Stationarity Diagnostics with Relative Entropy and Wilcoxon Signed Rank in Iterated-Source Monte Carlo Methods

The stationarity diagnostics of source distribution in the iterated-source Monte Carlo computation for nuclear criticality and static nuclear reactor analysis have been studied using relative entropy and the Wilcoxon signed rank sum. Novel aspects of the diagnostics are (a) the relative entropy of permuted and nonpermuted source distributions and (b) a series of differenced relative entropies. Item (a) combined with averaging over random permutations has some smoothing effect on the fluctuation through iteration cycles. The benefit of item (b) is twofold: The differencing works as decorrelation, and the mean in stationarity of a differenced series is exactly zero. Therefore, the Wilcoxon signed rank sum has been applied to check the stationarity of the differenced relative entropy series. Another novel aspect of the diagnostics is the use of a problem-independent number of iteration cycles preceding the current iteration cycle upon the computation of the Wilcoxon signed rank sum. In addition, it has been shown that the progressive relative entropy in previous work can be used and the moving average of the Wilcoxon signed rank sums of its differenced series is a stringent measure of stationarity. Numerical results are presented for two- and three-dimensional modeling of an initial core of pressurized water reactors.