Uncertainty evaluation of delayed neutron decay parameters

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Title: Uncertainty evaluation of delayed neutron decay parameters
Author: Wang, Jinkai
Abstract: 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 .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -3210
Date: 2009-05-15

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Uncertainty evaluation of delayed neutron decay parameters. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -3210 .

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