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Results for “structural uncertainty quantification”

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 307 records · Page 17

Quantifying uncertainty in the process-structure relationship for Al–Cu solidification

Phase field method (PFM) is a simulation tool to predict microstructural evolution during solidification and is helpful to establish the process-structure relationship for alloys. The robustness of the relationship however is affected by model-form and parameter uncertainties in PFM. In this paper, the uncertainty associated with the thermodynamic and process parameters of PFM is studied and quantified. Surrogate modeling is used to interpolate four quantities of interests (QoIs), including dendritic perimeter, area, primary arm length, and solute segregation, as functions of thermodynamic and process parameters. A sparse grid approach is applied to mitigate the curse-of-dimensionality computational burden in uncertainty quantification. Polynomial chaos expansion is employed to obtain the probability density functions of the QoIs. The effect of parameter uncertainty on the Al–Cu dendritic growth during solidification simulation are investigated. Here, the results show that the dendritic morphology varies significantly with respect to the interface mobility and the initial temperature.

36 MATERIALS SCIENCE↗

Assessing decision boundaries under uncertainty

In order to make design decisions, engineers may seek to identify regions of the design domain that are acceptable in a computationally efficient manner. A design is typically considered acceptable if its reliability with respect to parametric uncertainty exceeds the designer’s desired level of confidence. Despite major advancements in reliability estimation and in design classification via decision boundary estimation, the current literature still lacks a design classification strategy that incorporates parametric uncertainty and desired design confidence. To address this gap, this paper offers a novel interpretation of the acceptance region by defining the decision boundary as the hypersurface which isolates the designs that exceed a user-defined level of confidence given parametric uncertainty. This work addresses the construction of this novel decision boundary using computationally efficient algorithms that were developed for reliability analysis and decision boundary estimation. The approach proposed in this paper is verified on two physical examples from structural and thermal analysis using Support Vector Machines and Efficient Global Optimization-based contour estimation.

97 MATHEMATICS AND COMPUTING↗

Large Scale Study of Ligand–Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

The accurate and reliable prediction of protein–ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the “enhanced sampling” method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurement of the 252 Cf ⁢(sf) prompt fission neutron spectrum utilizing 12 C ⁡(𝑛, 𝑛) and 9 Be ⁢(𝑛, 𝑛) neutron scattering reference measurements

The 252 Cf spontaneous fission (sf), prompt fission neutron spectrum (PFNS) is a fundamental quantity for nuclear physics measurements of neutron-emitting reactions. This energy distribution of neutrons emitted from fission has been considered a neutron data standard for decades and has been utilized as a reference for neutron detection efficiency, validation of Monte Carlo simulations, benchmarking of dosimetry standards, and more. A significant portion of the global collection of nuclear data on neutron-induced reactions is correlated with the 252 Cf ⁢(sf) PFNS. Despite the reliance on this quantity by the nuclear physics community, the historical collection of 252 Cf PFNS measurements display systematic disagreements that are not understood or easily explained. These experimental discrepancies could potentially bias the 252 Cf PFNS Standard evaluation. On top of this, these past experiments frequently employed correlated experimental measurement or analysis methods. The artificial intelligence (AI)/machine learning (ML)-informed californium chi-nuclear data experiment (AIACHNE) project was formed to (a) investigate these discrepancies utilizing AI/ML methods to identify outlying regions of literature data, assign these regions to features of the experiment itself, and perform an improved evaluation of the 252 Cf PFNS and (b) perform a new experimental measurement of this quantity designed to improve upon the existing literature database. Here, in this work, we report on the AIACHNE 252 Cf PFNS experiment utilizing a new analysis method uncorrelated with all previous measurements: neutron efficiency determinations based on elastic neutron scattering on 12 C and 9 Be . This new method provides an independent test of the existing literature data and evaluation of the 252 Cf ⁢(sf) PFNS. The method is described with detailed covariance quantification procedures, as well as a direct discussion of the sources of uncertainty described as requirements in the “Templates” series of papers. The 252 Cf ⁢(sf) PFNS reported in this work agrees well with the overall shape of the existing standard PFNS evaluation as well as many literature measurements, thus verifying the current evaluation utilizing new techniques. However, the results suggest that there are deficiencies in the angle-differential 12 C and 9 Be ⁢(𝑛, 𝑛) evaluated nuclear data, which produce unphysical structures in the reported result. While these structures are relatively minor, they become obvious because of the high statistical precision of the data and the expected smooth continuity of the 252 Cf ⁢(sf) PFNS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

