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At least 217 records · Page 12

Uncertainty quantification for competing failure mechanisms in unidirectionally reinforced carbon–carbon composites

Microstructure-informed finite element models play a key role in the carbon–carbon composite design process. Variability in manufacturing process parameters and experimental limitations introduce model parameter uncertainty. This study quantifies the effect of model parameter uncertainty on transverse tensile fracture behavior and proposes a methodology to predict the failure mode based on competing microscale damage mechanisms. Finite element simulations incorporate fiber–matrix interface debonding with cohesive zones and matrix damage with a smeared crack band approach in a unidirectional carbon–carbon composite. Results from a variance-based global sensitivity analysis identifies interfacial and matrix damage parameters as the primary source of variability in fracture behavior. Sobol’ indices indicate that matrix and cohesive zone strengths contribute 94% of the variance in the effective ultimate stress. A local analysis elucidates the relationship between these constituent strength parameters and failure mode by estimating the probability of cohesive, matrix, and mixed-mode dominated failure. Based on the results for 4000 simulations, 93% exhibit mixed-mode or interfacial dominated failure, which underscores the crucial role of fiber–matrix interface debonding in the transverse tensile failure of carbon–carbon composites. These uncertainty quantification results facilitate more efficient model calibration and provide a framework for microstructure-informed failure predictions in the face of manufacturing-induced uncertainty.

36 MATERIALS SCIENCE↗

A Vertically Resolved Analysis of Radiative Feedbacks on Moist Static Energy Variance in Tropical Cyclones

Abstract A vertically resolved moist static energy (MSE) variance budget framework is used to diagnose processes associated with the development of tropical cyclones (TCs) in a general circulation model (GCM) under realistic boundary conditions. Previous studies have shown that interactions between radiation and MSE promote TC development. Here, we examine the vertical contributions of radiation and its interactions with MSE by performing several mechanism-denial experiments in which synoptic-scale radiative interactions are suppressed either in the boundary layer or in the free troposphere. Partly suppressing radiative interactions results in a reduction in global TC frequency. However, the magnitude of reduction and structure of the feedback depend on the intensity and structure of the TCs in these mechanism-denial experiments, indicating that both the magnitude and the vertical location of radiative interactions can impact global TC frequency. Using instantaneous 6-hourly outputs, an explicit computation reveals distinct spatial patterns of the advection term: the vertical component is positive in the mid- to upper troposphere, which reflects an upward transport of MSE by deep convection, whereas the horizontal component is positive in the boundary layer. These results illustrate the impact of the vertical distribution of radiative interactions and vertically varied contribution of the advection term in the development of TCs.

Meteorology & Atmospheric Sciences↗

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

Hydrological models are always composed of multiple components that represent processes key to intended model applications. When a process can be simulated by multiple conceptual-mathematical models (process models), model uncertainty in representing the process arises. While global sensitivity analysis methods have been widely used for identifying important processes in hydrologic modeling, the existing methods consider only parametric uncertainty but ignore the model uncertainty for process representation. To address this problem, this study develops a new method to probe multimodel process sensitivity by integrating the model averaging methods into the framework of variance-based global sensitivity analysis, given that the model averaging methods quantify both parametric and model uncertainty. A new process sensitivity index is derived as a metric of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and model parameters. For demonstration, the new index is used to evaluate the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that converting precipitation to recharge, and the geology process is also simulated by two models of different parameterizations of hydraulic conductivity; each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.

Dai, Heng↗

Fast variance reduction for steady-state simulation and sensitivity analysis of stochastic chemical systems using shadow function estimators

We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest, these systems are analytically intractable, and one has to resort to computational methods to estimate stationary values of cost functions. In this work, we introduce a novel variance reduction algorithm for stochastic chemical kinetics, inspired by related methods in queueing theory, in particular the use of shadow functions. Using two numerical examples, we demonstrate the efficiency of the method for the calculation of steady-state parametric sensitivities and evaluate its performance in comparison to other estimation methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

