Nuclear thermal-hydraulics applications illustrating the key roles of adjoint-computed sensitivities for overcoming the curse of dimensionality in sensitivity analysis, uncertainty quantification and predictive modeling

摘要

This work is dedicated to the memory of Prof. Bal Raj Sehgal who, while a Program Manager at the Electric Power Institute (EPRI) in Palo Alto, USA, had foresightedly funded during 1979-1984 the author's pioneering work on conceiving the adjoint sensitivity analysis methodology for computing first-order sensitivities of responses of nonlinear systems to imprecisely known system parameters, and applying this methodology to a variety of ground-breaking investigations in nuclear reactor physics, thermal-hydraulics, dynamics, and safety. In the spirit of this dedication, the present original work highlights the application of the first-order adjoint sensitivity analysis methodology (1st-ASAM) to the generic thermal-hydraulics model that underlies the well-known reactor analysis codes COBRA/TRAC, RELAP5/MOD3.2, RELAP5/MOD3.3, and MARS, thus deriving the corresponding adjoint sensitivity model needed for the exact and most efficient computation of model response sensitivities to thermal-hydraulics parameters. This work also presents the fundamental role of the 1st-ASAM as the first step in the quest to overcome the curse of dimensionality in sensitivity analysis, uncertainty quantification and predictive modelling by presenting the concepts of a novel predictive modeling methodology that uses the maximum entropy principle in conjunction with saddle-point techniques to eliminate the widespread current use of arbitrarily defined "functionals to be minimized," thus significantly extending the currently used data assimilations procedures. Since this novel predictive modeling methodology provides best-estimate results with reduced uncertainties for either forward or inverse problems, it has been called the BERRU-PM methodology. This work also indicates the next steps, starting with the complete second-order predictive modeling methodology, currently undertaken by the author in the quest to develop practical high-order procedures that overcome in practice the "curse of dimensionality" in sensitivity analysis, uncertainty quantification, and predictive modelling, thereby enabling the future computation of non-Gaussian features of otherwise intractable distributions of results predicted by large-scale computational model, while using experimental information to reduce the uncertainties in the predicted results and implicitly calibrated model parameters.