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NASA NTRS2008

Uncertainty and Sensitivity Analyses of a Two-Parameter Impedance Prediction Model

This paper presents comparisons of predicted impedance uncertainty limits derived from Monte-Carlo-type simulations with a Two-Parameter (TP) impedance prediction model and measured impedance uncertainty limits based on multiple tests acquired in NASA Langley test rigs. These predicted and measured impedance uncertainty limits are used to evaluate the effects of simultaneous randomization of each input parameter for the impedance prediction and measurement processes. A sensitivity analysis is then used to further evaluate the TP prediction model by varying its input parameters on an individual basis. The variation imposed on the input parameters is based on measurements conducted with multiple tests in the NASA Langley normal incidence and grazing incidence impedance tubes; thus, the input parameters are assigned uncertainties commensurate with those of the measured data. These same measured data are used with the NASA Langley impedance measurement (eduction) processes to determine the corresponding measured impedance uncertainty limits, such that the predicted and measured impedance uncertainty limits (95% confidence intervals) can be compared. The measured reactance 95% confidence intervals encompass the corresponding predicted reactance confidence intervals over the frequency range of interest. The same is true for the confidence intervals of the measured and predicted resistance at near-resonance frequencies, but the predicted resistance confidence intervals are lower than the measured resistance confidence intervals (no overlap) at frequencies away from resonance. A sensitivity analysis indicates the discharge coefficient uncertainty is the major contributor to uncertainty in the predicted impedances for the perforate-over-honeycomb liner used in this study. This insight regarding the relative importance of each input parameter will be used to guide the design of experiments with test rigs currently being brought on-line at NASA Langley.

Jones, M. G.↗

NASA NTRS2014

Hypersonic Separated Flows About "Tick" Configurations With Sensitivity to Model Design

This paper presents computational results obtained by applying the direct simulation Monte Carlo (DSMC) method for hypersonic nonequilibrium flow about "tick-shaped" model configurations. These test models produces a complex flow where the nonequilibrium and rarefied aspects of the flow are initially enhanced as the flow passes over an expansion surface, and then the flow encounters a compression surface that can induce flow separation. The resulting flow is such that meaningful numerical simulations must have the capability to account for a significant range of rarefaction effects; hence the application of the DSMC method in the current study as the flow spans several flow regimes, including transitional, slip, and continuum. The current focus is to examine the sensitivity of both the model surface response (heating, friction and pressure) and flowfield structure to assumptions regarding surface boundary conditions and more extensively the impact of model design as influenced by leading edge configuration as well as the geometrical features of the expansion and compression surfaces. Numerical results indicate a strong sensitivity to both the extent of the leading edge sharpness and the magnitude of the leading edge bevel angle. Also, the length of the expansion surface for a fixed compression surface has a significant impact on the extent of separated flow.

Moss, J. N.↗

NASA NTRS1989

Improved Monte Carlo turbulence simulation for Shuttle reentry studies

A turbulence model for Space Shuttle reentry simulation is presented, which may be used to improve redline selection. It is suggested that the turbulence model in current use is overly conservative because it assumes severe turbulence from reentry altitude to the earth's surface. Two improved versions of the turbulence simulation equations are presented. These are third and fifth order approximations to the von Karman spectrum. The equations are in a form suitable for digital simulation. Both sets of equations can be used to generate a probability distribution of fuel remaining at landing.

Campbell, C. Warren↗

NASA NTRS1989

Monte Carlo turbulence simulation for Shuttle reentry studies

A realistic model for the Space Shuttle reentry which will permit more rational selection of the reaction control fuel redlines than did the current turbulence model, is described, with special attention given to the turbulence simulation difference equations, which are revised in this paper. The difference equations for the third-order approximation are presented for both the longitudinal turbulence and the transverse turbulence equations. Each set of equations can be used to generate a probability distribution of fuel remaining at landing.

Campbell, Warren C.↗

NASA NTRS1998

Aerospace Applications of Weibull and Monte Carlo Simulation with Importance Sampling

Recent developments in reliability modeling and computer technology have made it practical to use the Weibull time to failure distribution to model the system reliability of complex fault-tolerant computer-based systems. These system models are becoming increasingly popular in space systems applications as a result of mounting data that support the decreasing Weibull failure distribution and the expectation of increased system reliability. This presentation introduces the new reliability modeling developments and demonstrates their application to a novel space system application. The application is a proposed guidance, navigation, and control (GN&C) system for use in a long duration manned spacecraft for a possible Mars mission. Comparisons to the constant failure rate model are presented and the ramifications of doing so are discussed.

Bavuso, Salvatore J.↗

NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗

NASA NTRS1994

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Liu, Jiwen↗

NASA NTRS1973

Monte Carlo calculations of lunar regolith thickness distributions.