The Monte Carlo (MC) method is the 'gold standard' for performing nuclear reactor calculations and criticality safety analyses because of its ability to handle complex geometries and physics. Reactor and criticality safety analyses require solving eigenvalue problems in complex nuclear systems. Once a stationary fission source distribution is obtained in MC simulations, the sample mean of many stationary cycles is calculated. The MC simulation sample mean is typically referred to as a tally. Variance, or standard deviation, of the sample mean/tally is needed to indicate the level of statistical uncertainty in the simulation and to understand the convergence of the sample mean. Current MC codes typically use sample variance to estimate the statistical uncertainty of the simulation and assume that the MC stationary cycles are independent. However, it is known that cycles are correlated, and estimators of the variance that ignore these correlations systematically underestimate the variance. In this paper, we propose a novel method in the Fourier frequency domain to estimate the variance of the sample mean in MC eigenvalue calculations. Results indicate that the proposed estimator can be unbiased compared to the real variance. The proposed estimator requires minimal additional computing effort.

42 ENGINEERING↗

Analytical modeling and simulation of electrical contact resistance for elastic rough electrode surface contact including frictional temperature rise

An improved electrical contact resistance (ECR) model for elastic rough electrode contact is proposed, incorporating the effects of asperity interactions and temperature rise by frictional and joule heating. The analytical simulation results show that the ECR decreases steeply at the beginning of the contact between Al and Cu. However, it becomes stabilized after reaching a specific contact force. It is also found that the longer elapsed sliding contact time, the higher ECR due to the increase in electrical resistivity of electrode materials by the frictional temperature rise at the interface. The effects of surface roughness parameters on ECR are studied through the 3 2 full-factorial design-of-experiment analysis. Based on the two representative roughness parameters, i.e., root-mean-square (rms) roughness and asperity radius, their individual and coupled effects on the saturated ECR are examined. The saturated ECR increases with the rms roughness for a rough machined surface condition, but it is hardly affected by the asperity radius. On the other hand, the saturated ECR increases with both the rms roughness and the asperity radius under a smooth thin film surface condition.

42 ENGINEERING↗

Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

Monte Carlo (MC) simulation is widely used to solve the eigenvalue form of the Boltzmann transport equation that mathematically represents the neutron transport process through complex multiplying (fissionable) systems. Monte Carlo eigenvalue simulation starts with an assumed fission source distribution and uses the fission sites from the previous iteration (cycle) as the starting source in the current iteration. Important system parameters (MC tallies) such as fuel pin-power distribution are estimated over several cycles after the convergence of the fission source distribution to a stationary distribution. However, the MC fission source iteration algorithm that uses fission source sites from the previous cycle introduces a cycle-to-cycle correlation. Monte Carlo simulations that do not account for the cycle-to-cycle correlation systematically underestimate the variance of the estimated system parameters (sample mean). This paper presents the relationship between the spectral density in the frequency domain at frequency zero and the variance of the sample mean. This paper introduces a novel method in the frequency domain for the MC variance estimation. For the three test problems used in this paper, researchers have observed that the new method results in an improvement of more than one order of magnitude to the standard deviation of the sample mean. The new method also compares favorably with the previously introduced batch, bootstrap, and covariance-adjusted methods when applied to the three test problems investigated in this paper. This new method does not require modification of the MC eigenvalue algorithm (power iteration), is code agnostic, and is therefore easy to use when implementing in any existing MC code. In conclusion, the new estimate can be calculated without saving tally results of all active/stationary cycles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Global Sensitivity Analysis Using the Ultra‐Low Resolution Energy Exascale Earth System Model

