Improved generalized perturbation theory method for sensitivity analysis of generalized response function

Abstract

Sensitivity and uncertainty analyses of generalized response functions are essential for nuclear designs because they provide useful information about how changes in the input parameters influence the neutronics response. Several methods have been developed to compute generalized sensitivity coefficients for nuclear data. One method is the GEneralized Adjoint Responses in Monte Carlo (GEAR-MC) method which can be used to analyze the sensitivity coefficients of reaction rate ratios. However, this method requires the generalized adjoint function to estimate the sensitivity coefficients. The generalized adjoint function can be calculated using a method like the iterated fission probability (IFP) method which has a huge memory requirement. In this paper, the superhistory-based GEAR-MC method is developed to reduce the huge memory requirement induced by calculating the generalized adjoint function. This newly developed superhistory-based GEAR-MC method is found to be accurately predict the sensitivities of the reaction rate ratios for the Godiva, Flattop and the UAM TMI PWR pin cell benchmark problems. The calculations also show that the memory usage of the superhistory-based GEAR-MC method is 98% less than for the traditional power iteration-based GEAR-MC method. In addition, it is shown that the superhistory-based GEAR-MC method will increase the runtime and this increase is not totally linearly proportional to the number of inner generations in each superhistory for all test cases. Moreover, the equivalence of GEAR-MC method and first-order differential operator method are also proved in this paper.