Uncertainty evaluation of delayed neutron decay parameters
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In a nuclear reactor, delayed neutrons play a critical role in sustaining a controllable chain reaction. Delayed neutron’s relative yields and decay constants are very important for modeling reactivity control and have been studied for decades. Researchers have tried different experimental and numerical methods to assess these delayed neutron parameters. The reported parameter values vary widely, much more than the small statistical errors reported with these parameters. Interestingly, the reported parameters fit their individual measurement data well in spite of these differences. This dissertation focuses on evaluation of the errors and methods of delayed neutron relative yields and decay constants for thermal fission of U-235. Various numerical methods used to extract the delayed neutron parameter from the measured data, including Matrix Inverse, Levenberg-Marquardt, and Quasi-Newton methods, were studied extensively using simulated delayed neutron data. This simulated data was Poisson distributed around Keepin’s theoretical data. The extraction methods produced totally different results for the same data set, and some of the above numerical methods could not even find solutions for some data sets. Further investigation found that ill-conditioned matrices in the objective function were the reason for the inconsistent results. To find a reasonable solution with small variation, a regularization parameter was introduced using a numerical method called Ridge Regression. The results from the Ridge Regression method, in terms of goodness of fit to the data, were good and often better than the other methods. Due to the introduction of a regularization number in the algorithm, the fitted result contains a small additional bias, but this method can guarantee convergence no matter how large the coefficient matrix condition number. Both saturation and pulse modes were simulated to focus on different groups. Some of the factors that affect the solution stability were investigated including initial count rate, sample flight time, initial guess values. Finally, because comparing reported delayed neutron parameters among different experiments is useless to determine if their data actually differs, methods are proposed that can be used to compare the delayed neutron data sets.
Wang, Jinkai (2008). Uncertainty evaluation of delayed neutron decay parameters. Doctoral dissertation, Texas A&M University. Available electronically from