Optimization of Thermal-Hydraulic Reactor System for SMRs via Data Assimilation and Uncertainty Quantification

This paper discusses the utilization of an uncertainty quantification methodology for nuclear power plant thermal-hydraulic transient predictions, with a focus on small modular reactors characterized by the integral pressurized water reactor design, to determine the value of completing experiments in reducing uncertainty. To accomplish this via the improvement of the prediction of key system attributes, e.g., minimum departure from nucleate boiling ratio, a thermal-hydraulic simulator is used to complete data assimilation for input parameters to the simulator employing experimental data generated by the virtual reactor. The mathematical approach that is used to complete this analysis depends upon whether the system responses, i.e., sensor signals, and the system attributes are or are not linearly dependent upon the parameters. For a transient producing mildly nonlinear response sensitivities, a Bayesian-type approach was used to obtain the a posteriori distributions of the parameters assuming Gaussian distributions for the input parameters and responses. For a transient producing highly nonlinear response sensitivities, the Markov chain Monte Carlo method was utilized based upon Bayes' theorem to estimate the a posteriori distributions of the parameters. To evaluate the value of completing experiments, an optimization problem was formulated and solved. The optimization addressed both the experiments to complete and the modifications to be made to the nuclear power plant made possible by using the increased margins resulting from data assimilation. The decision variables of the experiment optimization problem include the selection of sensor types and locations and experiment type imposing realistic constraints. The decision variables of the nuclear power plant modification optimization problem include various design specifications, e.g., power rating, steam generator size, and reactor coolant pump size, with the objective of minimizing cost as constrained by required margins to accommodate the uncertainty. Since the magnitude of the uncertainty is dependent upon the experiments via data assimilation, the nuclear power plant optimization problem is treated as a suboptimization problem within the experiment optimization problem. The experiment optimization problem objective is to maximize the net savings, defined as the savings in nuclear power plant cost due to the modified design specifications minus the cost of the experiments. Both the experiment and the nuclear power plant optimization problems were solved using the simulated annealing method.