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NASA NTRS1973

Analytical study to define a helicopter stability derivative extraction method, volume 1

A method is developed for extracting six degree-of-freedom stability and control derivatives from helicopter flight data. Different combinations of filtering and derivative estimate are investigated and used with a Bayesian approach for derivative identification. The combination of filtering and estimate found to yield the most accurate time response match to flight test data is determined and applied to CH-53A and CH-54B flight data. The method found to be most accurate consists of (1) filtering flight test data with a digital filter, followed by an extended Kalman filter (2) identifying a derivative estimate with a least square estimator, and (3) obtaining derivatives with the Bayesian derivative extraction method.

Molusis, J. A.↗

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 NTRS1975

Adaptive statistical pattern classifiers for remotely sensed data

A technique for the adaptive estimation of nonstationary statistics necessary for Bayesian classification is developed. The basic approach to the adaptive estimation procedure consists of two steps: (1) an optimal stochastic approximation of the parameters of interest and (2) a projection of the parameters in time or position. A divergence criterion is developed to monitor algorithm performance. Comparative results of adaptive and nonadaptive classifier tests are presented for simulated four dimensional spectral scan data.

Gonzalez, R. C.↗

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 NTRSDate not supplied

Composite Bond Line Measurements Based on A Bayesian Analysis of Flash Thermography Data

For bonded composite materials, an accurate characterization of the adhesive bond line is needed to predict failure modes and fracture toughness. In this paper, bond line thickness was estimated from data obtained using through transmission flash thermography. The forward model that predicts back surface temperature is based on a three layer heat diffusion equation with varying diffusivity and flux boundary conditions. The corresponding inverse problem of estimating bond line thickness from measurement data was solved using a Bayesian approach that assumed Gaussian priors for the bond line thickness and thermal diffusivity of the adherends. Finally, the outputs of the thermography based method were compared to measurements that were collected using a micrometer and ultrasound testing.

Flash thermography↗

NASA NTRSDate not supplied

Composite Bond Line Measurements Based on a Bayesian Analysis of Flash Thermography Data

Flash thermography↗

NASA NTRS1977

Orbit determination accuracies using satellite-to-satellite tracking

The uncertainty in relay satellite sate is a significant error source which cannot be ignored in the reduction of satellite-to-satellite tracking data. Based on simulations and real data reductions, it is numerically impractical to use simultaneous unconstrained solutions to determine both relay and user satellite epoch states. A Bayesian or least squares estimation technique with an a priori procedure is presented which permits the adjustment of relay satellite epoch state in the reduction of satellite-to-satellite tracking data without the numerical difficulties introduced by an ill-conditioned normal matrix.

Vonbun, F. O.↗

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 NTRS2010

Comparison of Postural Recovery Following Short and Long Duration Spaceflights

INTRODUCTION: Post-flight postural ataxia reflects adaptive changes to vestibulo-spinal reflexes and control strategies adopted for movement in weightlessness. Quantitative measures obtained during computerized dynamic posturography (CDP) from US and Russian programs provide insight into the effect of spaceflight duration in terms of both the initial decrements and recovery of postural stability. METHODS: CDP was obtained on 117 crewmembers following Shuttle flights lasting 4-17 days, and on 64 crewmembers following long-duration missions lasting 48-380 days. Although the number and timing of sessions varied, the goal was to characterize postural recovery pooling similar measures from different research and flight medicine programs. This report focuses on eyes closed, head erect conditions with either a fixed or sway-referenced base of support. A smaller subset of subjects repeated the sway-referenced condition while making pitch head movements (+/- 20deg at 0.33Hz). Equilibrium scores were derived from peak-to-peak anterior-posterior sway. Fall probability was modeled using Bayesian statistical methods to estimate parameters of a logit function. RESULTS: The standard Romberg condition was the least sensitive. Longer duration flights led to larger decrements in stability with sway-reference support during the first 1-2 days, although the timecourse of recovery was similar across flight duration with head erect. Head movements led to increased incidence of falls during the first week, with a significantly longer recovery following long duration flights. CONCLUSIONS: The diagnostic assessment of postural instability, and differences in the timecourse of postural recovery between short and long flight durations, are more pronounced during unstable support conditions requiring active head movements.

Wood, S. J.↗

NASA NTRS2021

Global irrigation contribution to wheat and maize yield

Irrigation is the largest sector of human water use and an important option for increasing crop production and reducing drought impacts. However, the potential for irrigation to contribute to global crop yields remains uncertain. Here, we quantify this contribution for wheat and maize at global scale by developing a Bayesian framework integrating empirical estimates and gridded global crop models on new maps of the relative difference between attainable rainfed and irrigated yield (ΔY). At global scale, ΔY is 34 ± 9% for wheat and 22 ± 13% for maize, with large spatial differences driven more by patterns of precipitation than that of evaporative demand. Comparing irrigation demands with renewable water supply, we find 30–47% of contemporary rainfed agriculture of wheat and maize cannot achieve yield gap closure utilizing current river discharge, unless more water diversion projects are set in place, putting into question the potential of irrigation to mitigate climate change impacts.

