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At least 19 records

Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation

The multivariate adaptive regression spline (MARS) approach of Friedman and its Bayesian counterpart are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. Here, we propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.

97 MATHEMATICS AND COMPUTING↗

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↗

Discovering Active Subspaces for High-Dimensional Computer Models

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this paper, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Furthermore, using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9,372 model runs in under half an hour.

97 MATHEMATICS AND COMPUTING↗

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↗

Bayesian Inference and the Effects of Varying Uncertainty Models in Charring Ablator Calibration and Uncertainty Quantification Problems

The Mars Science Laboratory (MSL) vehicle utilized a heat shield constructed from NASA’s Phenolic-Impregnated Carbon Ablator (PICA) material to protect the main structure from the high enthalpy environment encountered during hypersonic atmospheric entry. During the vehicle’s descent through Martian atmosphere, multiple thermocouples embedded within the heat shield captured in-depth material temperature data that allow for studies to be conducted on current material response reconstruction tools. In the present work, material temperature data obtained from thermocouples within the MISP-4 plug (MEDLI (Mars Science Laboratory Entry, Descent, and Landing Instrument) Integrated Sensor Plug) are utilized in the calibration of Theoretical Ablative Composite for Open Testing (TACOT) model parameters in conjunction with NASA’s Porous material Analysis Toolbox (PATO) through Bayesian inference where uncertainty due to parametric, modeling, and experimental sources is simultaneously quantified. Prior to the study, a sensitivity analysis is performed through computation of the robust Sobol indices in an effort to study the relationship between input space and model response and to reduce the dimensionality of the statistical inverse problem. The Bayesian inference methodology necessitates an a-priori choice to be made for the uncertainty model for which numerous possibilities are available. Across most works, however, only basic additive or multiplicative models are utilized with pre-defined magnitudes of uncertainty based on a-priori knowledge or to-be-calibrated multipliers of static covariance matrix structures. The present effort explores the effects of informed uncertainty models, ones with temporal dependence that are simultaneously calibrated through Bayesian inference, on calibrated results for parameters that make up the uncertain input space.

Sensitivity Analysis↗

The Growth of Mass and Reliability Source Database and Me

Mass and Reliability Source (MaRS) is a database which draws together information from multiple other sources and databases (MADS, VMDB, ISS PART, Bayesian PowerPoint, etc.). Information such as mass, operating hours, and failure data are compiled to create a tool for the building of probabilistic Risk Assessment (PRA) models. MaRS also has great potential for deep space mission planning. Understanding the lowest point of failure within an ORU helps to inform the efficient selection of spare parts necessary for a journey where mass and volume are at a premium and resupply is not possible.

George, Cory A.↗

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↗

Bayesian Framework for Bioburden Density Estimation in Planetary Protection

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 - MATHEMATICS AND COMPUTING↗

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗

Countermeasures for Mitigation of Sensorimotor Decrements Following Head-Down Bed Rest

