Analysis of correlations and their impact on convergence rates in Monte Carlo eigenvalue simulations

Abstract

This paper provides an analysis of the generation-to-generation correlations as observed when solving full core eigenvalue problems on PWR systems. Many studies have in the past looked at the impact of these correlations on reported variance and this paper extends the analysis to the observed convergence rate on the tallies, the effect of tally size and the effect of generation size. Since performing meaningful analysis on such a large problem is inherently difficult, a simple homogeneous reflective cube problem with analytical solution was developed that exhibits similar behavior to the full core PWR benchmark. The data in this problem was selected to match the dimensionality of the reactor problem and preserve the migration length traveled by neutrons. Results demonstrate that the variance will deviate significantly from the 1/N (N being the number of simulated particles) convergence rate associated with truly independent generations, but will eventually asymptote to 1/N after 1000's of generations regardless of the numbers of neutrons per generation. This indicates that optimal run strategies should emphasize lower number of active generations with greater number of neutrons per generation to produce the most accurate tally results. This paper also describes and compares three techniques to evaluate suitable confidence intervals in the presence of correlations, one based on using history statistics, one using generation statistics and one batching generations to reduce batch-to-batch correlation.

Predicting correlation coefficients for Monte Carlo eigenvalue simulations with multitype branching process

“…Following the above procedure, evolving the constructed MBP model for k generations gives ACC of generation lag k and thus correction for variance estimator after k active generations. In order to predict termination of Monte Carlo simulation to a given user determined variance criterion, very long calculation of MBP is required to evaluate ACC's up to arbitrary generation lag k. Alternatively, the method of fitting ACC to a sum of exponentially decaying terms can be applied on the ACC's found from MBP instead of the noisy estimated value as in [4]. With data fitting, the MBP model can be evolved for a fixed number of generations and the fit can be used to predict ACC and variance underestimation to any arbitrary number of generations.…”

“…Uncertainty of any tallied quantity is commonly represented by taking the sample variance over the active generations, which is based on the assumption that the neutron generations are independent. Correlation effects between neutrons in multiplying systems, particularly when performing power iteration to evaluate eigenvalues have been observed and quantified in previous work [1] [2] [3] [4]. Neglecting this correlation effect results in an underestimate of uncertainty reported by Monte Carlo calculations, the magnitude of which depends on the dominance ratio of the problem and the size of the phase space being tallied [5].…”

“…Neglecting this correlation effect results in an underestimate of uncertainty reported by Monte Carlo calculations, the magnitude of which depends on the dominance ratio of the problem and the size of the phase space being tallied [5]. Many studies have quantified this underestimation using post-processing techniques of the tallied quantities or by de-correlating batches using many generations per batch, both of which can become costly in either memory or runtime [4] [6].…”

Monte Carlo power iteration: Entropy and spatial correlations

“…In order to assess the behaviour of the entropy function in the presence of fission-induced correlations, we will work out 110 an example that is simple enough for exact results to be analytically derived and compared to the Monte Carlo simulations, and yet retains the key physical features of a real system (Miao et al, 2016).…”

Generalized equivalence methods for 3D multi-group neutron transport

“…Treatment of resolved resonance effects is implicit in continuous-energy Monte Carlo methods that represent resonances with hundreds of thousands of energy points. Unfortunately, full-core, steady state reactor calculations with Monte Carlo require tens of billions of neutron histories [13] to converge local fluxes and pin power distributions for cores that have near-unity dominance ratios, which is common in commercial light water reactors (LWRs). In addition, Monte Carlo methods are not easily extendable to transient reactor safety analysis where transients must be followed for 100s or 1000s of seconds.…”