Search NASA⌕ Search

SEARCH · Search NASA

Results for “Monte Carlo estimators”

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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Terrestrial impact rates for long and short-period comets

The present calculations of terrestrial impact rates for longand short-period comets crossing the earth's orbit respectively yield probabilities of 2.2 x 10 to the -9th/perihelion passage (with a probable velocity of 56.6 km/sec), and 6.6 x 10 to the -9th/perihelion passage (probable velocity, 28.9 km/sec). The total cratering rate from both long- and short-period comets is about 15 percent of the observed rate derived from known terrestrial astroblemes, although there is substantial uncertainty in both estimates. The estimated cratering rate from earth-crossing asteroids given by Shoemaker et al. (1979) is about twice the observed rate, and Monte Carlo simulations of the dynamical evolution of the Oort (1950) cloud yield cometary flux rate estimates for the early solar system of the order of 200 times the current flux.

Weissman, P. R.↗
NASA NTRS2010

Multiple Scattering of Laser Pulses in Snow Over Ice: Modeling the Potential Bias in ICESat Altimetry

The primary goal of NASA's current ICESat and future ICESat2 missions is to map the altitude of the Earth's land ice with high accuracy using laser altimetry technology, and to measure sea ice freeboard. Ice however is a highly transparent optical medium with variable scattering and absorption properties. Moreover, it is often covered by a layer of snow with varying depth and optical properties largely dependent on its age. We describe a modeling framework for estimating the potential altimetry bias caused by multiple scattering in the layered medium. We use both a Monte Carlo technique and an analytical diffusion model valid for optically thick media. Our preliminary numerical results are consistent with estimates of the multiple scattering delay from laboratory measurements using snow harvested in Greenland, namely, a few cm. Planned refinements of the models are described.

Davis, A. B.↗
NASA NTRS1972

Application of an approach and landing system model to the space shuttle orbiter vehicle

An analytic model and procedure are described which can be used to estimate probability distributions of touchdown conditions, without utilizing a Monte Carlo simulation. Example applications are presented, including one-step and two-step flare strategies for the space shuttle orbiter. The computed probability distributions for the two-step flare are compared with the corresponding histograms from an independent Monte Carlo simulation of the same situation. The computed distributions are very good fits to the Monte-Carlo-generated histograms for pertinent longitudinal and lateral variables at three points (including touchdown) along the vehicle's final approach trajectory. The model, thus verified, has more inherent power for assessing the effects of system element changes than conventional Monte Carlo techniques.

Johnson, W. A.↗
NASA NTRS1979

Monte Carlo simulation of single accident airport risk profile

A computer simulation model was developed for estimating the potential economic impacts of a carbon fiber release upon facilities within an 80 kilometer radius of a major airport. The model simulated the possible range of release conditions and the resulting dispersion of the carbon fibers. Each iteration of the model generated a specific release scenario, which would cause a specific amount of dollar loss to the surrounding community. By repeated iterations, a risk profile was generated, showing the probability distribution of losses from one accident. Using accident probability estimates, the risks profile for annual losses was derived. The mechanics are described of the simulation model, the required input data, and the risk profiles generated for the 26 large hub airports.

Source record↗
NASA NTRS1988

Variance and bias confidence criteria for ERA modal parameter identification

For the ERA system identification algorithm, perturbation methods are used to develop expressions for variance and bias of the identified modal parameters. Based on the statistics of the measurement noise, the variance results serve as confidence criteria by indicating how likely the true parameters are to lie within any chosen interval about their identified values. This replaces the use of expensive and time-consuming Monte Carlo computer runs to obtain similar information. The bias estimates help guide the ERA user in his choice of which data points to use and how much data to use in order to obtain the best results, performing the trade-off between the bias and scatter. Also, when the uncertainty in the bias is sufficiently small, the bias information can be used to correct the ERA results. In addition, expressions for the variance and bias of the singular values serve as tools to help the ERA user decide the proper modal order.

Longman, Richard W.↗
NASA NTRS1989

A correction algorithm for particle size distribution measurements made with the forward-scattering spectrometer probe

A correction algorithm for evaluating the particle size distribution measurements of atmospheric aerosols obtained with a forward-scattering spectrometer probe (FSSP) is examined. A model based on Poisson statistics is employed to calculate the average diameter and rms width of the particle size distribution. The dead time and coincidence errors in the measured number density are estimated. The model generated data are compared with a Monte Carlo simulation of the FSSP operation. It is observed that the correlation between the actual and measured size distribution is nonlinear. It is noted that the algorithm permits more accurate calculation of the average diameter and rms width of the distribution compared to uncorrected measured quantities.

