulation. The variables in which uncertainties are accounted for include constituent and void volume ratios, constituent elastic properties and strengths, and fiber misalignment. A graphite/epoxy unidirectional composite (ply) is studied to demonstrate fiber composite material property variations induced by random changes expected at the material micro level. Regression results are presented to show the relative correlation between predictor and response variables in the study. These computational procedures make possible a formal description of anticipated random processes at the intraply level, and the related effects of these on composite properties.

Stock, Thomas A.↗

Probabilistic Fiber Composite Micromechanics

Probabilistic composite micromechanics methods are developed that simulate expected uncertainties in unidirectional fiber composite properties. These methods are in the form of computational procedures using Monte Carlo simulation. The variables in which uncertainties are accounted for include constituent and void volume ratios, constituent elastic properties and strengths, and fiber misalignment. A graphite/epoxy unidirectional composite (ply) is studied to demonstrate fiber composite material property variations induced by random changes expected at the material micro level. Regression results are presented to show the relative correlation between predictor and response variables in the study. These computational procedures make possible a formal description of anticipated random processes at the intra-ply level, and the related effects of these on composite properties.

Stock, Thomas A.↗

Development of a Spectral Model Based on Charge Transport for the Swift/BAT 32K CdZnTe Detector Array

The properties of 32K CdZnTe (4 x 4 sq mm large, 2 mm thick) detectors have been studied in the pre-flight calibration of the Burst Alert Telescope (BAT) on-board the Swift Gamma-ray Burst Explorer (scheduled for launch in November 2004). In order to understand the energy response of the BAT CdZnTe array, we first quantify the mobility-lifetime (mu tau) products of carriers in individual CdZnTe detectors, which produce a position dependency in the charge induction efficiency and results in a low energy tail in the energy spectrum. Based on a new method utilizing (57)Co spectra obtained at different bias voltages, the mu tau for electrons ranges from 5.0 x 10(exp -4) to 1.0 x 10(exp -2) sq cm/V while the mu tau for holes ranges from 1.3 x 10(exp -5 to 1.8 x 10(exp -4) sq cm/V. We find that this wide distribution of mu tau products explains the large diversity in spectral shapes between CdZnTe detectors well. We also find that the variation of mu tau products can be attributed to the difference of crystal ingots or manufacturing harness. We utilize the 32K sets of extracted mu tau products to develop a spectral model of the detector. In combination with Monte Carlo simulations, we can construct a spectral model for any photon energy or any incident angle.

Sato, Goro↗

Some Interesting Applications of Probabilistic Techiques in Structural Dynamic Analysis of Rocket Engines

Numerical and Analytical methods developed to determine damage accumulation in specific engine components when speed variation included. Dither Life Ratio shown to be well over factor of 2 for specific example. Steady‐State assumption shown to be accurate for most turbopump cases, allowing rapid calculation of DLR. If hot‐fire speed data unknown, Monte Carlo method developed that uses speed statistics for similar engines. Application of techniques allow analyst to reduce both uncertainty and excess conservatism. High values of DLR could allow previously unacceptable part to pass HCF criteria without redesign. Given benefit and ease of implementation, recommend that any finite life turbomachine component analysis adopt these techniques. Probability Values calculated, compared, and evaluated for several industry‐proposed methods for combining random and harmonic loads. Two new excel macros written to calculate combined load for any specific probability level. Closed form Curve fits generated for widely used 3(sigma) and 2(sigma) probability levels. For design of lightweight aerospace components, obtaining accurate, reproducible, statistically meaningful answer critical.

Brown, Andrew M.↗

Stochastic robustness of linear control systems

A simple numerical procedure for estimating the stochastic robustness of a linear, time-invariant system is described. Monte Carlo evaluation of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This definition of robustness is an alternative to existing deterministic definitions that address both structured and unstructured parameter variations directly. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variations. Trivial extensions of the procedure admit alternate discriminants to be considered. Thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions also can be estimated. Results are particularly amenable to graphical presentation.

Stengel, Robert F.↗