Light Water Reactor Sustainability Program Advanced Seismic Soil Structure Modeling

Risk calculations should focus on providing best estimate results, and associated insights, for evaluation and decision-making. Specifically, seismic probabilistic risk assessments (SPRAs) are intended to provide best estimates of the various combinations of structural and equipment failures that can lead to a seismic induced core damage event. However, in some instances the current SPRA approach has large uncertainties, and potentially masks other important events (for instance, it was not the seismic motions that caused the Fukushima core melt events, but the tsunami ingress into the facility). SPRA’s are performed by convolving the seismic hazard (this is the estimate of all likely damaging earthquakes at the site of interest) with the seismic fragility (the conditional probability of failure of a structure, system, or component given the occurrence of earthquake ground motion). In this calculation, there are three main pieces to seismic risk quantification, 1) seismic hazard and nuclear power plants (NPPs) response to the hazard, 2) fragility or capacity of structures, systems and components (SSC), and 3) systems analysis. Two areas where NLSSI effects may be important in SPRA calculations are, 1) when calculating in-structure response at the area of interest, and 2) calculation of seismic fragilities (current fragility calculations assume a lognormal distribution for probability of failure of components). Some important effects when using NLSSI in the SPRA calculation process include, 1) gapping and sliding, 2) inclined seismic waves coupled with gapping and sliding of foundations atop soil, 3) inclined seismic waves coupled with gapping and sliding of deeply embedded structures, 4) soil dilatancy, 5) soil liquefaction, 6) surface waves, 7) buoyancy, 8) concrete cracking and 9) seismic isolation The focus of the research task presented here-in is on implementation of NLSSI into the SPRA calculation process when calculating in-structure response at the area of interest. The specific nonlinear soil behavior included in the NLSSI calculation presented in this report is gapping and sliding. Other NLSSI effects are not included in the calculation. The results presented in this report document initial model runs in the linear and nonlinear analysis process. Final comparisons between traditional and advanced SPRA will be presented in the September 30th deliverable.

54 ENVIRONMENTAL SCIENCES↗

FY24 Progress Report: Disposition of Cracks & Features Observed in the Inner Can Closure Weld Region (ICCWR) of the 3013 Package

The long-term integrity of the 3013 containers is of interest for the safe storage of Pu materials. Although the 3013 standard embodies multiple barrier concept, the integrity of the inner container is considered to be crucial since it protects the Safety Class outer container from its contents. The container is designed to withstand high pressures that could result from the complete radiolysis of the maximum water content permissible by the 3013 standard. Shelf-life studies and destructive examination have not found high gas pressures but have found that corrosive gases are generated. Pitting and stress corrosion cracking (SCC) are considered to be critical corrosion modes for the performance of the inner container and have been observed during destructive examinations. Considerable research has been conducted on the possibility of aqueous electrolytes condensing on the inner container that can promote SCC. These studies indicate the uncertainties surrounding the formation of corrosive environments and the corrosion behavior of container materials. In this initial report, a Bayesian network (BN) model is described that can consider the uncertainties and the causal connections between various factors influencing the corrosion modes of the inner container. The BN model is preliminary and provides an initial framework to identify the necessary information. The report also provides initial experimental results on the electrochemical behavior of stainless steels in anticipated condensed environments from gas phase migration of acidic gases. The experimental results are consistent with the corrosion model. Recommendation for further work on the BN model include assembling an expert group to provide input to the BN structure and quantification of the conditional probability matrix, experimental studies to characterize the microstructure of the container, electrochemical studies to identify critical potentials for localized corrosion and SCC, and crack growth rate studies

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.