Lock, James A.↗
NASA NTRS1990

Statistical circuit design for yield improvement in CMOS circuits

This paper addresses the statistical design of CMOS integrated circuits for improved parametric yield. The work uses the Monte Carlo technique of circuit simulation to obtain an unbiased estimation of the yield. A simple graphical analysis tool, the yield factor histogram, is presented. The yield factor histograms are generated by a new computer program called SPICENTER. Using the yield factor histograms, the most sensitive circuit parameters are noted, and their nominal values are changed to improve the yield. Two basic CMOS example circuits, one analog and one digital, are chosen and their designs are 'centered' to illustrate the use of the yield factor histograms for statistical circuit design.

Kamath, H. J.↗
NASA NTRS2000

Leonid Storm Flux Analysis From One Leonid MAC Video AL50R

A detailed meteor flux analysis is presented of a seventeen-minute portion of one videotape, collected on November 18, 1999, during the Leonid Multi-instrument Aircraft Campaign. The data was recorded around the peak of the Leonid meteor storm using an intensified CCD camera pointed towards the low southern horizon. Positions of meteors on the sky were measured. These measured meteor distributions were compared to a Monte Carlo simulation, which is a new approach to parameter estimation for mass ratio and flux. Comparison of simulated flux versus observed flux levels, seen between 1:50:00 and 2:06:41 UT, indicate a magnitude population index of r = 1.8 +/- 0.1 and mass ratio of s = 1.64 +/- 0.06. The average spatial density of the material contributing to the Leonid storm peak is measured at 0.82 +/- 0.19 particles per square kilometer per hour for particles of at least absolute visual magnitude +6.5. Clustering analysis of the arrival times of Leonids impacting the earth's atmosphere over the total observing interval shows no enhancement or clumping down to time scales of the video frame rate. This indicates a uniformly random temporal distribution of particles in the stream encountered during the 1999 epoch. Based on the observed distribution of meteors on the sky and the model distribution, recommendations am made for the optimal pointing directions for video camera meteor counts during future ground and airborne missions.

Gural, Peter S.↗
NASA NTRS2012

CREME96 and Related Error Rate Prediction Methods

Predicting the rate of occurrence of single event effects (SEEs) in space requires knowledge of the radiation environment and the response of electronic devices to that environment. Several analytical models have been developed over the past 36 years to predict SEE rates. The first error rate calculations were performed by Binder, Smith and Holman. Bradford and Pickel and Blandford, in their CRIER (Cosmic-Ray-Induced-Error-Rate) analysis code introduced the basic Rectangular ParallelePiped (RPP) method for error rate calculations. For the radiation environment at the part, both made use of the Cosmic Ray LET (Linear Energy Transfer) spectra calculated by Heinrich for various absorber Depths. A more detailed model for the space radiation environment within spacecraft was developed by Adams and co-workers. This model, together with a reformulation of the RPP method published by Pickel and Blandford, was used to create the CR ME (Cosmic Ray Effects on Micro-Electronics) code. About the same time Shapiro wrote the CRUP (Cosmic Ray Upset Program) based on the RPP method published by Bradford. It was the first code to specifically take into account charge collection from outside the depletion region due to deformation of the electric field caused by the incident cosmic ray. Other early rate prediction methods and codes include the Single Event Figure of Merit, NOVICE, the Space Radiation code and the effective flux method of Binder which is the basis of the SEFA (Scott Effective Flux Approximation) model. By the early 1990s it was becoming clear that CREME and the other early models needed Revision. This revision, CREME96, was completed and released as a WWW-based tool, one of the first of its kind. The revisions in CREME96 included improved environmental models and improved models for calculating single event effects. The need for a revision of CREME also stimulated the development of the CHIME (CRRES/SPACERAD Heavy Ion Model of the Environment) and MACREE (Modeling and Analysis of Cosmic Ray Effects in Electronics). The Single Event Figure of Merit method was also revised to use the solar minimum galactic cosmic ray spectrum and extended to circular orbits down to 200 km at any inclination. More recently a series of commercial codes was developed by TRAD (Test & Radiations) which includes the OMERE code which calculates single event effects. There are other error rate prediction methods which use Monte Carlo techniques. In this chapter the analytic methods for estimating the environment within spacecraft will be discussed.

