Introducing the n^th-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n^th-FASAM-N): II. Illustrative Example

This work highlights the unparalleled efficiency of the “n^th-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n^th-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The n^th-FASAM-N methodology is compared to the extant “n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n^th-CASAM-N) showing that: (i) the 1^st-FASAM-N and the 1^st-CASAM-N methodologies are equally efficient for computing the first-order sensitivities; each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1^st-LASS); (ii) the 2^nd-FASAM-N methodology is considerably more efficient than the 2^nd-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;