BACKGROUND Astronauts experience postflight disturbances in postural and locomotor control due to sensorimotor adaptations during spaceflight. These alterations may have adverse consequences if a rapid egress is required after landing. Although exercise is partially effective for mitigating cardiovascular and muscular deconditioning, additional countermeasures are needed to further preserve sensorimotor function for exploration missions. We have identified proprioceptive training and electrical muscle stimulation (EMS) as promising in-flight countermeasures. Since prolonged head down bed rest (HDBR) is a spaceflight analog for body unloading and causes postural and locomotor control decrements that parallel those observed after spaceflight, it can be used to facilitate the development of these countermeasures. METHODS This study will determine the effects of proprioceptive training and EMS on functional task performance and sensorimotor function following 60 days of 6° HDBR. Subjects will be randomly assigned to one of four groups: 1)an EMS arm, 2) a proprioceptive training arm, 3) an exercise plus proprioceptive training arm, and 4) a control arm. The EMS countermeasure will include daily bilateral stimulation of selected bilateral lower extremity muscles (30 minutes per session). Proprioceptive training will be performed three days per week (20 minutes per session) consisting of body-loaded postural tasks in the horizontal position on an air bearing sled. Exercise training will mimic current protocols used on the International Space Station, but treadmill aerobic exercise will be replaced with additional cycling aerobic exercise. Primary outcome measures will include pre and post HDBR functional tests that are representative of high priority exploration mission tasks and require high demand for dynamic control of postural stability. Additional measures will be used to identify the key physiological factors contributing to countermeasure benefits. Given the constrained samples size, a Bayesian modelling approach will be used to quantify the probability that there is an effect of a given magnitude. HARDWARE AND PROTOCOL DEVELOPMENT Proprioceptive countermeasure design enhancements continued as part of the Mars Campaign Office (MCO) Crew Health and Performance (CHP) Crew Health Countermeasures (CHC). The primary goals of this work were to assemble a portable version of the countermeasure system that can be used at the :envihab facility, expand the software feedback system’s capabilities, and develop an actuator loading system that mimics what could be used on the International Space Station. In addition, one major piece of exercise hardware used in previous HDBR studies, the Horizontal Squat Device, was reassembled and restored to full functionality. Human-in-the-loop pilot testing is ongoing, prior to shipping both devices to the :envihab HDBR facility. Evaluations are also underway for the best EMS device technologies and specific methods. Finally, assessment techniques are being translated for administration in the horizontal position (e.g., leg dexterity and foot sole skin sensitivity). Our current goals are to refine the countermeasure training and assessment techniques and integrate protocols across multiple modalities. RELEVANCE The deliverable from this project will be proof-of-concept sensorimotor countermeasure designs for functional task performance with full assessment of efficacy in a spaceflight analog. If one or more countermeasures are effective, they will be translated for validation with the suite of operationally implemented in-flight countermeasures. ACKNOWLEDGEMENT This work is supported by NASA’s Human Research Program Human Health Countermeasures Element and by the Canadian Space Agency (L. Bent).

T R Macaulay↗

Accounting for Epistemic Uncertainty in Mission Supportability Assessment: A Necessary Step in Understanding Risk and Logistics Requirements

Future crewed missions to Mars present a maintenance logistics challenge that is unprecedented in human spaceflight. Mission endurance – defined as the time between resupply opportunities – will be significantly longer than previous missions, and therefore logistics planning horizons are longer and the impact of uncertainty is magnified. Maintenance logistics forecasting typically assumes that component failure rates are deterministically known and uses them to represent aleatory uncertainty, or uncertainty that is inherent to the process being examined. However, failure rates cannot be directly measured; rather, they are estimated based on similarity to other components or statistical analysis of observed failures. As a result, epistemic uncertainty – that is, uncertainty in knowledge of the process – exists in failure rate estimates that must be accounted for. Analyses that neglect epistemic uncertainty tend to significantly underestimate risk. Epistemic uncertainty can be reduced via operational experience; for example, the International Space Station (ISS) failure rate estimates are refined using a Bayesian update process. However, design changes may re-introduce epistemic uncertainty. Thus, there is a tradeoff between changing a design to reduce failure rates and operating a fixed design to reduce uncertainty. This paper examines the impact of epistemic uncertainty on maintenance logistics requirements for future Mars missions, using data from the ISS Environmental Control and Life Support System (ECLS) as a baseline for a case study. Sensitivity analyses are performed to investigate the impact of variations in failure rate estimates and epistemic uncertainty on spares mass. The results of these analyses and their implications for future system design and mission planning are discussed.

Owens, Andrew↗

Science Target Assessment for Mars Rover Instrument Deployment

This paper introduces the system being developed at NASA Ames Research Center, intended for the Mars '09 Smart Lander, to robustly place sensors or tools against rocks in a single communications cycle. Science targets must be assessed prior to instrument placement in order to segment them from the background and determine where, if possible, to position the instrument. An initial result of this research effort is a novel Bayesian based method for segmenting rocks from the ground using 3D data.

