Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework

Abstract

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, over-fitting can be avoided while extrapolation is not required. A sequential approach was also developed for test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first select tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it select tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that inverse UQ can extract the most information for posteriors of calibration parameters using only a relatively small number of tests. The inverse UQ process successfully quantified the uncertainties associated with input parameters that are consistent with the experimental observations. The quantified uncertainties are necessary for future uncertainty and sensitivity study of nuclear reactor simulators in system design and safety analysis. We applied and extended several advanced metamodeling approaches to nuclear engineering practice to greatly reduce the computational cost. The current research bridges the gap between models and data by solving ``lack of uncertainty information'' issue, as well as providing guidance for improving nuclear reactor simulators through the validation process.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 6 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.