Berru-Sms Forward And Inverse Predictive Modeling Applied To A Spent Fuel Dissolver System
This Chapter presents the application of the BERRU-SMS methodology to perform forward and inverse predictive modeling of a paradigm dissolver model that is representative for material separations and international safeguards activities. This dissolver model comprises eight active compartments in which the time-dependent nonlinear differential equations modeling the physical and chemical processes comprise sixteen time-dependent spatially dependent state functions and 635 model parameters related to the model’s equation of state and inflow conditions. The most important response for the dissolver model is the computed nitric acid concentration in the compartment furthest away from the inlet, where measurements are available for comparisons. The sensitivities to all model parameters of the acid concentration at each of the instances in time when measurements were performed are computed exactly and efficiently using the adjoint sensitivity analysis method for nonlinear systems (ASAM). When using the traditional “ASAM for functional-type responses,” 307 adjoint computations are needed for computing exactly the sensitivities of the time-dependent nitric concentration response in compartment #1, at the measured time instances, to all model parameters. Alternatively, the “ASAM for operator-type responses” developed by Cacuci (1981b) reduces the number of required adjoint computations from 307 to 17, with an overall loss of accuracy of less than 0.05% over the entire time-span of 10.5 hours (307 time steps). Similarly significant reductions in the number of computations when using the “adjoint sensitivity analysis methodology for operator-type responses” were also obtained when computing the sensitivities of the time-dependent responses (nitric acid concentrations) in the other dissolver compartments, e.g., compartments #4 and #7. These sensitivities are subsequently used for uncertainty analysis and predictive modeling, combining the computational results with experiments performed solely in the compartment furthest from the inlet. The application of the BERRU-SMS predictive modeling methodology yields optimally calibrated values for all 635 model parameters, with reduced predicted uncertainties, as well as optimal (“best-estimate”) predicted values for the acid concentrations, also with reduced predicted uncertainties. Notably, even though the experimental data pertains solely to the compartment furthest from the inlet (where the data was measured), the predictive modeling methodology actually improves the predictions and reduces the predicted uncertainties not only in the compartment in which the data was actually measured, but throughout the entire dissolver, including the compartment furthest from the measurements (i.e., at the inlet). This is because the predictive modeling methodology combines and transmits information simultaneously over the entire phase-space, comprising all time steps and spatial locations.
This Chapter also presents an application of the BERRU-SMS predictive modeling methodology 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 the dissolver model by using measurements of the state function (specifically: the time-dependent acid concentration) at a specified location (specifically: in the dissolver’s compartment furthest from the inlet). The unknown time-dependent boundary condition is described by 635 unknown discrete scalar parameters. In general, the maximum entropy principle which underlies the BERRU-SMS predictive modeling methodology enables the construction of an intrinsic regularizing metric for solving any inverse problem. Specifically for the dissolver model, the unknown time-dependent boundary condition is predicted by the BERRU-SMS methodology within an a priori selected convergence criterion, without user intervention and/or introduction of arbitrary “regularization parameters.”
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