Pedersen, Liam↗

Probabilistic Classification Using Elemental Abundance Distributions and Lossless Image Compression in Apollo 17 Lunar Dust Samples from Mare Serenitatis

We have previously outlined a strategy for the detection of fossils [Storrie-Lombardi and Hoover, 2004] and extant microbial life [Storrie-Lombaudi and Hoover, 20051 during robotic missions to Mars using co-registered structural and chemical signatures. Data inputs included image lossless compression indices to estimate relative textural complexity and elemental abundance distributions. Two exploratory classification algorithms (principal component analysis and hierarchical cluster analysis) provide an initial tentative classification of all targets. Nonlinear stochastic neural networks are then trained to produce a Bayesian estimate of algorithm classification accuracy. The strategy previously has been successful in distinguishing regions of biotic and abiotic alteration of basalt glass from unaltered samples. [Storrie-Lombardi and Fisk, 2004; Storrie-Lombardi and Fisk, 2004] Such investigations of abiotic versus biotic alteration of terrestrial mineralogy on Earth are compromised by .the difficulty finding mineralogy completely unaffected by the ubiquitous presence of microbial life on the planet. The renewed interest in lunar exploration offers an opportunity to investigate geological materials that may exhibit signs of aqueous alteration, but are highly unlikely to contain contaminating biological weathering signatures. We here present an extension of our earlier data set to include lunar dust samples obtained during the Apollo 17 mission. Apollo 17 landed in the Taurus-Littrow Valley in Mare Serenitatis. Most of the rock samples from this region of the lunar highlands are basalts comprised primarily of plagioclase and pyroxene and selected examples of orange and black volcanic glass. SEM images and elemental abundances (C6, N7, O8, Na11, Mg12, Al13, Si14, P15, S16, Cll7, K19, Ca20, Fe26) for a series of targets in the lunar dust samples are compared to the extant cyanobacteria, fossil trilobites, Orgueil meteorite, and terrestrial basalt targets previously discussed. The data set provides a first step in producing a quantitative probabilistic methodology for geobiological analysis of returned lunar samples or in situ exploration.

Storrie-Lombardi, Michael C.↗

Bayesian Deep Learning for Segmentation for Autonomous Safe Planetary Landing

Hazard detection is critical for enabling autonomous landing on planetary surfaces. Current state-of-the-art methods leverage traditional computer vision approaches to automate the identification of safe terrain from input digital elevation models (DEMs). However, performance for these methods can degrade for input DEMs with increased sensor noise. In the last decade, deep learning techniques have been developed for various applications. Nevertheless, their applicability to safety-critical space missions has often been limited due to concerns regarding their outputs’ reliability. In response to these limitations, this paper proposes an application of the Bayesian deep learning segmentation method for hazard detection. The developed approach enables reliable, safe landing site detection by i) generating simultaneously a safety prediction map and its uncertainty map via Bayesian deep learning and semantic segmentation, and ii) using the uncertainty map to filter out the uncertain pixels in the prediction map so that the safe site identification is performed only based on the certain pixels (i.e., pixels for which the model is certain about its safety prediction). Experiments are presented with simulated data based on a Mars HiRISE digital terrain model by varying uncertainty threshold and noise levels to demonstrate the performance of the proposed approach.

Kento Tomita↗

Probabilisitc Geobiological Classification Using Elemental Abundance Distributions and Lossless Image Compression in Recent and Modern Organisms