Adams, James H., Jr.↗
NASA NTRS1973

Use of Polarization Lidar for Investigation of Meteorological Formations

This paper presents the results of theoretical and experimental, investigations of depolarization characteristics of different meteorological formations. Experimental investigations are carried out with a monostatic lidar. The ruby laser radiation is polarized in a vertical plane. The radiation reflected is accepted by a lens system of 150 rom in diameter and a viewing angle of 12' and further it is divided by Wollaston prism into the components polarized orthogonally. In this case the principal plane of the prism is exposed parallel with the laser polarization plane. Investigations show the degree of radiation polarization, reflected from water clouds, to be changed within 1/0.7 (seldom up to 0.6) depending on their density. In most cases a signal reflected from the cloud leading edge is polarized completely. The time shift is observed between polarized and crosspolarized components of a Fignal, reflected from a cloud, depending on the density of a meteorological object. While penetrating into the cloud depth a degree of polarization decreases up to 0.8-0.7, and the character of this decrease is different for various types of clouds. For crystal clouds the shift between the components of the reflected signal is not observed and the magnitude of polarization degree amounts to 0.1/0.3 in comparison with water clouds. The polarization degree of radiation reflected by fog is not less than 0.6, and that in the rains of average intensity (about 5 mm/h) is always about 1. The authors have suggested an algorithm of numerical solution of nonstationary transfer equation in the vector form to forecast the influence of multiple scattering effects on polarization characteristics of the lidar light signal. The method of statistical simulation (Monte-Carlo technique) forms the basis of the algorithm. Numerical estimates obtained for a model of stratocumulus at lambda = 0.6943 microns under boundary conditions close to the conditions of natural experiment being discussed proved to be in a good agreement with the results of observation. Specifically, Fig. 1 shows the profiles of polarization (p) versus depth (L) of the following drop formations: fog (curve 1) with horizontal meteorological visibility of 4 km two stratocumulus at a height of 1100 m with the attenuation factors delta = 0.01m(exp -1) (curve 2) and delta = 0.05m(exp -1) (curve 3). Curve 3 shows the results of numerical estimates and the value of their statistical error.

Balin, Yu. S.↗
NASA NTRS2019

MultiLayer Clustered Sampling (MLCS) technique for near-earth asteroid impact hazard assessment

Because of planetary encounters, the motion of near-Earth asteroids is chaotic and small differences in the initial conditions tend to diverge exponentially. Linear approximations for propagating orbital uncertainties can lead to inaccurate estimates of the probability of an Earth collision. We present a novel fully nonlinear strategy for estimating the probability of an asteroid impact using sequential Monte Carlo layers. The method first explores a low-resolution layer to locate potentially relevant regions. Then, we conduct localized searches on deeper layers with higher resolution. The method retains the accuracy of brute-force Monte Carlo sampling while reducing the computational cost by only sampling relevant regions.

Farnocchia, Davide↗
NASA NTRS2023

Uncertainty Analysis of the NASA Glenn 8- by 6-Foot Supersonic Wind Tunnel 2019 Characterization Test 14-Foot, 5.8 Percent Test Section Porosity

This paper presents methods and results of a measurement uncertainty analysis that was performed for the 8- by 6-foot Supersonic Wind Tunnel located at the NASA Glenn Research Center. The uncertainty analysis is based on data collected during a characterization test following major structural modifications to the facility and upgrades to the facility’s data and control systems. The statistical methods and engineering judgments used to estimate elemental uncertainties are described in this report. The Monte Carlo method of propagating uncertainty was selected to determine the uncertainty of calculated variables of interest. A description of the Monte Carlo method as applied for this analysis is provided. The primary variable of interest (VOI) for this facility is free stream Mach number. In addition to determining the uncertainty in Mach number, the uncertainty in free stream values of static pressure, total pressure, dynamic pressure, total temperature, static temperature, Reynolds number, and air speed were also calculated. Uncertainty results are presented as random (unpredictable variation in repeated measurements), systematic (potential offset between observed and true value), and total (random and systematic combined) uncertainty for Mach number. Systematic uncertainty results are presented for the other VOIs. Individual uncertainty sources are presented both dimensionally and as percent contributions to uncertainty in all VOIs, to aid in the identification of primary uncertainty sources.

