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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

On the Use of the Beta Distribution in Probabilistic Resource Assessments

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Data Driven Temperature Control of Heat Exchangers

The following poster presents a couple of approaches for temperature control at heat exchanger’s exit. One of the approaches is based on using n-step ahead neural network while the other approach utilizes a combination of control + learning module for temperature control. Designing robust controllers for typical heat exchangers is very challenging primarily because of complexities associated with the synthesis of dynamics of industrial heat exchangers. Even if a dynamics model is synthesized, the accuracy of it would be called into question as there can be lot of unmodeled system dynamics and random noise in input parameters. In many situations, the degree of uncertainty in the model of system being controlled limits the utility of optimal control design. Controller can be manually tuned on the field but it is very difficult to determine manual adjustments that result in overall improvement. These practical challenges call for learning based approaches for temperature control that would result in optimal heat exchanger performance. We utilize the existing mathematical model for air-water system synthesized by Underwood and Crawford for testing our algorithms. Underwood and Crawford developed a model of heating coil by fitting a second-order non-linear equations to measurements of air and water temperature and flow rates obtained from the actual coil. The uncertainties in the model include air and water inlet temperatures and air-flow rate. These uncertainties are modeled as random variables that are sampled from a uniform distribution. The control variable is the water flow rate which is controlled for regulating the air-outlet temperature. Neural networks are frequently used in various literatures for learning time-series. We propose a modified version of neural networks known as n-step ahead neural network that take the state variables and output at time t as input to successfully predict output at time t+n. The variable n is a hyper-parameter which can be optimized based on performance constraints. The n-step ahead neural network was then trained on training data generated from experimental model to high training accuracies. This trained model performed appreciably in its objective to regulate outlet temperature of a heat exchanger. The second approach uses a combination of control and learning module for temperature regulation. The control module used is a proportional controller while the learning module used is steady state neural network. The steady state neural network is used to learn the controller output as a function of random variables and temperature set-point. The proportional controller is then used to compensate for transient behavior of linearized system around various operating points. The algorithm works effectively for temperature regulation as neural network captures the non-linear input-output behavior of closed loop system leaving proportional controller to compensate for steady state errors of a linearized plant. The proposed algorithm’s performances were evaluated against the performance of a PI controller. Further, the robustness of the algorithms were also studied in great detail under small perturbations around tuned parameters of the proposed algorithms.

Sundar, Sreenath↗
DOE OSTI2015

Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

The formation of oscillating phase clusters in a network of identical Hodgkin–Huxley neurons is studied, along with their dynamic behavior. The neurons are synaptically coupled in an all-to-all manner, yet the synaptic coupling characteristic time is heterogeneous across the connections. In a network of N neurons where this heterogeneity is characterized by a prescribed random variable, the oscillatory single-cluster state can transition—through (possibly perturbed) period-doubling and subsequent bifurcations—to a variety of multiple-cluster states. The clustering dynamic behavior is computationally studied both at the detailed and the coarse-grained levels, and a numerical approach that can enable studying the coarse-grained dynamics in a network of arbitrarily large size is suggested. Among a number of cluster states formed, double clusters, composed of nearly equal sub-network sizes are seen to be stable; interestingly, the heterogeneity parameter in each of the double-cluster components tends to be consistent with the random variable over the entire network: Given a double-cluster state, permuting the dynamical variables of the neurons can lead to a combinatorially large number of different, yet similar “fine” states that appear practically identical at the coarse-grained level. For weak heterogeneity we find that correlations rapidly develop, within each cluster, between the neuron’s “identity” (its own value of the heterogeneity parameter) and its dynamical state. For single- and double-cluster states we demonstrate an effective coarse-graining approach that uses the Polynomial Chaos expansion to succinctly describe the dynamics by these quickly established “identity-state” correlations. This coarse-graining approach is utilized, within the equation-free framework, to perform efficient computations of the neuron ensemble dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimal Eco-Driving Control of Connected and Autonomous Vehicles Through Signalized Intersections

This article focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving problem is formulated as a data-driven chance-constrained robust optimization problem. Effective red-light duration (ERD) is defined as a random variable, and describes the feasible passing time through the signalized intersections. Usually, the true probability distribution for ERD is unknown. Consequently, a data-driven approach is adopted to formulate chance constraints based on empirical sample data. This incorporates robustness into the eco-driving control problem with respect to uncertain signal timing. Dynamic programming (DP) is employed to solve the optimization problem. The simulation results demonstrate that the proposed method can generate optimal speed reference trajectories with 40% less vehicle fuel consumption, while maintaining the arrival time at a similar level compared to a modified intelligent driver model (IDM). The proposed control approach significantly improves the controller's robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2015

Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the influence of conformational uncertainty in biomolecular solvation

Biomolecules exhibit conformational fluctuations near equilibrium states, inducing uncertainty in various biological properties in a dynamic way. We have developed a general method to quantify the uncertainty of target properties induced by conformational fluctuations. Using a generalized polynomial chaos (gPC) expansion, we construct a surrogate model of the target property with respect to varying conformational states. We also propose a method to increase the sparsity of the gPC expansion by defining a set of conformational “active space” random variables. With the increased sparsity, we employ the compressive sensing method to accurately construct the surrogate model. We demonstrate the performance of the surrogate model by evaluating fluctuation-induced uncertainty in solvent-accessible surface area for the bovine trypsin inhibitor protein system and show that the new approach offers more accurate statistical information than standard Monte Carlo approaches. Further more, the constructed surrogate model also enables us to directly evaluate the target property under various conformational states, yielding a more accurate response surface than standard sparse grid collocation methods. In particular, the new method provides higher accuracy in high-dimensional systems, such as biomolecules, where sparse grid performance is limited by the accuracy of the computed quantity of interest. Our new framework is generalizable and can be used to investigate the uncertainty of a wide variety of target properties in biomolecular systems.

coarse graining↗
DOE OSTI2018

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.

Modelling↗
DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems

Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest in a model, where just a few orthogonal basis polynomials are required. In this work, we consider linear dynamical systems consisting of ordinary differential equations with random variables. The aim of this paper is to explore methods for producing low-dimensional approximations of the quantity of interest further. We investigate two numerical techniques to compute a low-dimensional representation, which both fit the approximation to a set of samples in the time domain. On the one hand, a frequency domain analysis of a stochastic Galerkin system yields the selection of the basis polynomials. It follows a linear least squares problem. On the other hand, a sparse minimization yields the choice of the basis polynomials by information from the time domain only. An orthogonal matching pursuit produces an approximate solution of the minimization problem. Finally, we compare the two approaches using a test example from a mechanical application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Biological Sampling Variability Study

There are many sources of variability that exist in the sample collection and analysis process. This paper addresses many, but not all, sources of variability. The main focus of this paper was to better understand and estimate variability due to differences between samplers. Variability between days was also studied, as well as random variability within each sampler. Experiments were performed using multiple surface materials (ceramic and stainless steel), multiple contaminant concentrations (10 spores and 100 spores), and with and without the presence of interfering material. All testing was done with sponge sticks using 10-inch by 10-inch coupons. Bacillus atrophaeus was used as the BA surrogate. Spores were deposited using wet deposition. Grime was coated on the coupons which were planned to include the interfering material (Section 3.3). Samples were prepared and analyzed at PNNL using CDC protocol (Section 3.4) and then cultured and counted. Five samplers were trained so that samples were taken using the same protocol. Each sampler randomly sampled eight coupons each day, four coupons with 10 spores deposited and four coupons with 100 spores deposited. Each day consisted of one material being tested. The clean samples (no interfering materials) were run first, followed by the dirty samples (coated with interfering material). There was a significant difference in recovery efficiency between the coupons with 10 spores deposited (mean of 48.9%) and those with 100 spores deposited (mean of 59.8%). There was no general significant difference between the clean and dirty (containing interfering material) coupons or between the two surface materials; however, there was a significant interaction between concentration amount and presence of interfering material. The recovery efficiency was close to the same for coupons with 10 spores deposited, but for the coupons with 100 spores deposited, the recovery efficiency for the dirty samples was significantly larger (65.9% - dirty vs. 53.6% - clean) (see Figure 4.1). Variance component analysis was used to estimate the amount of variability for each source of variability. There wasn’t much difference in variability for dirty and clean samples, as well as between materials, so these results were pooled together. There was a significant difference in amount of concentration deposited, so results were separated for the 10 spore and 100 spore deposited tests. In each case the within sampler variability was the largest with variances of 426.2 for 10 spores and 173.1 for 100 spores. The within sampler variability constitutes the variability between the four samples of similar material, interfering material, and concentration taken by each sampler. The between sampler variance was estimated to be 0 for 10 spores and 1.2 for 100 spores. The between day variance was estimated to be 42.1 for 10 spores and 78.9 for 100 spores. Standard deviations can be calculated in each case by taking the square root of the variance.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Droplet Growth or Evaporation Does Not Buffer the Variability in Supersaturation in Clean Clouds

