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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗
NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗
NASA NTRS2015

A Massively Parallel Bayesian Approach to Planetary Protection Trajectory Analysis and Design

The NASA Planetary Protection Office has levied a requirement that the upper stage of future planetary launches have a less than 10(exp -4) chance of impacting Mars within 50 years after launch. A brute-force approach requires a decade of computer time to demonstrate compliance. By using a Bayesian approach and taking advantage of the demonstrated reliability of the upper stage, the required number of fifty-year propagations can be massively reduced. By spreading the remaining embarrassingly parallel Monte Carlo simulations across multiple computers, compliance can be demonstrated in a reasonable time frame. The method used is described here.

parallel computing↗
NASA NTRS2013

Bayesian Approach for Reliability Assessment of Sunshield Deployment on JWST

Deployable subsystems are essential to mission success of most spacecraft. These subsystems enable critical functions including power, communications and thermal control. The loss of any of these functions will generally result in loss of the mission. These subsystems and their components often consist of unique designs and applications, for which various standardized data sources are not applicable for estimating reliability and for assessing risks. In this study, a Bayesian approach for reliability estimation of spacecraft deployment was developed for this purpose. This approach was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the observatory's telescope and science instruments. In order to collect the prior information on deployable systems, detailed studies of "heritage information", were conducted extending over 45 years of spacecraft launches. The NASA Goddard Space Flight Center (GSFC) Spacecraft Operational Anomaly and Reporting System (SOARS) data were then used to estimate the parameters of the conjugative beta prior distribution for anomaly and failure occurrence, as the most consistent set of available data and that could be matched to launch histories. This allows for an emperical Bayesian prediction for the risk of an anomaly occurrence of the complex Sunshield deployment, with credibility limits, using prior deployment data and test information.

Kaminskiy, Mark P.↗
NASA NTRS2016

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Warner, James E.↗
NASA NTRS2006

In-situ resource utilization for the human exploration of Mars : a Bayesian approach to valuation of precursor missions

The need for sufficient quantities of oxygen, water, and fuel resources to support a crew on the surface of Mars presents a critical logistical issue of whether to transport such resources from Earth or manufacture them on Mars. An approach based on the classical Wildcat Drilling Problem of Bayesian decision theory was applied to the problem of finding water in order to compute the expected value of precursor mission sample information. An implicit (required) probability of finding water on Mars was derived from the value of sample information using the expected mass savings of alternative precursor missions.

water↗
NASA NTRS2004

A Bayesian approach to tracking patients having changing pharmacokinetic parameters

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.

Bayes Theorem↗
NASA NTRS1972

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Canavos, G. C.↗
NASA NTRS2003

A Bayesian Approach to Sensor Characterization

The physical model of a generic electro-optic sensor is derived and incorporated into a Bayesian framework for the estimation of key instrument parameters from calibration data. The sensor characterization thus achieved enables optimal subsequent removal of instrument effects from field data, leading to the highest possible accuracy in the retrieved physical quantities.

Timucin, Dogan A.↗
NASA NTRS2020

Bayesian Approach for Determining Microlens System Properties with High-angular resolution Follow-up Imaging

We present the details of the Bayesian analysis of the planetary microlensing event MOA-2016-BLG-227, whose excess flux is likely due to a source/lens companion or an unrelated ambient star, as well as of the assumed prior distributions. Furthermore, we apply this method to four reported planetary events, MOA-2008-BLG-310, MOA2011-BLG-293, OGLE-2012-BLG-0527, and OGLE-2012-BLG-0950, where adaptive optics observations have detected excess flux at the source star positions. For events with small angular Einstein radii, our lens mass estimates are more uncertain than those of previous analyses, which assumed that the excess was due to the lens. Our predictions for MOA-2008-BLG-310 and OGLE-2012-BLG-0950 are consistent with recent results on these events obtained via Keck and Hubble Space Telescope observations when the source star is resolvable from the lens star. For events with small angular Einstein radii, we find that it is generally difficult to conclude whether the excess flux comes from the host star. Therefore, it is necessary to identify the lens star by measuring its proper motion relative to the source star to determine whether the excess flux comes from the lens star. Even without such measurements, our method can be used to statistically test the dependence of the planet-hosting probability on the stellar mass.

