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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Stochastic Approaches for Calculating and Aggregating Detection Probabilities for Nuclear Material Diversion

The authors built and tested a stochastic simulation to estimate achieved detection probabilities (DPs) on a stratum basis, over a tailorable range of diverted amounts from 0 to 2 significant quantities (SQ), using typical International Atomic Energy Agency (IAEA) inspection data: i.e., SQ in stratum, number of items, number of gross/partial/bias defect measurements conducted, and realistic relative standard deviation (RSD) values for typical IAEA verification measurements. For bulk strata, the model calculates achieved DP at 0.01 SQ diversion increments; for item strata, the model calculates DP using the smallest realistic diversion increment (e.g., a plate, pin, or coupon). After successfully benchmarking against IAEA deterministic models, the simulation was used to test the sensitivity of DP to certain standard assumptions and selected input parameters. First, the equal defect assumption was tested; the results suggest significant complexity in the effectiveness of partial defect measurements. Next, the authors explored the sensitivity of DP to the assumed RSD of attribute tests. Then, the authors compared non-normal models for instrument performance (e.g., logistic, step, or arbitrary functions) to the typical results from a normal distribution (characterized by RSD). This last comparison was supplemented with experimentally derived performance data for an HM-5 gamma spectrometer. The HM-5 was used to make enrichment measurements on both LEU and HEU MTR fuel elements as plates were removed, and the results fit with logistic and step curves and applied in the simulation. These stochastic DP results were compared to DP estimates from a deterministic model assuming a normal curve and typical RSD, yielding insights that could improve effectiveness in the field. These early results illustrate the potential of stochastic models to better understand achieved DP and to improve safeguards effectiveness.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Improbability of Post-Closure Criticality in Array of Transuranic Waste Containers after Compaction by Salt Creep at Waste Isolation Pilot Plant

Based on the rationale presented, post-closure nuclear criticality is improbable when room closure compacts containers disposing transuranic (TRU) waste emplaced at the Waste Isolation Pilot Plant (WIPP), an operating repository in bedded salt in southeastern New Mexico. As described in the original WIPP certification, a qualitative estimate of the probability of post-closure criticality in TRU waste produced from atomic energy defense activities has been low either because remote-handled TRU waste canisters are neutronically isolated by the bedded salt or because the low fissile mass in an array of contact-handled TRU waste drums cannot be compacted sufficiently by room closure from salt creep. These situations are still valid for the majority of TRU waste that is disposed at WIPP without any disposal constraints, as updated herein. This report also qualitatively evaluates the probability of criticality after disposal of TRU waste in pipe overpack containers (POC) where every POC in a shipment may have the maximum 200 fissile gram equivalent of 239Pu content. The probability of criticality for a disposal room filled with POCs is estimated during four representative phases of repository evolution: (1) a large salt block falls onto POCs in the first 20 years, (2) salt creep closes a disposal room in the first 1000 years without brine seepage and subsequent gas generation, which permits maximum compaction, (3) some brine seepage occurs into the closed room, which initiates consumption of the fiberboard (cellulose) impact absorber in the POC in the second 1000 years, and (4) full brine inundation of a room and consumption of all fiberboard thereafter. Salt-block fall in the first phase does not greatly disrupt three tiers of POCs. The compacted spacing of POCs in the later three repository conditions is calculated through high-fidelity, geomechanical modeling. Criticality evaluation of compacted 200-g 239 Pu spheres at the compacted spacing shows that neither 12-inch nor 6-inch POCs are critical after the first 1000 years, the second 1000 years, or thereafter as the sea of reflector material changes to represent the three repository conditions. Specifically, fiberboard and iron isolates 239 Pu while dry, and brine reduces the reactivity when a room is partially and fully inundated. Because POC behavior bounds behavior of other standard TRU waste containers, post-closure criticality caused by room closure compacting containers is omitted in the performance assessments for the 2019 and 2026 WIPP compliance re-certification applications to the US Environmental Protection Agency.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Representing Complex Systems as Graphs for Debugging and Predictive Maintenance-Preliminary Thoughts

Representing complex systems as graphs enables use of mathematical tools to identify faults or predict failures. Graph nodes correspond to individual modules or subsystems, and edges link coupled system parts. ‘Probes’ measure the node outputs, monitoring the system health for unexpected behavior. Assuming one cannot probe every point, within a system, the fault correlates to a region—not necessarily the specific location. Bayesian networks trained to understand fault patterns can accurately identify the source. The diagnostic tool described aides debugging by pinpointing system failure causes. For predictive maintenance, probe data develop probability distribution functions describing subsystem mean time to failure. Unit lifetime can be estimated through these probability distributions. Two approaches include using Bayesian classifiers to infer the system failure source and developing maintenance schedules by treating systems as collections of random variables. When failure behavior does not follow a closed form function, use of similarity models is proposed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Purpose, Design, and Analysis of the NSTX-U Centerstack Casing Lateral Support Shims