54 ENVIRONMENTAL SCIENCES↗

A framework for assessment of predictive capability maturity and its application in nuclear thermal hydraulics

Here this work presents a formalized and computerized framework for the assessment of decision regarding the adequacy of a simulation tool for a nuclear reactor application. The decision regarding a code’s adequacy for an application is dependent on the assessment of different attributes that govern verification, validation, and uncertainty quantification of the code. In this work, the focus is on code validation. Therefore, the framework is developed and illustrated from the perspective of decision regarding the validation assessment of a code. Code validation assessment is performed based on the validation test results, data applicability, and process quality assurance factors. The process quality assurance factors warrant the trustworthiness of the evidence and help in checking people and process compliance with respect to the standard requirements. The proposed framework is developed using an argument modeling technique called Goal Structuring Notation (GSN). Goal structuring notation facilitates structural knowledge representation, information abstraction, evidence incorporation, and provides a skeletal structure for quantitative maturity assessment. The decision schema for the development of the decision model is based on the Predictive Capability Maturity Model (PCMM) and Analytic Hierarchy Process (AHP) and formalized using Goal structuring notation. Each decision attribute is formulated as a claim, where the degree of validity of the claim (attribute’s assessment) is expressed using different maturity levels. The GSN representation of the decision model is transformed into a confidence network to provide evidence-based quantitative maturity assessment using the Bayesian network. A metric based on the expected utility of maturity levels, called expected distance metric, is proposed to measure the distance between target maturity and achieved maturity on a scale of zero to one. Expected distance metric helps in comparing the assessment of different attributes and identification of major areas of concern in terms of modeling capability, data needs, and quality of assessment process. The practical application of the framework is demonstrated by a case study on validation assessment of a thermal-hydraulic code for a challenge problem called Departure from Nucleate Boiling (DNB).

42 ENGINEERING↗

FAST Model Calibration and Validation of the OC5-DeepCwind Floating Offshore Wind System Against Wave Tank Test Data

During the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project, which focused on the validation of numerical methods through comparison against tank test data, the authors created a numerical FAST model of the 1:50-scale DeepCwind semisubmersible system that was tested at the Maritime Research Institute Netherlands ocean basin in 2013. The OC5 project revealed a general underprediction of loads and motions by the participating numerical models. This paper discusses several model calibration studies that were conducted to identify potential model parameter adjustments that help to improve the agreement between the numerical simulations and the experimental test data. These calibration studies cover wind-field-specific parameters (coherence, turbulence), and hydrodynamic and aerodynamic modeling approaches, as well as rotor model (blade-pitch and blade-mass imbalances) and tower model (structural tower damping coefficient) adjustments. These calibration studies were conducted based on relatively simple calibration load cases (wave only/wind only). The agreement between the final FAST model and experimental measurements is then assessed based on more complex combined wind and wave validation cases. The analysis presented in this paper does not claim to be an exhaustive parameter identification study but is aimed at describing the qualitative impact of different model parameters on the system response. This work should help to provide guidance for future systematic parameter identification and uncertainty quantification efforts.

17 WIND ENERGY↗

Bayesian characterization of uncertainties surrounding fluvial flood hazard estimates

Fluvial floods drive severe risk to riverine communities. There is strong evidence of increasing flood hazards in many regions around the world. The choice of methods and assumptions used in flood hazard estimates can impact the design of risk management strategies. In this study, we characterize the expected flood hazards conditioned on the uncertain model structures, model parameters, and prior distributions of the parameters. We construct a Bayesian framework for river stage return level estimation using a nonstationary statistical model that relies exclusively on the Indian Ocean Dipole Index. We show that ignoring uncertainties can lead to biased estimation of expected flood hazards. We find that the considered model parametric uncertainty is more influential than model structures and model priors. Our results highlight the importance of incorporating uncertainty in extreme flood stage estimates, and are of practical use for informing water infrastructure designs in a changing climate.

