PreprintReviewVersion 1Preserved in Portico This version is not peer-reviewed
Review of Fourth-Order Maximum Entropy Based Predictive Modelling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis
Version 1
: Received: 25 March 2024 / Approved: 25 March 2024 / Online: 25 March 2024 (13:31:57 CET)
How to cite:
Cacuci, D.G.; Fang, R. Review of Fourth-Order Maximum Entropy Based Predictive Modelling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis. Preprints2024, 2024031485. https://doi.org/10.20944/preprints202403.1485.v1
Cacuci, D.G.; Fang, R. Review of Fourth-Order Maximum Entropy Based Predictive Modelling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis. Preprints 2024, 2024031485. https://doi.org/10.20944/preprints202403.1485.v1
Cacuci, D.G.; Fang, R. Review of Fourth-Order Maximum Entropy Based Predictive Modelling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis. Preprints2024, 2024031485. https://doi.org/10.20944/preprints202403.1485.v1
APA Style
Cacuci, D.G., & Fang, R. (2024). Review of Fourth-Order Maximum Entropy Based Predictive Modelling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis. Preprints. https://doi.org/10.20944/preprints202403.1485.v1
Chicago/Turabian Style
Cacuci, D.G. and Ruixian Fang. 2024 "Review of Fourth-Order Maximum Entropy Based Predictive Modelling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis" Preprints. https://doi.org/10.20944/preprints202403.1485.v1
Abstract
This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.
Keywords
predictive modeling; sensitivity analysis; uncertainty quantification; data assimilation; model calibration; reducing predicted uncertainties
Subject
Physical Sciences, Applied Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