The National Spherical Torus Experiment Upgrade (NSTX-U) centerstack casing surrounds the central magnet core of NSTXU. It provides the inner vacuum boundary of the plasma chamber and supports the radially inboard plasma facing components lining the plasma chamber. The casing is supported like a cantilever, fixed at the lower flange by a connection to the TF Bundle through a G-10 ring. It is flexibly supported at the top by bellows, and insulated shims intended to react the largest part of the inventory of the disruption loads at the upper support, thereby protecting the upper and lower connections from excessive loads. A large part of the qualification of the casing and tiles requires addressing and quantifying disruption loads. These have been estimated based on extensions of the behavior of NSTX during its run period roughly 15 years ago. Structural qualification of the Upgrade used these estimates of the loading as input to calculations to demonstrate adequacy for a “most probable” disruption. The estimates are included in a requirements document to guide conservative design of all components loaded by disruptions. However, the changes made for the upgrade made the extrapolation of disruption behavior uncertain. Disruptions include axisymmetric loading from axisymmetric currents induced in the vessel shells. In addition, more complex currents called Halo currents are a result of plasma poloidal currents impinging on the casing. The halo currents add another layer of uncertain behavior and net lateral loading to the casing. As a result, NSTX-U is equipped with a number of instruments intended to assess the nature and severity of disruptions. The casing shims are required for lateral support of the casing, but these have also been converted to load cells to provide another measure of the magnitude of symmetric and asymmetric loading. Some of the logic in the development of the requirements document are presented. Electromagnetic analysis of axisymmetric and halo loading is described. Global simulations of the casing transient dynamic response, and local analysis and testing of the shim/load cell are included. The shim load cells and other instrumentation will be an important guide in planning NSTX-U experiments beyond its next run period expected in late 2026 or early 2027.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)

A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Evaluating Probability of Containment Effectiveness at a GCS Sites using integrated assessment modeling approach with Bayesian decision Networks

Improved scientific and engineering understanding of the behavior of geologic CO2 storage together with established regulatory framework and incentive structures raise the prospects for accelerated, large-scale deployment of this greenhouse gas emissions reduction approach. Incentive structures call for the establishment of appropriate verification and accounting approaches to support claims of the integrity of a geologic storage complex and to justify taking credit for long-term storage. In this study, we present a framework for assessing the probability of containment effectiveness over the lifetime of a geologic carbon storage site (e.g., after 70 years of injection and post-injection site performance) using forward stochastic model realizations based on site characterization data and using a monitoring-informed Bayesian network based on hypothetical detectability from surface seismic surveys over the site injection and post-injection phases. The National Risk Assessment Partnership’s open-source Integrated Assessment Model (NRAP-Open-IAM) was utilized to develop an ensemble of 10,000 a priori stochastic forecasts of CO2 containment. Those simulations were used to train the Bayesian network model to estimate the prior probabilities of the CO2 leakage mass into overlying, monitorable aquifers considering the uncertainties in the reservoir properties, permeability of potentially leaky wells and the overlying aquifers. The conditional probabilities in the Bayesian network were either learned from the NRAP-Open-IAM simulations or derived from the predefined detection thresholds for the monitoring method. Observations obtained from monitoring, over time during the site operation phases were then used to generate updated posterior probabilities of containment (and any loss from containment) in the Bayesian network by propagating the prior probabilities through the conditional probabilities. We demonstrate how to construct and use the Bayesian network for verifying the long-term storage complex effectiveness informed by monitoring based on the NRAP-Open-IAM simulations previously developed for the FutureGen 2.0 site. This approach may have relevance for stake holders to demonstrate secure geologic storage, provide a defensible, probabilistic approach to claim credit for geologic storage, and to estimate the likelihood that any fraction of the claimed credit may need to be refunded to the creditor based on available monitoring information.

Bayesian network, Risk assessment, Monitoring, car↗
DOE OSTI2023

Dynamic Bayesian Networks for Fault Prognosis

A dynamic Bayesian Network (DBN)-based fault prognosis framework is proposed in this study to predict the future fault probabilities of gradual faults. The proposed framework utilizes the trend in prediction error generated from data driven forecasting models to estimate the future fault beliefs. The accuracy and scalability of the proposed method is evaluated using the data from a Modelica-based virtual testbed. Overall, the developed framework demonstrates good potential in estimating future fault probabilities of gradual faults.