Abstract For decades, Arctic temperatures have increased twice as fast as average global temperatures. As a first step toward quantifying parametric uncertainty in Arctic climate, we performed a variance‐based global sensitivity analysis (GSA) using a fully coupled, ultra‐low resolution (ULR) configuration of version 1 of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SMv1). Specifically, we quantified the sensitivity of six quantities of interests (QOIs), which characterize changes in Arctic climate over a 75 year period, to uncertainties in nine model parameters spanning the sea ice, atmosphere, and ocean components of E3SMv1. Sensitivity indices for each QOI were computed with a Gaussian process emulator using 139 random realizations of the random parameters and fixed preindustrial forcing. Uncertainties in the atmospheric parameters in the Cloud Layers Unified by Binormals (CLUBB) scheme were found to have the most impact on sea ice status and the larger Arctic climate. Our results demonstrate the importance of conducting sensitivity analyses with fully coupled climate models. The ULR configuration makes such studies computationally feasible today due to its low computational cost. When advances in computational power and modeling algorithms enable the tractable use of higher‐resolution models, our results will provide a baseline that can quantify the impact of model resolution on the accuracy of sensitivity indices. Moreover, the confidence intervals provided by our study, which we used to quantify the impact of the number of model evaluations on the accuracy of sensitivity estimates, have the potential to inform the computational resources needed for future sensitivity studies.

54 ENVIRONMENTAL SCIENCES↗

SU-F-T-19: The Consistency Dosimetric Analysis of the Accelerated Breast Brachytherapy

Purpose: To assess the best approach in accept a treatment plan for APBI Savi patients. Should we run a treatment verification test prior to delivering it to the patient? Should we check each CT scan in regards to the initial one in dosimetrical terms? Do we need deformable registration and adaptive planning for each fraction? These are the questions we want to answer running a dosimetric analysis of the dose variances for APBI treatments who receive 10 fractions and no re-planning has been done being considered unnecessary with today’s means of assessment. Methods: A retrospective analysis of 30 patients treated with SAVI applicators were considered for this study. The CT scans taken before each treatment were imported in the treatment planning system and registered with the initial CT scan. The images were fused together with respective to the applicator, using landmark registration. Dosimetric evaluations were performed. Dose received by skin, ribs and PTV on CT images with respect to the initial treatment plan were recorded including maximum, average and minimum dose Results: All the structures displayed changes in volume over the 10 fractions of treatment. The cavities reduction in volume was considerable with a maximum reduction of over 10%. The PTV-eval is covered better due to this fact while the critical organs manifest an increase in the total and maximum dose delivered. Ribs and skin surface that are required by B39 protocol to be monitored can acquire maximum doses of 20% to 30% respectively. Conclusion: A dosimetric evaluation prior to the initial treatment and prior to each of the 10 fractions is proven to be necessary. Deformable registration and adaptive planning have to be studied more and eventually implemented for every patient who received more than one fraction of any type of brachytherapy treatment. Immobilization ad localization methods must be improved and studied further.

60 APPLIED LIFE SCIENCES↗

Quantitative metrics for evaluating thermonuclear design codes and physics models applied to the National Ignition Campaign

In this study, physics models and design codes for hot dense plasmas undergoing thermonuclear burn are evaluated objectively using statistical metrics that compare the difference between calculations and data relative to the experimental uncertainties. The analysis is applied to the National Ignition Campaign (NIC) because it is relevant, comprehensive, and well documented. The statistics confirm that a key process afflicting NIC performance is mix driven by hydrodynamic instabilities as approximated here using the KL model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)]. New physics models are also presented for instability-driven magnetic fields [B. Srinivasan et al., Phys. Rev. Lett. 108, 165002 (2012)] and the Coulomb logarithm for electron–ion thermal relaxation [G. Dimonte and J. Daligault, Phys. Rev. Lett. 101, 135001 (2008)]. The plasma-generated magnetic fields improve the agreement between code and data in a statistically significant manner by reducing the electron thermal conduction in the hot-spot via the Hall term. The Coulomb logarithm is presented in a numerically practical form that incorporates recent theoretical advances. However, it does not improve the agreement between the code and data because the thermal relaxation is so fast in non-ignited NIC plasmas that the typical 20% error does not change the tight coupling between electrons and ions. Even with these improved physics models, the one-dimensional simulations presented here are not able to describe the high-convergence NIC implosions in a statistically acceptable manner. Of the heroic multi-dimensional simulations of Clark et al. [Phys. Plasmas 23, 056302 (2016)], only those in three-dimensions satisfy the statistical acceptance criterion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem

In this study, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory–epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.