It is pointed out that none of the existing models of lunar regolith evolution take into account the relationship between regolith thickness, crater shape, and volume of debris ejected. The results of a Monte Carlo computer simulation of regolith evolution are presented. The simulation was designed to consider the full effect of the buffering regolith through calculation of the amount of debris produced by any given crater as a function of the amount of debris present at the site of the crater at the time of crater formation. The method is essentially an improved version of the Oberbeck and Quaide (1968) model.

Oberbeck, V. R.↗

NASA NTRSDate not supplied

Launch Vehicle Design and Requirements Verification Using Statistical Methods

- This presentation applies statistics to launch vehicle design, but the methods may be used for other engineering applications - Vehicle Models: What do we know when? How to separate parameters for making Monte Carlo runs - Known when assembling the vehicle but not during design - Known prior to committing to flight - Unknown at lift off - How do we correctly model the vehicle during the design phases? - Number of Monte Carlo samples - Requirements success - Design parameter values

Monte Carlo↗

NASA NTRS2014

Kinematic Modeling of Separation Compression for Paired Approaches to Closely-Spaced Parallel Runways

In a simultaneous paired approach to closely-spaced parallel runways, a pair of aircraft flies in close proximity on parallel approach paths. The longitudinal separation between the aircraft must be maintained within a range that avoids wake encounters and, if one of the aircraft blunders, avoids collision. To increase operational availability, the approach procedure must accommodate a mixture of aircraft sizes and, consequently, approach speeds. In these procedures, the slower aircraft is placed in the lead position. The faster aircraft maintains separation from the slow aircraft in a dependent operation until final approach and flies independently afterward. Due to the higher approach speed of the fast aircraft, longitudinal separation will decrease during final approach. Therefore, the fast aircraft must position itself before the final approach so that it will remain within the safe range of separation as separation decreases. Given the approach geometry and speed schedule for each aircraft, one can use kinematics to estimate the separation loss between a pair of aircraft. A kinematic model can complement fast-time Monte-Carlo simulations of the approach by enabling a tailored reduction in the variation of starting position for the fast aircraft. One could also implement the kinematic model in ground-based or on-board decision support tools to compute the optimal initial separation for a given pair of aircraft. To better match the auto-coupled flight of real aircraft, the paper derives a kinematic model where the speed schedule is flown using equivalent airspeed. The predicted time of flight using the equivalent airspeed kinematic model compares well against a high-fidelity aircraft simulation performing the same approach. This model also demonstrates a modest increase in the predicted loss of separation when contrasted against a kinematic model that assumes the scheduled speed is true airspeed.

Madden, Michael M.↗

NASA NTRS1993

The power spectrum of IRAS galaxies

A technique is presented for removing the power spectrum in flux-limited galaxy catalogs is presented and tested using Monte Carlo simulations of the IRAS survey based on N-body realizations of a standard CDM universe. The technique is applied to the 1.2 Jy IRAS catalog, comparing the resulting IRAS power spectrum with previous results in the literature. A qualitative comparison of the IRAS power spectrum with various theoretical models is shown. An extensive set of Monte Carlo experiments designed to test quantitatively the validity of standard CDM on large scales is described.

Fisher, Karl B.↗

NASA NTRS1977

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.↗

NASA NTRS2001

Free Vibration of Uncertain Unsymmetrically Laminated Beams

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

Kapania, Rakesh K.↗

NASA NTRS2016

Developing Atmospheric Retrieval Methods for Direct Imaging Spectroscopy of Gas Giants in Reflected Light I: Methane Abundances and Basic Cloud Properties

Reflected light spectroscopy and photometry of cool, directly imaged extrasolar giant planets are expected to be performed in the next decade by space-based telescopes equipped with optical wavelength coronagraphs and integral field spectrographs, such as the Wide-Field Infrared Survey Telescope (WFIRST). We are developing a new atmospheric retrieval methodology to help assess the science return and inform the instrument design for such future missions, and ultimately interpret the resulting observations. Our retrieval technique employs an albedo model coupled with both a Markov chain Monte Carlo Ensemble Sampler (emcee) and a multimodal nested sampling algorithm (MultiNest) to map the posterior distribution. This combination makes the global evidence calculation more robust for any given model, and highlights possible discrepancies in the likelihood maps. Here we apply this methodology to simulated spectra of cool giant planets. As a proof-of-concept, our current atmospheric model contains 1 or 2 cloud layers, methane as a major absorber, and a H2-He background gas. This 6-to-9 parameter model is appropriate for Jupiter-like planets and can be easily expanded in the future. In addition to deriving the marginal likelihood distribution and confidence intervals for the model parameters, we perform model selection to determine the significance of methane and cloud detection as a function of expected signal-to-noise, in the presence of spectral noise correlations. After internal validation, the method is applied to realistic reflected-light spectra of Jupiter, Saturn, and HD 99492 c, a likely observing target. We find that the presence or absence of clouds and methane can be determined with high accuracy, while parameters uncertainties are model-dependent.