Pradhan, Ojas↗
DOE OSTI2026

Asymptotic inconsistency of the cumulative algorithm for laser-induced damage probability analysis

The “cumulative algorithm” is a data analysis method that has been proposed to provide an objective, nonparametric determination of laser-induced damage probability as a function of fluence from experimental data that contain both damaged sites and undamaged sites (i.e., 1-on-1 or S-on-1 testing protocols). In this work, the limitations of this approach are explored by considering the asymptotic limit of a large number of test sites. It is shown that the cumulative algorithm does not converge to the true probability distribution and significantly underestimates the damage probability near the damage onset. Here, based on the results of this work, the cumulative algorithm is not recommended for accurate estimation of damage probability.

Computational methods↗
DOE OSTI2025

Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis

Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of control variates (CV) and importance sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework—a creative take on a coupled CV and IS estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and sidestepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. Furthermore, the task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.

Markov chain Monte Carlo↗
DOE OSTI2022

Advanced Laboratory and Field Arrays: Debris Modeling, Detection,& Mitigation (Task 1)

The statement of project objectives for this task was: develop tools, methods and models to assess, and mitigate the risk of damage to MHK infrastructure from woody debris. Develop the capability to detect woody debris using sonar and/or physical methods for purposes of characterizing debris statistics in river (at UAF’s Tanana River Test Site) and near-shore wave (at Yakutat, AK) environments and to activate debris mitigation measures. Develop debris impact risk maps and tables using statistics on debris size, geometry, type, prevalence, mobility and location. Improve and apply the COUPi discrete element method (DEM) to develop models of debris movement and impact on MHK infrastructure to evaluate risk of damage, and interference, to operations from debris. The proposed final deliverable for the task was a set of tools or techniques for providing estimates of the probability of debris impact, and resulting impact forces, on MHK infrastructure as a function of debris size, type, wave regime, and current velocity. Such estimates are required to assess damage risks to operational MHK infrastructure.

13 HYDRO ENERGY↗
DOE OSTI2024

Impact of solar geoengineering on temperature-attributable mortality

Decisions about solar geoengineering (SG) entail risk–risk tradeoffs between the direct risks of SG and SG’s ability to reduce climate risks. Quantitative comparisons between these risks are needed to inform public policy. We evaluate idealized SG’s effectiveness in reducing deaths from warming using two climate models and an econometric analysis of temperature-attributable mortality. We find SG’s impact on temperature-attributable mortality is uneven with decreases for hotter, poorer regions and increases in cooler, richer regions. Relative to no SG, global mortality is reduced by over 400,000 deaths annually [90% CI: (−1.2 million,2.7 million)] for cooling of 1 °C from 2.5 °C above preindustrial in 2080. We find no evidence that mortality reduction achieved by SG is smaller than the reduction from equivalent cooling by emissions reductions. Combining our estimates with existing estimates of sulphate aerosol injection direct mortality risk from air quality and UV-attributable cancer enables the first quantitative risk-risk comparison of SG. We estimate with 61% probability that the mortality benefits of cooling outweigh these direct SG risks. We find the benefits outweigh these risks by 13 times for our central estimates, or 4 deaths per 100,000 per 1 °C per year [90% CI: (−11,23)]. This is not a comprehensive evaluation of the risk–risk tradeoffs around SG, yet by comparing some of the most consequential impacts on human welfare it is a useful first step. While these findings are robust to a variety of alternative assumptions, considerable uncertainties remain and require further investigation.

Harding, Anthony (ORCID:0000000262898253)↗
DOE OSTI2022

Radiative transition probabilities of neutral and singly ionized Europium estimated by laser-induced breakdown spectroscopy (LIBS)

Laser-induced breakdown spectroscopy (LIBS) is a versatile technique for compositional analysis for solids, liquids, or gasses. LIBS is an asset for the quantitative or qualitative analysis of resource limited materials like actinides and rare earths because it is quasi-nondestructive. Two Eu 2 O 3 pellets were synthesized to be a test and validation set, respectively. Spectral lines identified from the National Institute of Standards and Technology database with fundamental data reported were used to form Saha-Boltzmann plots. The Saha-Boltzmann plots were used to determine the plasma temperatures and electron densities of the laser-induced plasmas for both samples. These Saha-Boltzmann plots were then used to calculate previously unreported transition probabilities associated with identified peaks. Additionally, the transition probabilities presented in this paper provide the capability for calibration free LIBS to be performed more readily on europium samples and the spectroscopic analysis of stellar bodies. Eight previously unreported transition probabilities are presented in this paper; five for Eu I and three for Eu II. The transition probabilities for Eu I ranged from 0.172 to 7.38 × 10 7 s -1 and those for Eu II ranged from 1.56 to 6.75 × 10 7 s -1 .