97 MATHEMATICS AND COMPUTING↗

SU-E-T-41: Analysis of GI Dose Variability Due to Intrafraction Setup Variance

Purpose: Proton SBRT (stereotactic body radiation therapy) can be an effective modality for treatment of gastrointestinal tumors, but limited in practice due to sensitivity with respect to variation in the RPL (radiological path length). Small, intrafractional shifts in patient anatomy can lead to significant changes in the dose distribution. This study describes a tool designed to visualize uncertainties in radiological depth in patient CT's and aid in treatment plan design. Methods: This project utilizes the Shadie toolkit, a GPU-based framework that allows for real-time interactive calculations for volume visualization. Current SBRT simulation practice consists of a serial CT acquisition for the assessment of inter- and intra-fractional motion utilizing patient specific immobilization systems. Shadie was used to visualize potential uncertainties, including RPL variance and changes in gastric content. Input for this procedure consisted of two patient CT sets, contours of the desired organ, and a pre-calculated dose. In this study, we performed rigid registrations between sets of 4DCT's obtained from a patient with varying setup conditions. Custom visualizations are written by the user in Shadie, permitting one to create color-coded displays derived from a calculation along each ray. Results: Serial CT data acquired on subsequent days was analyzed for variation in RPB and gastric content. Specific shaders were created to visualize clinically relevant features, including RPL (radiological path length) integrated up to organs of interest. Using pre-calculated dose distributions and utilizing segmentation masks as additional input allowed us to further refine the display output from Shadie and create tools suitable for clinical usage. Conclusion: We have demonstrated a method to visualize potential uncertainty for intrafractional proton radiotherapy. We believe this software could prove a useful tool to guide those looking to design treatment plans least insensitive to motion for patients undergoing proton SBRT in the GI tract.

60 APPLIED LIFE SCIENCES↗

Toward witnessing molecular exciton entanglement from spectroscopy

Entanglement is a defining feature of quantum mechanics that can be a resource in engineered and natural systems, but measuring entanglement in experiment remains elusive especially for large chemical systems. Most practical approaches require determining and measuring a suitable entanglement witness which provides some level of information about the entanglement structure of the probed state. A fundamental quantity of quantum metrology is the quantum Fisher information (QFI), which is a rigorous witness of multipartite entanglement that can be evaluated from linear response functions for certain states. Here, in this paper, we explore measuring the QFI of molecular exciton states of the first-excitation subspace from spectroscopy. In particular, we utilize the fact that the linear response of a pure state subject to a weak electric field over all possible driving frequencies encodes the variance of the collective dipole moment in the probed state, which is a valid measure for QFI. The systems that are investigated include the molecular dimer, N-site linear aggregate with nearest-neighbor coupling, and N-site circular aggregate, all modeled as a collection of interacting qubits. Our theoretical analysis shows that the variance of the collective dipole moment in the brightest dipole-allowed eigenstate is the maximum QFI. The optical response of a thermally equilibrated state in the first-excitation subspace is also a valid QFI. Theoretical predictions of the measured QFI for realistic linear dye aggregates as a function of temperature and energetic disorder due to static variations of the host matrix show that two- to three-partite entanglement is realizable. This paper lays some groundwork and inspires measurement of multipartite entanglement of molecular excitons with ultrafast pump-probe experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-Model and Multi-Scale Global Sensitivity Analysis for Identifying Controlling Processes of Complex Systems

