GPT-Free Sensitivity Analysis for Monte Carlo Models

This paper extends the applicability of the generalized perturbation theory (GPT)–free methodology, earlier developed for deterministic models, to Monte Carlo stochastic models. The objective of the GPT-free method is to calculate nuclear data sensitivity coefficients for generalized responses without solving the GPT response-specific inhomogeneous adjoint eigenvalue problem. The GPT-free methodology requires the capability to generate the eigenvalue sensitivity coefficients. This capability is readily available in several of the state-of-the-art Monte Carlo codes. The eigenvalue sensitivity coefficients are sampled using a statistical approach to construct a subspace of small dimension that is subsequently sampled for sensitivity information using a forward sensitivity analysis. A boiling water reactor assembly model is developed using the Oak Ridge National Laboratory Monte Carlo code KENO to demonstrate the application of the GPT-free methodology in Monte Carlo models. The response variations estimated by the GPT-free agree with the exact variations calculated by direct forward perturbations. The GPT-free method is also implemented in OpenMC and tested with the Godiva model to show its capability and feasibility in the estimation of the energy-dependent sensitivity coefficients for generalized responses in Monte Carlo models. The sensitivity results are compared against the ones acquired by the standard GPT-based methodologies. A higher order of accuracy in the sensitivity estimation is observed in the GPT-free method.