Sensitivity and uncertainty analysis of the fractional neutron point kinetics equations

The aim of the present work is to evaluate the sensitivity and uncertainty of the anomalous diffusion coefficient in the Fractional Neutron Point Kinetics (FNPK) equations. This analysis was carried out through Monte Carlo simulations of sizes up to 65,000; the size of 50,000 was considered as valid for routine applications. The sensitivity was evaluated in terms of 99% confidence intervals of the mean to understand the range of mean values that may represent the entire statistical population of performance variables. The regression analysis with anomalous diffusion coefficient as the predictor variable showed statistically valid quadratic relationship for neutronic density and the delayed neutron precursor concentration. The uncertainties were propagated as follows: in a 1% change in the anomalous diffusion exponent the responses for neutron density, and precursor density changed by 0.017% and 0.0000125% for short times, and for long times by 0.012% and 0.000267%, respectively.

► An evaluation of the sensitivity and uncertainty in the FNPK equations is performed.
► The analysis was carried out to the ADC through Monte Carlo simulations.
► The sensitivity was evaluated in terms of 99% confidence intervals.
► The regression analysis shows a statistically valid quadratic relationship.
► The uncertainties were propagated by less than 1% in general terms.