Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation-maximization under non-Bayesian and Bayesian framework

inverse uncertainty;expectation-maximization;bayesian;maximum a posteriori;thermal hydraulics code parameters

Shrestha, Rijan Prasad

关键词: inverse uncertainty;    expectation-maximization;    bayesian;    maximum a posteriori;    thermal hydraulics code parameters;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/78728/SHRESTHA-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Uncertainty quantification of computer simulation response requires knowledge of input model parameter uncertainty. However, like most system codes, nuclear thermal-hydraulics code TRACE does not provide any information on statistical properties of input model parameters. Moreover, the input model parameters in TRACE code are built using correlations from experiments performed under steady-state low pressure low flow conditions. Hence, they might not be accurate for use in analyses of high pressure high flow transients in a reactor core. This further highlights the need for quantification of input model parameter uncertainty.A mathematical framework is developed where Expectation-Maximization (EM) algorithm is implemented to quantify input model parameter uncertainty using the Maximum Likelihood Estimate (MLE) and Maximum a Posteriori (MAP) estimate. The difference between experimental measurements and nominal code predictions, which are the observables, are considered scalar random variables. A dispersed normal prior is assumed on the mean and an inverse gamma prior is assumed on the variance of the observable to determine MAP estimate. A log-normal transformation is used to transform input model parameter probability distribution function to pseudo-parameter space. The theory is formulated such that the observables are expressed either as a linear or a quadratic combination of pseudo parameters for MLE. MAP estimate, on the other hand, uses a linear model. In addition, the pseudo parameters are assumed to be normally distributed. Experimental data is collected from reflooding facility that simulates post Loss of Coolant Accident (LOCA). Thermal-hydraulics system code TRACE is used for calibration purposes. Discussion of results obtained from the implementation of the developed methodology is presented. The comparisons show that calibrated code results obtained using MAP estimates show consistent improvement over those obtained from MLE. The mean and variance of the input parameters hence calculated can be used along with the underlying distribution to perform uncertainty quantification on output code responses. Moreover, MAP estimates of variance are consistently lower compared to MLE due to regularization in the form of prior knowledge, hence providing greater credibility to inverse estimation.