Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Random variables”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Interannual variability of global dust storms on Mars

Under the assumption that the cross-equatorial Hadley circulation plays a key role in the onset of Martian global dust storms, numerical simulations indicate that a northern hemisphere dust haze weakens its intensity and, thereby, its contribution to the surface stress in the southern hemisphere. Since this in turn reduces the possibility of global dust storm development, the interannual variability observed is the result of either a competition between circulations in opposite hemispheres, in which case the variability has a random component, or it is the result of dust cycling between hemispheres, so that the variability is related to the characteristics of the global dust storms themselves.

Haberle, Robert M.↗
NASA NTRS1987

Interannual variability of global dust storms on Mars

Global dust storms on Mars occur in some years but not in others. In years with global dust storms, dust is raised in the Southern Hemisphere and spread over much of the planet by an intensified Hadley circulation. In years without global dust storms, dust is raised in the Northern Hemisphere by relatively active midlatitude storm systems, but does not spread globally. In both cases the dusty season is winter in the north. It is shown from numerical simulations that a Northern Hemisphere dust haze weakens the intensity of the cross equatorial Hadley circulation and the contribution it makes to the surface stress in the Southern Hemisphere. This, in turn, reduces the possibility of global dust storm development. The interannual variability is the result either of a competition between circulation in opposite hemispheres, in which case the variability has a random component; or it is the result of the cycling of dust between hemispheres, in which case the variability is related to the characteristics of global dust storms themselves.

Haberle, R. M.↗
NASA NTRS1995

Integrated Logistics Support Analysis of the International Space Station Alpha, Background and Summary of Mathematical Modeling and Failure Density Distributions Pertaining to Maintenance Time Dependent Parameters

The process of predicting the values of maintenance time dependent variable parameters such as mean time between failures (MTBF) over time must be one that will not in turn introduce uncontrolled deviation in the results of the ILS analysis such as life cycle costs, spares calculation, etc. A minor deviation in the values of the maintenance time dependent variable parameters such as MTBF over time will have a significant impact on the logistics resources demands, International Space Station availability and maintenance support costs. There are two types of parameters in the logistics and maintenance world: a. Fixed; b. Variable Fixed parameters, such as cost per man hour, are relatively easy to predict and forecast. These parameters normally follow a linear path and they do not change randomly. However, the variable parameters subject to the study in this report such as MTBF do not follow a linear path and they normally fall within the distribution curves which are discussed in this publication. The very challenging task then becomes the utilization of statistical techniques to accurately forecast the future non-linear time dependent variable arisings and events with a high confidence level. This, in turn, shall translate in tremendous cost savings and improved availability all around.

Sepehry-Fard, F.↗
NASA NTRSDate not supplied

Techniques in Assessing Random Uncertainty of Wind Tunnel Replicate Test Data

The preferred method to determine the random uncertainty of variables of interest during wind tunnel tests is by direct analysis of replicate data. However, current information is limited to analysis of a single replicate set condition that does not consider data covariance. This paper provides additional information on considerations for quantifying random uncertainty including the evaluation and correction of replicate data covariance, the selection of replicate set conditions for the test, and the interpolation of random uncertainty at other than replicate set conditions. The analysis and techniques are supported by data from a conventional aircraft configuration test at the Oran Nicks Low-Speed Wind Tunnel and an ASME nozzle flow characterization at the Propulsion Systems Laboratory.

Uncertainty↗
NASA NTRS1992

Prediction of space sickness in astronauts from preflight fluid, electrolyte, and cardiovascular variables and Weightless Environmental Training Facility (WETF) training