Uncertainty Analysis↗
NASA NTRS2005

New Algorithms for Estimating Spacecraft Position Using Scanning Techniques for Deep Space Network Antennas

As more and more nonlinear estimation techniques become available, our interest is in finding out what performance improvement, if any, they can provide for practical nonlinear problems that have been traditionally solved using linear methods. In this paper we examine the problem of estimating spacecraft position using conical scan (conscan) for NASA's Deep Space Network antennas. We show that for additive disturbances on antenna power measurement, the problem can be transformed into a linear one, and we present a general solution to this problem, with the least square solution reported in literature as a special case. We also show that for additive disturbances on antenna position, the problem is a truly nonlinear one, and we present two approximate solutions based on linearization and Unscented Transformation respectively, and one 'exact' solution based on Markov Chain Monte Carlo (MCMC) method. Simulations show that, with the amount of data collected in practice, linear methods perform almost the same as MCMC methods. It is only when we artificially reduce the amount of collected data and increase the level of noise that nonlinear methods show significantly better accuracy than that achieved by linear methods, at the expense of more computation.

Metropolis-Hastings (MH)↗
NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Navagation↗
NASA NTRS2004

Uncertainties in estimates of the risks of late effects from space radiation

Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Using the linear-additivity model for radiation risks, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain an estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including a deep space outpost and Mars missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative metrics, e.g., the number of days in space without exceeding a given risk level within well-defined confidence limits. Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗
NASA NTRS2002

Probabilistic Analysis and Density Parameter Estimation Within Nessus

This NASA educational grant has the goal of promoting probabilistic analysis methods to undergraduate and graduate UTSA engineering students. Two undergraduate-level and one graduate-level course were offered at UTSA providing a large number of students exposure to and experience in probabilistic techniques. The grant provided two research engineers from Southwest Research Institute the opportunity to teach these courses at UTSA, thereby exposing a large number of students to practical applications of probabilistic methods and state-of-the-art computational methods. In classroom activities, students were introduced to the NESSUS computer program, which embodies many algorithms in probabilistic simulation and reliability analysis. Because the NESSUS program is used at UTSA in both student research projects and selected courses, a student version of a NESSUS manual has been revised and improved, with additional example problems being added to expand the scope of the example application problems. This report documents two research accomplishments in the integration of a new sampling algorithm into NESSUS and in the testing of the new algorithm. The new Latin Hypercube Sampling (LHS) subroutines use the latest NESSUS input file format and specific files for writing output. The LHS subroutines are called out early in the program so that no unnecessary calculations are performed. Proper correlation between sets of multidimensional coordinates can be obtained by using NESSUS' LHS capabilities. Finally, two types of correlation are written to the appropriate output file. The program enhancement was tested by repeatedly estimating the mean, standard deviation, and 99th percentile of four different responses using Monte Carlo (MC) and LHS. These test cases, put forth by the Society of Automotive Engineers, are used to compare probabilistic methods. For all test cases, it is shown that LHS has a lower estimation error than MC when used to estimate the mean, standard deviation, and 99th percentile of the four responses at the 50 percent confidence level and using the same number of response evaluations for each method. In addition, LHS requires fewer calculations than MC in order to be 99.7 percent confident that a single mean, standard deviation, or 99th percentile estimate will be within at most 3 percent of the true value of the each parameter. Again, this is shown for all of the test cases studied. For that reason it can be said that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ; furthermore, the newest LHS module is a valuable new enhancement of the program.

Godines, Cody R.↗
NASA NTRS1993

A Monte Carlo approach to the analysis of control system robustness

Stochastic robustness, a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems, is described. The scalar probability of instability is introduced as a measure of stability robustness. Examples are given of stochastic performance robustness measures based on classical time-domain specifications. The relationship between stochastic robustness measures and control system design parameters is discussed. The technique is demonstrated by analyzing an LQG/LTR system designed for a flexible robot arm. It is concluded that the analysis of stochastic robustness offers a good alternative to existing robustness metrics.

Ray, Laura R.↗