Naoki Koshimoto↗
NASA NTRS1981

Software models: A Bayesian approach to parameter estimation in the Jelenski-Moranda software reliability model

Maximum likelihood estimation procedures for the Jelinski-Moranda software reliability model often give misleading answers. A reparameterization and a Bayesian analysis eliminate some of the problems incurred by MLE methods and often give better predictions on sets of real and simulated data. Practical difficulties in estimating the initial number of errors N and the failure rate of each error phi by the method of maximum likelihood are: N, the MLE of N, is occasionally infinite (i.e., the routines for calculating N and phi do not converge). It is shown that N is finite sub i only if the regression line of the interevent times t sub i vs. i has positive slope. A serious problem is that often N approximates n, the sample size, and sometimes N = n. Thus the MLE predicts that the program is perfect even when it is far from being so. Only when almost all failures have been removed can N and phi be trusted near the end of debugging.

Littlewood, B.↗
NASA NTRS2005

Point process algorithm: a new Bayesian approach for TPF-I planet signal extraction

TPF-I capability for planetary signal extraction, including both detection and spectral characterization, can be optimized by taking proper account of instrumental characteristics and astrophysical prior information. We have developed the Point Process Algorithm, a Bayesian technique for estracting planetary signals using the sine/cosine chopped outputs of a dual nulling interferometer.

stars↗
NASA NTRS1989

A Bayesian approach to reliability and confidence

The historical evolution of NASA's interest in quantitative measures of reliability assessment is outlined. The introduction of some quantitative methodologies into the Vehicle Reliability Branch of the Safety, Reliability and Quality Assurance (SR and QA) Division at Johnson Space Center (JSC) was noted along with the development of the Extended Orbiter Duration--Weakest Link study which will utilize quantitative tools for a Bayesian statistical analysis. Extending the earlier work of NASA sponsor, Richard Heydorn, researchers were able to produce a consistent Bayesian estimate for the reliability of a component and hence by a simple extension for a system of components in some cases where the rate of failure is not constant but varies over time. Mechanical systems in general have this property since the reliability usually decreases markedly as the parts degrade over time. While they have been able to reduce the Bayesian estimator to a simple closed form for a large class of such systems, the form for the most general case needs to be attacked by the computer. Once a table is generated for this form, researchers will have a numerical form for the general solution. With this, the corresponding probability statements about the reliability of a system can be made in the most general setting. Note that the utilization of uniform Bayesian priors represents a worst case scenario in the sense that as researchers incorporate more expert opinion into the model, they will be able to improve the strength of the probability calculations.

Barnes, Ron↗
NASA NTRS2005

Optimizing observing sequence design for periodic and non-periodic phenomena : a Bayesian approach

In this paper we report on our progress on addressing these issues. We have developed an approximate expression for the uniformity of phase coverage that can be used when scheduling to assess candidate sample times. We describe the results obtained using this estimator, and compare them with detailed simulations. We describe our progress and plans for integrating optimizing criteria for both periodic and non-periodic observations into a single observation sequence.

Bayesian↗
NASA NTRS1985

A Bayesian approach to nonlinear inversion

Powerful methods are now available for solving linear parametric inverse problems. However, many inverse problems which arise in geohysics are nonlinear. Fortunately, it is possible to treat most of these with the air of linear perturbation theory and liner inversion. But a convenient method is needed for assessing the importance of nonlinearity in these quasi-linear problems. The present paper provides such a method. Matsu'ura and Jackson (1984) have presented a simple algorithm for evaluating the asymptotic covariance matrix fo estimation errors. In the present investigation, aspects of linear inversion are discussed, taking into account linear parametric inverse problems, nonuniqueness, prior information, confidence limits, conditional and marginal statistics, the relative importance of the prior and observational data, and standardized variables. Attention is also given to nonlinear inversion, and the application of the considered approaches to a number of examples.

Jackson, D. D.↗
NASA NTRS1995

A Bayesian approach to microwave precipitation profile retrieval

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Evans, K. Franklin↗