Nine preflight variables related to fluid, electrolyte, and cardiovascular status from 64 first-time Shuttle crewmembers were differentially weighted by discrimination analysis to predict the incidence and severity of each crewmember's space sickness as rated by NASA flight surgeons. The nine variables are serum uric acid, red cell count, environmental temperature at the launch site, serum phosphate, urine osmolality, serum thyroxine, sitting systolic blood pressure, calculated blood volume, and serum chloride. Using two methods of cross-validation on the original samples (jackknife and a stratefied random subsample), these variables enable the prediction of space sickness incidence (NONE or SICK) with 80 percent sickness and space severity (NONE, MILD, MODERATE, of SEVERE) with 59 percent success by one method of cross-validation and 67 percent by another method. Addition of a tenth variable, hours spent in the Weightlessness Environment Training Facility (WETF) did not improve the prediction of space sickness incidences but did improve the prediction of space sickness severity to 66 percent success by the first method of cross-validation of original samples and to 71 percent by the second method. Results to date suggest the presence of predisposing physiologic factors to space sickness that implicate fluid shift etiology. The data also suggest that prior exposure to fluid shift during WETF training may produce some circulatory pre-adaption to fluid shifts in weightlessness that results in a reduction of space sickness severity.

Simanonok, K.↗
NASA NTRS1988

Temporal variations of particle fluxes in the deep subtropical and tropical North Atlantic - Eulerian versus Lagrangian effects

The flux of particles measured by sediment traps in the deep water of the Sargasso Sea and western tropical North Atlantic undergoes pronounced temporal variation. In the Sargasso Sea the variability is largely due to seasonal changes in mixed-layer depth and attendant changes in primary productivity affecting a wide region. By contrast, the variability in the western tropical Atlantic appears to be caused by patches of elevated nutrient and pigment concentrations which have their origin in the plumes of the Amazon and Orinoco rivers. Coastal zone color scanner scenes demonstrate the great seasonal and interannual differences in the direction and dispersal patterns of the plumes. The river plumes break up into irregular patches which may pass through the catchment area of a sediment trap at varying rates, thereby creating the impression of almost random temporal flux variability at a fixed trap site.

Deuser, W. G.↗
NASA NTRS1989

Review of probabilistic analysis of dynamic response of systems with random parameters

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

Kozin, F.↗
NASA NTRS2022

Regression Bias in using Solar Wind Measurements

Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.

magnetosphere↗
NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

Crespo, Luis G.↗
NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

Crespo, Luis G.↗
NASA NTRS2001

Uncertainty Optimization Applied to the Monte Carlo Analysis of Planetary Entry Trajectories

Recently, strong evidence of liquid water under the surface of Mars and a meteorite that might contain ancient microbes have renewed interest in Mars exploration. With this renewed interest, NASA plans to send spacecraft to Mars approx. every 26 months. These future spacecraft will return higher-resolution images, make precision landings, engage in longer-ranging surface maneuvers, and even return Martian soil and rock samples to Earth. Future robotic missions and any human missions to Mars will require precise entries to ensure safe landings near science objective and pre-employed assets. Potential sources of water and other interesting geographic features are often located near hazards, such as within craters or along canyon walls. In order for more accurate landings to be made, spacecraft entering the Martian atmosphere need to use lift to actively control the entry. This active guidance results in much smaller landing footprints. Planning for these missions will depend heavily on Monte Carlo analysis. Monte Carlo trajectory simulations have been used with a high degree of success in recent planetary exploration missions. These analyses ascertain the impact of off-nominal conditions during a flight and account for uncertainty. Uncertainties generally stem from limitations in manufacturing tolerances, measurement capabilities, analysis accuracies, and environmental unknowns. Thousands of off-nominal trajectories are simulated by randomly dispersing uncertainty variables and collecting statistics on forecast variables. The dependability of Monte Carlo forecasts, however, is limited by the accuracy and completeness of the assumed uncertainties. This is because Monte Carlo analysis is a forward driven problem; beginning with the input uncertainties and proceeding to the forecasts outputs. It lacks a mechanism to affect or alter the uncertainties based on the forecast results. If the results are unacceptable, the current practice is to use an iterative, trial-and-error approach to reconcile discrepancies. Therefore, an improvement to the Monte Carlo analysis is needed that will allow the problem to be worked in reverse. In this way, the largest allowable dispersions that achieve the required mission objectives can be determined quantitatively.