Last year we presented techniques for the detection of fossils during robotic missions to Mars using both structural and chemical signatures[Storrie-Lombardi and Hoover, 2004]. Analyses included lossless compression of photographic images to estimate the relative complexity of a putative fossil compared to the rock matrix [Corsetti and Storrie-Lombardi, 2003] and elemental abundance distributions to provide mineralogical classification of the rock matrix [Storrie-Lombardi and Fisk, 2004]. We presented a classification strategy employing two exploratory classification algorithms (Principal Component Analysis and Hierarchical Cluster Analysis) and non-linear stochastic neural network to produce a Bayesian estimate of classification accuracy. We now present an extension of our previous experiments exploring putative fossil forms morphologically resembling cyanobacteria discovered in the Orgueil meteorite. Elemental abundances (C6, N7, O8, Na11, Mg12, Ai13, Si14, P15, S16, Cl17, K19, Ca20, Fe26) obtained for both extant cyanobacteria and fossil trilobites produce signatures readily distinguishing them from meteorite targets. When compared to elemental abundance signatures for extant cyanobacteria Orgueil structures exhibit decreased abundances for C6, N7, Na11, All3, P15, Cl17, K19, Ca20 and increases in Mg12, S16, Fe26. Diatoms and silicified portions of cyanobacterial sheaths exhibiting high levels of silicon and correspondingly low levels of carbon cluster more closely with terrestrial fossils than with extant cyanobacteria. Compression indices verify that variations in random and redundant textural patterns between perceived forms and the background matrix contribute significantly to morphological visual identification. The results provide a quantitative probabilistic methodology for discriminating putatitive fossils from the surrounding rock matrix and &om extant organisms using both structural and chemical information. The techniques described appear applicable to the geobiological analysis of meteoritic samples or in situ exploration of the Mars regolith. Keywords: cyanobacteria, microfossils, Mars, elemental abundances, complexity analysis, multifactor analysis, principal component analysis, hierarchical cluster analysis, artificial neural networks, paleo-biosignatures

Storrie-Lombardi, Michael C.↗

Monitoring a Complex Physical System using a Hybrid Dynamic Bayes Net

The Reverse Water Gas Shift system (RWGS) is a complex physical system designed to produce oxygen from the carbon dioxide atmosphere on Mars. If sent to Mars, it would operate without human supervision, thus requiring a reliable automated system for monitoring and control. The RWGS presents many challenges typical of real-world systems, including: noisy and biased sensors, nonlinear behavior, effects that are manifested over different time granularities, and unobservability of many important quantities. In this paper we model the RWGS using a hybrid (discrete/continuous) Dynamic Bayesian Network (DBN), where the state at each time slice contains 33 discrete and 184 continuous variables. We show how the system state can be tracked using probabilistic inference over the model. We discuss how to deal with the various challenges presented by the RWGS, providing a suite of techniques that are likely to be useful in a wide range of applications. In particular, we describe a general framework for dealing with nonlinear behavior using numerical integration techniques, extending the successful Unscented Filter. We also show how to use a fixed-point computation to deal with effects that develop at different time scales, specifically rapid changes occuring during slowly changing processes. We test our model using real data collected from the RWGS, demonstrating the feasibility of hybrid DBNs for monitoring complex real-world physical systems.

Lerner, Uri↗

Sparse Superpixel Unmixing for Exploratory Analysis of CRISM Hyperspectral Images

Fast automated analysis of hyperspectral imagery can inform observation planning and tactical decisions during planetary exploration. Products such as mineralogical maps can focus analysts' attention on areas of interest and assist data mining in large hyperspectral catalogs. In this work, sparse spectral unmixing drafts mineral abundance maps with Compact Reconnaissance Imaging Spectrometer (CRISM) images from the Mars Reconnaissance Orbiter. We demonstrate a novel "superpixel" segmentation strategy enabling efficient unmixing in an interactive session. Tests correlate automatic unmixing results based on redundant spectral libraries against hand-tuned summary products currently in use by CRISM researchers.

Image Segmentation↗

Nondeterministic data base for computerized visual perception

A description is given of the knowledge representation data base in the perception subsystem of the Mars robot vehicle prototype. Two types of information are stored. The first is generic information that represents general rules that are conformed to by structures in the expected environments. The second kind of information is a specific description of a structure, i.e., the properties and relations of objects in the specific case being analyzed. The generic knowledge is represented so that it can be applied to extract and infer the description of specific structures. The generic model of the rules is substantially a Bayesian representation of the statistics of the environment, which means it is geared to representation of nondeterministic rules relating properties of, and relations between, objects. The description of a specific structure is also nondeterministic in the sense that all properties and relations may take a range of values with an associated probability distribution.

Yakimovsky, Y.↗