54 ENVIRONMENTAL SCIENCES↗

A probabilistic graphical model based stochastic input model construction

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

Determination of nuclear PDFs using Markov chain Monte Carlo methods

Global QCD analyses of nuclear parton distribution functions (nPDFs) have traditionally relied on the Hessian method for uncertainty estimation. However, the inherent Gaussian approximation and reliance on local curvature often prove insufficient for nPDF fits, which are frequently characterized by limited data constraints and non-Gaussian likelihoods. In this paper, we present the first nPDF determination based on Markov Chain Monte Carlo (MCMC) techniques, implemented within the nCTEQ framework using an adaptive Metropolis-Hastings algorithm. The MCMC approach enables a direct mapping of the posterior distribution and reveals a highly nontrivial parameter-space structure, including multiple modes and pronounced non-Gaussian behavior, particularly for the valence PDFs. We perform the first single-nucleus global analysis of lead PDFs using exclusively lead data and compare it to a multi-nuclei fit employing a standard analytic A dependence. The inclusion of lighter nuclei reduces quark uncertainties and modifies the shape of the lead PDFs, while leaving the gluon distribution largely unaffected. A complementary Hessian analysis exposes systematic limitations of the Gaussian approximation. Our results demonstrate that MCMC methods provide a more reliable framework for uncertainty quantification in nPDF determinations.

Derakhshanian, N. [Institute of Nuclear Physics Po↗

Combustion energy frontier research center (CEFRC) final report (August 1, 2009 – July 31, 2016)

The Combustion Energy Frontier Research Center (CEFRC) was established to tackle the single overarching grand challenge of energy sustainability, energy security and global warming: to develop a “validated, predictive, multi-scale, combustion modeling capability to optimize the design and operation of evolving fuels in advanced engines for transportation applications,” as identified in the DOE report on “Basic Energy Needs for Clean and Efficient Combustion of 21st Century Transportation Fuels”. The challenge is particularly daunting since energy conversion efficiencies and exhaust emissions are governed by coupled chemical and transport processes at multiple length scales ranging from electron excitation to molecular rearrangements to nanoscale particulate formation to turbulent fuel/air mixing. To tackle this challenge, the CEFRC assembled a world-class team of 15 principal investigators, with the objectives to: 1) develop and test theoretical models to predict elementary reaction rates, molecule thermalization rates, chemical bond dissociation energies, and nonequilibrium transport properties using quantum chemistry calculations that account for strong electron correlation and multiple electronic potential energy surfaces; 2) develop automated kinetic mechanism generation, reduction, and error control methods for predicting alternative fuel including biofuel oxidation, fuel droplet decomposition, and NOx and particulate formation; 3) validate and improve the predictions of these models by measuring ignition delay times, species profiles, flame structures, burning limits, turbulence-kinetic coupling, and NOx and soot emissions at high-pressures and near-limit conditions, by using advanced experimental diagnostic techniques including multiple laser techniques, molecular beam sampling and synchrotron photoionization, and by conducting the measurements in high-pressure shock tubes, jet-stirred and flow reactors, flame bombs, counterflow flames, and advanced-design rapid compression ignition instruments; and 4) develop a suite of validated petascale high-fidelity simulation and modeling capabilities to understand and predict chemistry-turbulence-radiation coupling for new fuels in new regimes, including the high pressure, low-temperature combustion in advanced engine and turbine designs, and 5) establish a knowledge highway between researchers and engineers in academia, national laboratories, and industry to facilitate the dissemination and exchange of knowledge on national and international levels, and enrich the talent pool and capabilities of the next generation of combustion scientists and engineers. The technical activities of the CEFRC were conducted through three Disciplinary Working Groups – Chemistry Theory, Experiment and Mechanism, and Reacting Flows, which coordinated the Center’s research on the development of combustion chemistry of Foundation Fuels (C0–C4 hydrocarbons), Alcohols, and Biodiesel through three corresponding Mechanism Thrust Groups. Such a two-dimensional coordinated and tightly interwoven research structure has been proven to be highly effective in assuring the interplay between the developments of the fundamentals of combustion science and the utilization of the various categories of fuels. The Center has accomplished the above goals over the five year period (August 1, 2009 – July 31, 2014) with appropriated funding, followed by two additional no-cost-extension (NCE) years. The research results are documented in 230 journal publications, with six legacy review papers on the study of combustion chemistry using shock tubes, flow reactors, rapid compression machines, and flames, on uncertainty quantification, and on theoretical reaction dynamics and chemical modeling of combustion. A robust outreach program complemented these PI-led research activities, consisting of: 1) a roving post-doc program comprised of a corps of Center-appointed, co- or multi-sponsored post-doctoral fellows with rotating assignments to conduct seed projects initiated by at least two PIs, in residence with these sponsoring PIs, to rapidly pursue new and high-risk, high-payoff interdisciplinary ideas; 2) an annual summer school on combustion heavily attended (~200) by senior graduate students and practicing researchers covering advanced topics on chemical kinetics, fluid mechanics, turbulent combustion, engine combustion, new technologies, etc.; 3) a robust open web-site providing Center and community information as well as the lecture videos and notes of the summer school; and 4) widely distributed biannual newsletters.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Uncertainty Quantification of Classifying Mechanical Breach in the Crash and Burn Problem