Irrigation↗

NASA NTRSDate not supplied

Defining Change Thresholds: What Change Is Outside Typical Sources of Variation?

Researchers often have a difficult time defining meaningful thresholds for change. We sometimes identify subtle changes but what amount of change is beyond typical sources of variation? This is especially complicated when trying to understand new disease pathogenesis like the constellation of eye changes leading to Spaceflight-associated Neuro-ocular Syndrome (SANS). To support decision makers in defining minimal meaningful change, we used a Bayesian hierarchical model to estimate innate sources of variability such as natural day to day variation. Healthy subjects were recruited and imaged with MRI, OCT, and US on separate days and measured by several technicians. Models were developed specifying random effects for the sources of variation – between left and right eyes, within-individuals over time, between raters, and finally between individuals. This allowed us to find the posterior distribution for the total typical variation, within an eye, which we use to define a threshold where change beyond typical sources of variation is likely. This threshold is now used as our earliest indicator of systematic increase in Total Retinal Thickness (a precursor to optic disc edema).

Millennia Young↗

NASA NTRS2023

Kmt-2022-Blg-0440lb: A New q < 10 −4 Microlensing Planet With the Central-Resonant Caustic Degeneracy Broken

We present the observations and analysis of a high-magnification microlensing planetary event, KMT-2022-BLG-0440, for which the weak and short-lived planetary signal was covered by both the KMTNet survey and follow-up observations. The binary-lens models with a central caustic provide the best fits, with a planet/host mass ratio, q = 0.75–1.00 ×10 −4 at 1 σ. The binary-lens models with a resonant caustic and a brown-dwarf mass ratio are both excluded by ∆χ 2 > 70. The binary-source model can fit the anomaly well but is rejected by the ‘colour argument’ on the second source. From Bayesian analyses, it is estimated that the host star is likely a K or M dwarf located in the Galactic disc, the planet probably has a Neptune-mass, and the projected planet-host separation is 1.9 +0.6 −0.7 or 4.6 +1.4 −1.7 au, subject to the close/wide de generac y. This is the third q < 10 −4 planet from a high-magnification planetary signal ( A ≳ 65). Together with another such planet, KMT-2021-BLG-0171Lb, the ongoing follow-up program for the KMTNet high-magnification events has demonstrated its ability to detect high-magnification planetary signals for q < 10 −4 planets, which are challenging for the current microlensing surveys.

planets and satellites: detection↗

NASA NTRS1999

Bayesian Super-Resolved Surface Reconstruction From Multiple Images

Bayesian inference has been wed successfully for many problems where the aim is to infer the parameters of a model of interest. In this paper we formulate the three dimensional reconstruction problem as the problem of inferring the parameters of a surface model from image data, and show how Bayesian methods can be used to estimate the parameters of this model given the image data. Thus we recover the three dimensional description of the scene. This approach also gives great flexibility. We can specify the geometrical properties of the model to suit our purpose, and can also use different models for how the surface reflects the light incident upon it. In common with other Bayesian inference problems, the estimation methodology requires that we can simulate the data that would have been recoded for any values of the model parameters. In this application this means that if we have image data we must be able to render the surface model. However it also means that we can infer the parameters of a model whose resolution can be chosen irrespective of the resolution of the images, and may be super-resolved. We present results of the inference of surface models from simulated aerial photographs for the case of super-resolution, where many surface elements project into a single pixel in the low-resolution images.

Smelyanskiy, V. N.↗

NASA NTRS2024

Under-Constrained SEE Data: Implications for Estimating and Bounding SEE Rates

Increasingly scarce SEE testing resources and rapid growth of the New Space sector have increased the prevalence of under-constrained SEE data. We develop Monte Carlo tools to assess implications for SEE rate estimation. We also show that Bayesian Priors based on large datasets of SEL susceptible parts can augment under-constrained data and improve bounds on SEL rates. The resulting Bayesian Priors are also useful for bounding system SEL risk.

Single-event effect↗

NASA NTRS2017

A Framework for Inferring Taxonomic Class of Asteroids.

