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University of Illinois – Urbana-Champaign

1. Wu, Xu. Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework.

Degree: PhD, Nuclear, Plasma, Radiolgc Engr, 2017, University of Illinois – Urbana-Champaign

Mathematical modeling and computer simulations have long been the central technical topics in practically all branches of science and technology. Tremendous progress has been achieved in revealing quantitative connections between numerical predictions and real-world observations. However, because computer models are reduced representations of the real phenomena, there are always discrepancies between ideal in silico designed systems and real-world manufactured ones. As a consequence, uncertainties must be quantified along with the simulation outputs to facilitate optimal design and decision making, ensure robustness, performance or safety margins. Forward uncertainty propagation requires knowledge in the statistical information for computer model random inputs, for example, the mean, variance, Probability Density Functions (PDFs), upper and lower bounds, etc. Historically, ``expert judgment'' or ``user self-evaluation'' have been used to specify the uncertainty information associated with random input parameters. Such ad hoc characterization is unscientific and lacks mathematical rigor. In this thesis, we attempt to solve such ``lack of uncertainty information'' issue with inverse Uncertainty Quantification (UQ). Inverse UQ is the process to seek statistical descriptions of the random input parameters that are consistent with available high-quality experimental data. We formulate the inverse UQ process under the Bayesian framework using the ``model updating equation''. Markov Chain Monte Carlo (MCMC) sampling is applied to explore the posterior distributions and generate samples from which we can extract statistical information for the uncertain input parameters. To greatly alleviate the computational burden during MCMC sampling, we used systematically and rigorously developed metamodels based on stochastic spectral techniques and Gaussian Processes (also known as Kriging) emulators. We demonstrated the developed methodology based on three problems with different levels of sophistication: (1) Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model based on synthetic experimental data; (2) best-estimate system thermal-hydraulics code TRACE physical model parameters based on OECD/NRC BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data; (3) fuel performance code BISON Fission Gas Release (FGR) model based on Risø-AN3 on-line time-dependent FGR measurement data. Metamodels constructed with generalized Polynomial Chaos Expansion (PCE), Sparse Gird Stochastic Collocation (SGSC) and GP were applied respectively for these three problems to replace the full models during MCMC sampling. We proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain. The improved approach is organized in a structure such that the posteriors achieved with data in inverse UQ domain is informed by data in the validation domain. Therefore,… Advisors/Committee Members: Kozlowski, Tomasz (advisor), Kozlowski, Tomasz (Committee Chair), Meidani, Hadi (committee member), Uddin, Rizwan (committee member), Stubbins, James F (committee member).

Subjects/Keywords: Inverse Uncertainty Quantification; Bayesian Calibration; Bayesian Analysis; Model Discrepancy; Modular Bayesian Approach; Metamodel; Surrogate Model; Gaussian Process; Polynomial Chaos Expansion; Sparse Grid Stochastic Collocation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Wu, X. (2017). Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/99335

Chicago Manual of Style (16th Edition):

Wu, Xu. “Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 25, 2020. http://hdl.handle.net/2142/99335.

MLA Handbook (7th Edition):

Wu, Xu. “Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework.” 2017. Web. 25 Jan 2020.

Vancouver:

Wu X. Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jan 25]. Available from: http://hdl.handle.net/2142/99335.

Council of Science Editors:

Wu X. Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/99335

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