The prediction of mechanical breach in the Crash and Burn problem is important for designing the full system to minimize the probability of loss of containment. Due to uncertainties in the impact angle, material properties, and material models, it is not possible to define an exact critical impact speed at which the system breaches. Furthermore, the cost of running a large scale sampling study to determine the empirical probability of breach is prohibitive. In this work, surrogate models from machine learning, namely logistic regression and artificial neural networks, are introduced to predict binary classification of pass versus breach from a limited set of samples. The structure and calibration of these classifiers is discussed, and a set of metrics for describing the performance of the classifiers is introduced. The classifiers are used on the UUR version of the Crash model to attempt prediction of failure probability and perform variable sensitivity analysis. Where a single sample of the computational model can take hundreds of CPU-hours, training and evaluating a classifier can take seconds or less, thus giving high predictive power in a relatively short time.

42 ENGINEERING↗

Evaluation of average leaf inclination angle quantified by indirect optical instruments in crop fields

Average leaf inclination angle ($\overline{θ}$ L ) is an important canopy structure variable that influences light regime, photosynthesis, and evapotranspiration of plants. $\overline{θ}$ L can be measured through direct methods (e.g., protractor), which are labor-intensive and time-consuming, or through indirect optical instruments, which are more efficient than the direct methods. However, uncertainties of different indirect optical instruments for quantifying $\overline{θ}$ L remain largely unquantified. In this study, we evaluated and compared the performances of three major indirect optical instruments: (1) LAI-2200, (2) 30°-tilted camera, and (3) digital hemispherical photography (DHP), in different crop fields over a growing season, benchmarked with direct measurements. LAI-2200 and 30°-tilted camera showed higher agreement with direct $\overline{θ}$ measurements (R 2 = 0.54, RMSE = 7.37°; R 2 = 0.58, RMSE = 8.08°) than DHP (R 2 = 0.14, RMSE = 13.96°). Different performances of indirect optical instruments could be attributed to the accuracy of gap fraction measurement and the performance of the $\overline{θ}$ L quantification algorithms. When using the LAI-2200 algorithm, larger gap fraction gradients over view zenith angles led to larger $\overline{θ}$ L values, and smaller gap fraction gradients led to smaller $\overline{θ}$ L values. Such error propagation was larger in sparse canopy than in dense canopy. The Wilson G function of the LAI-2200 algorithm performed better in estimating $\overline{θ}$ L than the G function based on the ellipsoidal LAD function used by the CAN_EYE algorithm. We also proposed a modification of the LAI-2200 algorithm, which further improved the performance of LAI-2200 and 30°-tilted cameras in estimating $\overline{θ}$ L . We envision that the low-cost 30°-tilted cameras provide a promising sensor solution to continuously monitor canopy structure for various ecosystems.

30°-tilted camera↗