Introduction: Taxonomic classification of asteroids based on their visible / near-infrared spectra or multi band photometry has proven to be a useful tool to infer other properties about asteroids. Meteorite analogs have been identified for several taxonomic classes, permitting detailed inference about asteroid composition. Trends have been identified between taxonomy and measured asteroid density. Thanks to NEOWise (Near-Earth-Object Wide-field Infrared Survey Explorer) and Spitzer (Spitzer Space Telescope), approximately twice as many asteroids have measured albedos than the number with taxonomic classifications. (If one only considers spectroscopically determined classifications, the ratio is greater than 40.) We present a Bayesian framework that provides probabilistic estimates of the taxonomic class of an asteroid based on its albedo. Although probabilistic estimates of taxonomic classes are not a replacement for spectroscopic or photometric determinations, they can be a useful tool for identifying objects for further study or for asteroid threat assessment models. Inputs and Framework: The framework relies upon two inputs: the expected fraction of each taxonomic class in the population and the albedo distribution of each class. Luckily, numerous authors have addressed both of these questions. For example, the taxonomic distribution by number, surface area and mass of the main belt has been estimated and a diameter limited estimate of fractional abundances of the near earth asteroid population was made. Similarly, the albedo distributions for taxonomic classes have been estimated for the combined main belt and NEA (Near Earth Asteroid) populations in different taxonomic systems and for the NEA population specifically. The framework utilizes a Bayesian inference appropriate for categorical data. The population fractions provide the prior while the albedo distributions allow calculation of the likelihood an albedo measurement is consistent with a given taxonomic class. These inputs allows calculation of the probability an asteroid with a specified albedo belongs to any given taxonomic class.

Asteroids↗

NASA NTRS2022

Bayesian Rules of Thumb: Robust Uncertainty Quantification in Early Project Cost Estimation

Systems engineers often make use of cost Rules ofThumb in order to estimate cost during early phases of projectformulation. These Rules of Thumb typically take the form ofa sequence of percentages over which a total cost is allocatedacross NASA WBS elements. Rules of Thumb can then be usedto extrapolate cost from one or more known WBS elements tothe remaining unknown WBS elements, assisting early projectformulation architecture studies (such as those in JPL’s Team Xand A Team).A number of issues can arise when generating and using costRules of Thumb. For example, many records of project costsconsist of incomplete data. Typical methods of dealing withincomplete cost allocation data include (a) ignoring missionswith incomplete data, or (b) taking averages of the non-zero percentagesacross missions, but both of these methods can result inbiased estimates if the existence of incomplete data correlateswith total mission cost or any particular WBS element. Anothercommon example is cost reported in one or more incorrect WBSelements. This is especially prevalent in smaller missions whereit is more common for engineers to perform tasks that fall underthe purview of multiple WBS elements.Furthermore, a Rule of Thumb estimate is typically reported asa point estimate; there is no reported uncertainty around thepercentages used to generate an allocation. Even in the rarecase in which confidence intervals around mean percentages areprovided, there may be positive or negative correlations betweenWBS elements which can skew estimates.Here we attempt to address these problems by formulatingprobabilistic Rules of Thumb in which a distribution of allocationschemes, rather than a single allocation scheme, is generated.We use a bootstrap imputation method to simultaneouslyaccount for uncertainty in the missing data while using allavailable information contained in the dataset. The imputeddatasets are then input into a multivariate Bayesian modelwhich accounts for correlations between WBS elements andproperly accounts for uncertainty in the final Rule of Thumbpercentages and predictions. We describe the mathematicalmodel and provides snippets of R code utilizing the brms(Bayesian Regression Models using Stan) package. To illustratethis model, we generate a Bayesian Level 2 WBS Cost Rule ofThumb for MIDEX (Medium-Class Explorers) missions withdata extracted from NASA’s CADRe. We then compare thismethod’s performance with the classical Rule of Thumb method.

Hooke, Melissa A↗

NASA NTRS2017

Methods for Probabilistic Uncertainty Analysis and Bayesian Analysis with Examples of Statistically Analyzing Data to Revise MMOD Risk Estimates and Compare Models

Probabilistic methods are presented for characterizing and quantifying uncertainties in models and model predictions. Techniques are given for constructing specific uncertainty distributions based on available information. Alternative techniques are given for propagating uncertainties in model inputs to obtain the uncertainty in the model result or prediction. Bayesian techniques are also described for utilizing data and information to update and revise model results and predictions. The focus is on applications with numerous specific examples given. The use of data to revise Micrometeoroid and Orbital Debris (MMOD) risk prediction models are among the examples given.

Risk↗

NASA NTRS1979

Orbit/attitude estimation with Landsat-1 and -2 landmark data

The accuracy of spacecraft orbit and attitude determination is investigated using Landsat-1 and -2 picture data. The data consists of ground control points, of known geodetic coordinates, which are identified on a series of Landsat pictures. Both sequential (extended Kalman filter) and batch (nonlinear Bayesian weighted least-squares) estimation techniques have been implemented in two software systems. Discussion of these systems includes a system overview, mathematical formulation, and sample numerical results. Particular emphasis is given to the application of a spectral analysis technique to derive spacecraft attitude models.

Hall, D. L.↗