Abstract Water vapor supersaturation in clouds is a random variable that drives activation and growth of cloud droplets. The Pi Convection–Cloud Chamber generates a turbulent cloud with a microphysical steady state that can be varied from clean to polluted by adjusting the aerosol injection rate. The supersaturation distribution and its moments, e.g., mean and variance, are investigated for varying cloud microphysical conditions. High-speed and collocated Eulerian measurements of temperature and water vapor concentration are combined to obtain the temporally resolved supersaturation distribution. This allows quantification of the contributions of variances and covariances between water vapor and temperature. Results are consistent with expectations for a convection chamber, with strong correlation between water vapor and temperature; departures from ideal behavior can be explained as resulting from dry regions on the warm boundary, analogous to entrainment. The saturation ratio distribution is measured under conditions that show monotonic increase of liquid water content and decrease of mean droplet diameter with increasing aerosol injection rate. The change in liquid water content is proportional to the change in water vapor concentration between no-cloud and cloudy conditions. Variability in the supersaturation remains even after cloud droplets are formed, and no significant buffering is observed. Results are interpreted in terms of a cloud microphysical Damköhler number (Da), under conditions corresponding to , i.e., the slow-microphysics regime. This implies that clouds with very clean regions, such that is satisfied, will experience supersaturation fluctuations without them being buffered by cloud droplet growth. Significance Statement The saturation ratio (humidity) in clouds controls the growth rate and formation of cloud droplets. When air in a turbulent cloud mixes, the humidity varies in space and time throughout the cloud. This is important because it means cloud droplets experience different growth histories, thereby resulting in broader size distributions. It is often assumed that growth and evaporation of cloud droplets buffers out some of the humidity variations. Measuring these variations has been difficult, especially in the field. The purpose of this study is to measure the saturation ratio distribution in clouds with a range of conditions. We measure the in-cloud saturation ratio using a convection cloud chamber with clean to polluted cloud properties. We found in clouds with low concentrations of droplets that the variations in the saturation ratio are not suppressed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Automated Thermal Image Processing for Detection and Classification of Birds and Bats (FY2012 Annual Report)

Surveying wildlife at risk from offshore wind energy development is difficult and expensive. Infrared video can be used to record birds and bats that pass through the camera view, but it is also time consuming and expensive to review video and determine what was recorded. We proposed to conduct algorithm and software development to identify and to differentiate thermally detected targets of interest that would allow automated processing of thermal image data to enumerate birds, bats, and insects. During FY2012 we developed computer code within MATLAB to identify objects recorded in video and extract attribute information that describes the objects recorded. We tested the efficiency of track identification using observer-based counts of tracks within segments of sample video. We examined object attributes, modeled the effects of random variability on attributes, and produced data smoothing techniques to limit random variation within attribute data. We also began drafting and testing methodology to identify objects recorded on video. We also recorded approximately 10 hours of infrared video of various marine birds, passerine birds, and bats near the Pacific Northwest National Laboratory (PNNL) Marine Sciences Laboratory (MSL) at Sequim, Washington. A total of 6 hours of bird video was captured overlooking Sequim Bay over a series of weeks. An additional 2 hours of video of birds was also captured during two weeks overlooking Dungeness Bay within the Strait of Juan de Fuca. Bats and passerine birds (swallows) were also recorded at dusk on the MSL campus during nine evenings. An observer noted the identity of objects viewed through the camera concurrently with recording. These video files will provide the information necessary to produce and test software developed during FY2013. The annotation will also form the basis for creation of a method to reliably identify recorded objects.

Bats↗
DOE OSTI2019

Geometric Estimation of Multivariate Dependency

This paper proposes a geometric estimator of dependency between a pair of multivariate random variables. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate samples. This estimator converges to a quantity that we call the geometric mutual information (GMI), which is equivalent to the Henze–Penrose divergence. between the joint distribution of the multivariate samples and the product of the marginals. The GMI has many of the same properties as standard MI but can be estimated from empirical data without density estimation; making it scalable to large datasets. The proposed empirical estimator of GMI is simple to implement, involving the construction of an minimal spanning tree (MST) spanning over both the original data and a randomly permuted version of this data. We establish asymptotic convergence of the estimator and convergence rates of the bias and variance for smooth multivariate density functions belonging to a Hölder class. We demonstrate the advantages of our proposed geometric dependency estimator in a series of experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Variational Bayesian strategies for high-dimensional, stochastic design problems

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual difficulties encountered in UQ tasks (e.g. the high computational cost of each forward simulation, the large number of random variables) but also by the need to solve a nonlinear optimization problem involving large numbers of design variables and potentially constraints. We propose a framework that is suitable for a class of such problems and is based on the idea of recasting them as probabilistic inference tasks. To that end, we propose a Variational Bayesian (VB) formulation and an iterative VB–Expectation-Maximization scheme that is capable of identifying a local maximum as well as a low-dimensional set of directions in the design space, along which, the objective exhibits the largest sensitivity. We demonstrate the validity of the proposed approach in the context of two numerical examples involving thousands of random and design variables. In all cases considered the cost of the computations in terms of calls to the forward model was of the order of 100 or less. The accuracy of the approximations provided is assessed by information-theoretic metrics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Information transmission with continuous variable quantum erasure channels

Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different types of channels, evaluating the corresponding quantum capacity, and finding the capacity-approaching coding scheme are the major tasks in quantum communication theory. Quantum channel in discrete variables has been discussed enormously based on various error models, while error model in the continuous variable channel has been less studied due to the infinite dimensional problem. In this paper, we investigate a general continuous variable quantum erasure channel. By defining an effective subspace of the continuous variable system, we find a continuous variable random coding model. We then derive the quantum capacity of the continuous variable erasure channel in the framework of decoupling theory. The discussion in this paper fills the gap of a quantum erasure channel in continuous variable setting and sheds light on the understanding of other types of continuous variable quantum channels.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Modelling individual variability in growth of bull trout in the Walla Walla River Basin using a hierarchical von Bertalanffy growth model

Abstract We examined growth in length of fluvial bull trout ( Salvelinus confluentus ) in the Walla Walla River Basin, Washington and Oregon. Our objectives were to quantify individual variability in growth; examine growth within and among years, life history forms, life stages and sexes; and estimate von Bertalanffy growth parameters. Individual variability was evaluated by modelling asymptotic length ( L ∞ ) and the growth coefficient ( k ) as random variables. All models were fit with Bayesian methods and were evaluated for fit by the deviance information criterion. By incorporating individual variability, population‐level estimates of L ∞ and k appeared appropriate and estimated growth trajectories for specific bull trout fit individual observed patterns in growth. Growth trajectories and positive correlation between individual estimates of L ∞ and k suggest that some individuals grow at a faster rate and reach a larger maximum size than other individuals and those differences are maintained throughout life. Selected models suggest that fluvial migrants have higher estimates of L ∞ and k than residents, but there were only slight differences in parameter estimates among migrants from two adjacent spawning populations in the Walla Walla River Basin, as well as between males and females. Growth rates increased for fluvial migrants after subadult emigration. Individual variability in growth is consistent with the life history diversity assumed essential for bull trout population persistence. Quantifying this variability is important for modelling population dynamics and viability to conserve this threatened species.

Harris, Julianne E.↗
DOE OSTI2019

Approximate inference for constructing astronomical catalogs from images

Here, we present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a random variable with parameters that depend on the latent properties of stars and galaxies. These latent properties are themselves modeled as random. We compare two procedures for posterior inference. One procedure is based on Markov chain Monte Carlo (MCMC) while the other is based on variational inference (VI). The MCMC procedure excels at quantifying uncertainty, while the VI procedure is 1000 times faster. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50 terabytes of images in 14.6 minutes, demonstrating the scaling characteristics necessary to construct catalogs for upcoming astronomical surveys.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2012

Uncertainty Quantification of Hypothesis Testing for the Integrated Knowledge Engine

The Integrated Knowledge Engine (IKE) is a tool of Bayesian analysis, based on Bayesian Belief Networks or Bayesian networks for short. A Bayesian network is a graphical model (directed acyclic graph) that allows representing the probabilistic structure of many variables assuming a localized type of dependency called the Markov property. The Markov property in this instance makes any node or random variable to be independent of any non-descendant node given information about its parent. A direct consequence of this property is that it is relatively easy to incorporate new evidence and derive the appropriate consequences, which in general is not an easy or feasible task. Typically we use Bayesian networks as predictive models for a small subset of the variables, either the leave nodes or the root nodes. In IKE, since most applications deal with diagnostics, we are interested in predicting the likelihood of the root nodes given new observations on any of the children nodes. The root nodes represent the various possible outcomes of the analysis, and an important problem is to determine when we have gathered enough evidence to lean toward one of these particular outcomes. This document presents criteria to decide when the evidence gathered is sufficient to draw a particular conclusion or decide in favor of a particular outcome by quantifying the uncertainty in the conclusions that are drawn from the data. The material in this document is organized as follows: Section 2 presents briefly a forensics Bayesian network, and we explore evaluating the information provided by new evidence by looking first at the posterior distribution of the nodes of interest, and then at the corresponding posterior odds ratios. Section 3 presents a third alternative: Bayes Factors. In section 4 we finalize by showing the relation between the posterior odds ratios and Bayes factors and showing examples these cases, and in section 5 we conclude by providing clear guidelines of how to use these for the type of Bayesian networks used in IKE.

97 MATHEMATICS AND COMPUTING↗