spectroscopy↗

NASA NTRS1992

A model of the 8-25 micron point source infrared sky

We present a detailed model for the IR point-source sky that comprises geometrically and physically realistic representations of the Galactic disk, bulge, stellar halo, spiral arms (including the 'local arm'), molecular ring, and the extragalactic sky. We represent each of the distinct Galactic components by up to 87 types of Galactic source, each fully characterized by scale heights, space densities, and absolute magnitudes at BVJHK, 12, and 25 microns. The model is guided by a parallel Monte Carlo simulation of the Galaxy at 12 microns. The content of our Galactic source table constitutes a good match to the 12 micron luminosity function in the simulation, as well as to the luminosity functions at V and K. We are able to produce differential and cumulative IR source counts for any bandpass lying fully within the IRAS Low-Resolution Spectrometer's range (7.7-22.7 microns as well as for the IRAS 12 and 25 micron bands. These source counts match the IRAS observations well. The model can be used to predict the character of the point source sky expected for observations from IR space experiments.

Wainscoat, Richard J.↗

NASA NTRS2015

Assessing Disparities of Dengue Virus Transmission Risk across the US-Mexican Border Using a Climate Driven Vector-Epidemiological Model

Dengue fever is a mosquito‐borne viral disease reemerging throughout much of the tropical Americas. Dengue virus transmission is explicitly influenced by climate and the environment through its primary vector, Aedes aegypti. Temperature regulates Ae. aegypti development, survival, and replication rates as well as the incubation period of the virus within the mosquito. Precipitation provides water for many of the preferred breeding habitats of the mosquito, including buckets, old tires, and other places water can collect. Although transmission regularly occurs along the border region in Mexico, dengue virus transmission in bordering Arizona has not occurred. Using NASA's TRMM (Tropical Rainfall Measuring Mission) satellite for precipitation input and Daymet for temperature and supplemental precipitation input, we modeled dengue transmission along a US‐Mexico transect using a dynamic dengue transmission model that includes interacting vector ecology and epidemiological components. Model runs were performed for 5 cities in Sonora, Mexico and southern Arizona. Employing a Monte Carlo approach, we performed ensembles of several thousands of model simulations in order to resolve the model uncertainty arising from using different combinations of parameter values that are not well known. For cities with reported dengue case data, the top model simulations that best reproduced dengue case numbers were retained and their parameter values were extracted for comparison. These parameter values were used to run simulations in areas where dengue virus transmission does not occur or where dengue fever case data was unavailable. Additional model runs were performed to reveal how changes in climate or parameter values could alter transmission risk along the transect. The relative influence of climate variability and model parameters on dengue virus transmission is assessed to help public health workers prepare location specific infection prevention strategies.

Morin, Cory↗

NASA NTRS1977

The structure of the planets Jupiter and Saturn

Planetary models for Jupiter and Saturn are computed using a fourth-order theory and an equation of state for the molecular hydrogen and helium planetary envelopes taken from the Monte Carlo calculations of Slattery and Hubbard (1976). Models for Jupiter are found that have a small amount of heavy elements either mixed with hydrogen and helium throughout the interior of the planet or concentrated in a small dense core. Saturn is modeled with a solar-composition hydrogen and helium envelope and a small dense core. It is concluded that the molecular equation of state linked with suitable interior equations of state can produce Jovian models which satisfy the observational data. The planetary models show that the enrichment of heavy elements (relative to solar composition) is approximately 3 times for Jupiter and 10 times for Saturn.

Slattery, W. L.↗

NASA NTRS1985

The Characterization of Surface Variegation Effects on Remote Sensing

Improvements in remote sensing capabilities hinge very directly upon attaining an understanding of the physical processes contributing to the measurements. In order to devise new measurement strategies and to learn better techniques for processing remotely gathered data, it is necessary to understand and to characterize the complex radiative interactions of the atmosphere-surface system. In particular, it is important to understand the role of atmospheric structure, ground reflectance inhomogeneity and ground bidirectional reflectance type. The goals, then, are to model, analyze, and parameterize the observable effects of three dimensional atmospheric structure and composition and two dimensional variations in ground albedo and bidirectional reflectance. To achieve these goals, a Monte Carlo radiative transfer code is employed to model and analyze the effects of many of the complications which are present in nature.

Pearce, W. A.↗