An environmental model consists of multiple process level sub-models, and each sub-model represents a process that is key to the operation of the simulated system. Global sensitivity analysis methods have been widely used to identify important processes for system model development and improvement. The existing methods of global sensitivity analysis only consider parametric uncertainty, and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes. To address this problem, this project develops a new method to probe model output sensitivity to competing process models by integrating model averaging methods with variance-based global sensitivity analysis to address uncertainty in process models and parameters. The new method yields three process sensitivity indices. The first one is called first-order process sensitivity index, and it is derived as a single summary measure of relative process importance. Evaluating the index is computationally expensive, because it relies in a Monte Carlo scheme that requires thousands and even millions of model executions. To reduce computational cost, this project develops a computationally efficient, quasi Monte Carlo method, and this method is presented in Chapter 2 of this report with and a numerical example for demonstration. The numerical example shows that the results of the quasi Monte Carlo method are substantially close to those of the full Monte Carlo method, but the computational cost of the quasi Monte Carlo method is only 0.7% of that of the full Monte Carlo method. The second index is called total-effect process sensitivity index, and it measures interactions between different processes. Therefore, this sensitivity index includes the first-order process sensitivity index, and can be used to identify influential processes. On the other hand, the total-effect process sensitivity index can also be used to screen non-influential processes. This is demonstrated by two numerical examples using the Sobol-G* functions and groundwater flow models that consider recharge process, geological process, and snowmelt process. The numerical examples shows that the total-effect process sensitivity index is more informative than the first-order process sensitivity. The derivation of the process sensitivity index and the numerical examples are discussed in Chapter 3. Chapter 4 presents two computationally efficient methods for screening non-influential processes to exclude them from further investigation. The two methods are the multi-model difference-based sensitivity (MMDS) analysis method, which can be implemented using the Latin Hypercube Sampling. The second one is the implementation of MMDS method using a binning method. The numerical example for the Sobol-G* function indicates the two methods are capable of identifying non-influential models, and the numerical examples for the groundwater flow and reactive transport show that the two methods are effective for groundwater problems. However, it should be noted that the two methods are numerical approximations, and they can only be used for screening non-influential processes, not for ranking importance of system processes. All the sensitivity analysis methods are implemented by developing python codes, and the codes are in a software called SAMMPY: a python package for process sensitivity analysis under multiple models. The SAMMPY design and structure are discussed in Chapter 5, and the package is released to the public for free download.

54 ENVIRONMENTAL SCIENCES↗

Sensitivity analysis of generic deep geologic repository with focus on spatial heterogeneity induced by stochastic fracture network generation

Geologic Disposal Safety Assessment Framework is a state-of-the-art simulation software toolkit for probabilistic post-closure performance assessment of systems for deep geologic disposal of nuclear waste developed by the United States Department of Energy. This paper presents a generic reference case and shows how it is being used to develop and demonstrate performance assessment methods within the Geologic Disposal Safety Assessment Framework that mitigate some of the challenges posed by high uncertainty and limited computational resources. Variance-based global sensitivity analysis is applied to assess the effects of spatial heterogeneity using graph-based summary measures for scalar and time-varying quantities of interest. Behavior of the system with respect to spatial heterogeneity is further investigated using ratios of water fluxes. This analysis shows that spatial heterogeneity is a dominant uncertainty in predictions of repository performance which can be identified in global sensitivity analysis using proxy variables derived from graph descriptions of discrete fracture networks. New quantities of interest defined using water fluxes proved useful for better understanding overall system behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Updimensioning strategy derived from synthetic equiaxed grain structures for approximating 3D grain size distributions from 2D visualizations with 1D parameters

We generated synthetic equiaxed grain structures using computer graphics software to explore the relationship between various grain size determination methods and true three-dimensional (3D) grain diameters. Mirroring grain measurement techniques, the synthetic 3D grain structures are imaged as 2D micrographs which are measured to yield 1D grain size parameters. Synthetic grain structures provide data at a mass scale and permit exploration of both polished and fractured surface micrographs, revealing one-to-one correspondence between exposed 2D grain cross-sections and individual 3D grains. Analysis of this correspondence yielded a procedure to approximate 3D equiaxed grain size and volume distributions based on the mode of the 2D fractograph grain size distribution. The 3D approximation procedure is shown to be less susceptible to different imaging conditions that affect small, undiscernible grains compared to the standard planimetric and linear intercept methods, which by design also tend to underestimate the 3D grain diameter. The procedure requires larger sample sizes to lower variance and a deeper analysis which could become more practical with machine learning (ML) models for grain boundary segmentation, which synthetic grain structures can help train. This work lays the foundation for analyzing other grain distributions such as columnar and composite grains in similar depth.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