Demonstrating predictive confidence for a paradigm dissolver model using methods for evaluating higher order moments. A ''case study'' for nuclear nonproliferation

Through an exhaustive process of verification, validation and uncertainty quantification, this dissertation performs sensitivity analysis, uncertainty quantification up to 3^rd-order (including covariance and skewness), and forward and inverse predictive modeling for a dissolver model of interest to nonproliferation activities regarding aqueous reprocessing of spent nuclear fuel. This dissolver model comprises sixteen nonlinear differential equations, which include 1291 model parameters characterizing the underlying physical and chemical processes. The original results presented in this dissertation highlight the effects of uncertainties which necessarily characterize measurements and computations, and the reduction in the predicted uncertainties by combining optimally the experimental and computational information. The uncertainties in the dissolver model parameters are propagated to compute uncertainties in the model responses by using first-order sensitivities (i.e., functional derivatives) of the respective responses to the model parameters. The first-order sensitivities to all model parameters of the time-dependent acid concentrations are computed by applying the adjoint sensitivity analysis method for nonlinear systems with function-valued responses originally conceived by Cacuci (1981a). Furthermore, this work also develops a reduced-order surrogate dissolver model, and extends Cacuci's original adjoint technique to enable the computation of second-order sensitivities. As shown in this work, the second-order sensitivities are essential for computing the skewness (i.e., third-order moment) of the response distribution, highlighting the latter's asymmetrical (non-Gaussian) features. The response sensitivities also serve as the weighting functions for combining experimental and computational information for the dissolver model using the comprehensive predictive modeling methodology originally developed by Cacuci and Ionescu-Bujor (2010b). The only experimental information available in the open literature for this dissolver model are the measurements performed by Lewis and Weber (1980) of the nitric acid in the compartment furthest away from the inlet. Using this experimental information with the forward and inverse predictive modeling formalism is shown to yield optimal predictions throughout the entire dissolver, reducing everywhere the uncertainties in these predicted results. This stems from the fact that the predictive modeling methodology combines and transmits information simultaneously over the entire phase-space, comprising all time steps and spatial locations. Another remarkable original result obtained in this dissertation is the innovative use of the predictive modeling framework of Cacuci and Ionescu-Bujor (2010b) in an inverse prediction mode for inferring unknown model parameters (specifically: the time-dependent inlet boundary condition) from measurements of the acid concentration in the compartment furthest from the inlet. This is particularly useful in applications where inferences on a target of interest can only be made from indirect measurements. In summary, this dissertation presents an efficient mathematical model for a dissolver of spent nuclear fuel of interest to international nuclear safeguards and nonproliferation, and demonstrates the procedure for rigorous uncertainty quantification and validation of this model. The dissertation also introduces an innovative adjoint procedure for computing second-order response sensitivities to model parameters, and highlights the latter's essential role for computing non-Gaussian features of the distributions of model responses of interest. The methodology demonstrated in this dissertation will serve as a role model for rigorous forward and inverse predictive modeling of other nuclear facilities of interest to international nuclear safeguards and nonproliferation, aiming at optimizing predictions for ''signatures'' and ''causes'' of interest while reducing drastically the accompanying uncertainties, thus enabling more accurate risk-informed decision processes.