Uncertainty analysis of multilayer feedforward networks using generalized adjoint and model adjustment theories for nuclear reactor physics applications

Sensitivity and uncertainty analyses are leading characteristics of any system performance assessment. The role of sensitivity analysis is to provide a quantitative measure of the effect of system parameters upon key performance indices. It also limits the scope of uncertainty analysis by providing a ranking of the uncertain parameters with respect to their contribution to system output uncertainty. Uncertainty analysis provides a quantitative measure of the combined impact of parameter uncertainties on the output responses of a system. It also supports reliability studies, insures compliance with regulatory criteria, and helps identify important research and development needs. A study of uncertainty analysis, based on sensitivity methodology, of multilayer feedforward neural networks using generalized adjoint and model adjustment theories is presented. Nuclear reactor physics and mathematical model applications for data field sets were evaluated in this study. These model applications include Reactor Noise Analysis (RNA) model, nuclear in-core fuel management, and Positron Emission Tomography (PET) model. The Oak Ridge National Laboratory (ORNL) large-scale sensitivity code system "GRESS," which incorporates the adjoint theory methodology, has been used in this research to study the effects of given input and weight vector parameters on the responses of interest, and to report model sensitivity functions required for uncertainty analysis. A general adjustment algorithm of multilayer feedforward networks using a model adjustment methodology was developed. Uncertainty and data adjustment analyses associated with model output predictions of neural networks relative to input data field and model parameter covariances were reported. It was concluded that the uncertainty analysis as well as the use of data adjustment method for improving the response uncertainties have shown a considerable amount of improvement in the calculation of uncertainties of adjusted responses of interest. Hence, the adjustment algorithm can be a useful tool for improving the learning rate of multilayer feedforward networks.