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Estimation of sensor measurement errors in reactor coolant systems using multi-sensor fusion

A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Performance evaluation of cosmic ray muon trajectory estimation algorithms

Muons, being elementary particles with minimal interaction with nuclear materials and abundant at sea level, have sparked interest in utilizing them for imaging various applications, such as mining [Borselli et al., Sci. Rep. 12, 22329 (2022)], volcano imaging [Nagamine et al., Nucl. Instrum. Meth. A, 356, 585(1995)], and underground tunnel detection [Guardincerri et al., Pure Appl. Geophys. 174, 2133 (2017)]. Recently, their use in nuclear nonproliferation and safeguard verification has gained attention, particularly in cargo screening for nuclear waste smuggling [Baesso et al., J. Instrum. 9, C10041 (2014)], source localization [L. J. Schultz et al., Nucl. Instrum. Meth. A 519, 687 (2004)], and locating nuclear fuel debris in reactors [Borozdin et al., Phys. Rev. Let. 109, 152501 (2012)]. However, the resolution of muon image reconstruction techniques is limited due to multiple Coulomb scattering (MCS) within the target object. To achieve robust muon tomography, it is crucial to develop efficient and flexible physics-based algorithms that can model the MCS process accurately and estimate the most probable trajectory of muons as they pass through the target object. To address this limitation, in this study, a novel algorithmic approach utilizing the Bayesian probability theory and Gaussian approximation of MCS is chosen. Different energy levels, materials, and target sizes were considered in the evaluations. The results demonstrate that the Generalized Muon Trajectory Estimation (GMTE) algorithm offers significant improvements over currently used algorithms. Across all test scenarios, the GMTE algorithm demonstrated ~50% and 38% increase in precision compared to Straight Line Path (SLP) and Point of Closest Approach (PoCA) algorithms, respectively. Furthermore, it exhibited 10%–35% and 10%–15% increases in muon flux utilization for high and medium Z materials, respectively, compared to the PoCA algorithm. In conclusion, the extensive simulations confirm the enhanced performance and efficiency of the GMTE algorithm, offering improved resolution and reduced measurement time for cosmic ray muon imaging compared to the current SLP and PoCA algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Regional Characteristics of Observable Foreshocks

Abstract Measures of foreshock occurrence are systematically examined using earthquake catalogs for eight regions (Italy, southern California, northern California, Costa Rica, Onshore Japan, Alaska, Turkey, and Greece) after imposing a magnitude ≥3.0 completeness level. Foreshocks are identified using three approaches: a magnitude-dependent space + fixed-time windowing method, a nearest-neighbor clustering method, and a modified magnitude-dependent space + variable-time windowing method. The method with fixed-time windows systematically yields higher counts of foreshocks than the other two clustering methods. We find similar counts of foreshocks across the three methods when the magnitude aperture is equalized by including only earthquakes in the magnitude range M*−2≤ M< M*, in which M* is the mainshock magnitude. For most of the catalogs (excluding Italy and southern California), the measured b-values of the foreshocks of all region-specific mainshocks are lower by 0.1–0.2 than b-values of respective aftershocks. Allowing for variable-time windows results in relatively high probabilities of having at least one foreshock in Italy (∼43%–56%), compared to other regional catalogs. Foreshock probabilities decrease to 14%–41% for regions such as Turkey, Greece, and Costa Rica. Similar trends are found when requiring at least five foreshocks in a sequence to be considered. Estimates of foreshock probabilities for each mainshock are method dependent; however, consistent regional trends exist regardless of method, with regions such as Italy and southern California producing more observable foreshocks than Turkey and Greece. Some regions with relatively high background seismicity have comparatively low probabilities of detectable foreshock activity when using methods that account for variable background, possibly due to depletion of near-failure fault conditions by background activity.

Geochemistry & Geophysics↗
DOE OSTI2021

An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An ”extended” polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). Here, the sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach.

Aleatory uncertainty↗
DOE OSTI2023

Extending the predictive power of perturbative QCD using the principle of maximum conformality and the Bayesian analysis

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: R e+e– and R τ , which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