Nuclear Science and Engineering / Volume 184 / Number 1 / September 2016 / Pages 1-15
Technical Paper / dx.doi.org/10.13182/NSE16-50
This work presents an application of the forward and inverse predictive modeling methodology of Cacuci and Ionescu-Bujor (2010) in the inverse mode to determine, within a tight a priori specified convergence criterion and overall accuracy, an unknown time-dependent boundary condition (specifically, the time-dependent inlet acid concentration) for a dissolver model case study by using measurements of the state function (specifically, the time-dependent acid concentration) at a specified location (specifically, in the dissolver’s compartment farthest from the inlet). The unknown time-dependent boundary condition is described by 635 unknown discrete scalar parameters. This forward and inverse predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution by using the a priori known mean values and uncertainties characterizing the model parameters, along with the computed and experimentally measured model responses and their covariances. This a priori distribution is subsequently combined using Bayes’ theorem with the likelihood provided by the computational model. The first-order response sensitivities serve as weighting functions in this objective combination of computational and experimental information.
The use of the maximum entropy principle enables the forward and inverse predictive modeling of Cacuci and Ionescu-Bujor (2010) to construct an intrinsic regularizing metric for solving any inverse problem. In the present dissolver case study, the unknown time-dependent boundary condition is predicted by the methodology within an a priori selected convergence criterion, without user intervention and/or introduction of arbitrary regularization parameters, as the currently popular procedures need to do. This predictive modeling methodology yields optimally calibrated values for all model parameters, with reduced predicted uncertainties, as well as optimal (best-estimate) predicted values for the model responses (in this case study, the time-dependent acid concentrations in the dissolver’s compartments), also with reduced predicted uncertainties. Notably, even though the experimental data pertain solely to the compartment farthest from the inlet (where the data were measured), the application of this predictive modeling methodology actually improves the predicted values and reduces their predicted uncertainties not only in the compartment in which the data were actually measured but also throughout the entire dissolver, including the compartment farthest from the measurements (i.e., at the inlet). This is because this forward and inverse predictive modeling methodology combines and transmits information simultaneously over the entire phase-space, comprising all time steps and spatial locations.
These results underscore the importance of this work in presenting the objective resolution (i.e., resolution in the absence of user-defined subjective adjustment of arbitrary regularization parameters) of a time-dependent inverse case study of potential importance to diversion activities associated with proliferation and international safeguards. The results obtained in this work establish confidence in the dissolver model’s accuracy for simulating the acid concentrations required to dissolve used nuclear fuel. In turn, these results will be used to generate source terms for key reprocessing facility components downstream and to support material accountability for nuclear safeguards.