Olds, John↗
NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗
NASA NTRSDate not supplied

Mapping Surface Vapor Pressure Deficits From Geostationary Satellites for Fire Weather Monitoring

The increase in the wildfires were observed globally in accordance with global warming, and to real- time monitoring of wildfire risk in broad scale is demanded for wildfire management to prevent the spread of wildfires. Scientists invented a lot of indices to assess the wildfire risk. Vapor Pressure Deficit (VPD) is one of the most important meteorological components for those indices. Compared to other components of fire weather indices, VPD can change quickly from lower risk to higher risk even in sub-hourly. Therefore, real-time fire risk monitoring requires high-resolution and high- temporal VPD spatial map. Here, we developed VPD estimation method using the GOES Advanced Baseline Imager (ABI) data. Unlike the polar-orbital satellite data, the ABI can observe target region every 10 minutes, so that we can estimate VPD for fire weather in real-time. The method used to estimate VPD is same with the algorithm of NASA Earth Exchange Gridded Daily Meteorology (NEX- GDM), which estimate meteorological variables from ground weather observation and spatial variables based on random forest (RF). We calculated RF importance to select bands of ABI as input of the model. To validate our results, we compared the spatial pattern of our VPD data with the Real- Time Mesoscale Analysis (RTMA) data over the conterminous USA. We sought possibility of applying our method to the region where no real-time high-resolution weather data is available, such as South America. The developed method can produce real-time high-resolution high-frequent VPD data in the continental scale. The derived data from GOES ABI could contribute to improve the fire weather monitoring and lead to prevent wildfires.

Hirofumi Hashimoto↗
NASA NTRS2006

The Modern Design of Experiments for Configuration Aerodynamics: A Case Study

The effects of slowly varying and persisting covariate effects on the accuracy and precision of experimental result is reviewed, as is the rationale for run-order randomization as a quality assurance tactic employed in the Modern Design of Experiments (MDOE) to defend against such effects. Considerable analytical complexity is introduced by restrictions on randomization in configuration aerodynamics tests because they involve hard-to-change configuration variables that cannot be randomized conveniently. Tradeoffs are examined between quality and productivity associated with varying degrees of rigor in accounting for such randomization restrictions. Certain characteristics of a configuration aerodynamics test are considered that may justify a relaxed accounting for randomization restrictions to achieve a significant reduction in analytical complexity with a comparably negligible adverse impact on the validity of the experimental results.

DeLoach, Richard↗
NASA NTRSDate not supplied

Machine Learning Applications to Metal-Silicate Equilibria and their Insights into Core Formation

An extensive number of studies have experimentally investigated how elements distribute between metal and silicate phases, to better constrain core-mantle chemical equilibrium. Here, we present a new database compiling all (to our knowledge) experimental data on liquid metal-silicate partitioning from 118 peer-reviewed publications. We applied various machine learning techniques to gain further insights into these partitioning equilibria and their dependencies. We performed a network analysis to investigate the relationship between experiments and partition coefficients, which enables visualizing gaps in the experimental dataset and biases related to varying experimental conditions and analytical setup. In addition, semi-empirical thermodynamic models are commonly used to extrapolate these chemical reactions to the wide range of pressure, temperature and compositional conditions of planetary differentiation. These models are based on linear regressions that assume continuous relationship between partition coefficients and experimental variables. Here, we considered random forest regressions, which are algorithms based on ensembles of decision trees and does not consider continuous effects of each variable. The application of this regression significantly improves the prediction of metal-silicate partitioning for several elements including Ni, Si and Cr. We will show how this new approach improves our understanding of elemental exchange between metal and silicate and their implications for the Earth’s core formation.

siderophile element↗
NASA NTRS1976

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.

Tsang, L.↗
NASA NTRS1983

Numerical experiments with a stochastic zonal climate model

A zonally averaged energy balance climate model is developed to generate zonal temperature variability through fluctuating meridional energy transports. Stochastic transport fluctuations are included in the model by multiplying the eddy diffusion coefficients by Gaussian random deviates. For a variability of eddy coefficients of 50 percent, the model is found to generate an interannual temperature variability of 0.03 K for the global temperature, and 0.04 and 0.05 K for the Northern and Southern Hemispheres, respectively. It is shown that the temperature variability level generated is linearly related to the transport variability level introduced. An increase in the level of model-generated temperature variability and a change in the shape of variance spectra of temperature anomaly time series are obtained by switching from the multiplicative noise model to an additive noise model. The results of these model studies are compared with a time series of central England temperatures as well as GCM generated climate variability.

Schneider, S. H.↗
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.↗