Generation of SFR few-group constants using the Monte Carlo code serpent

In this study, the Serpent Monte Carlo code was used as a tool for preparation of homogenized few-group cross sections for the nodal diffusion analysis of Sodium cooled Fast Reactor (SFR) cores. Few-group constants for two reference SFR cores were generated by Serpent and then employed by nodal diffusion code DYN3D in 2D full core calculations. The DYN3D results were verified against the references full core Serpent Monte Carlo solutions. A good agreement between the reference Monte Carlo and nodal diffusion results was observed demonstrating the feasibility of using Serpent for generation of few-group constants for the deterministic SFR analysis.

Coupled neutronic thermo-hydraulic analysis of full PWR core with Monte-Carlo based BGCore system

BGCore reactor analysis system was recently developed at Ben-Gurion University for calculating in-core fuel composition and spent fuel emissions following discharge. It couples the Monte Carlo transport code MCNP with an independently developed burnup and decay module SARAF. Most of the existing MCNP based depletion codes (e.g. MOCUP, Monteburns, MCODE) tally directly the one-group fluxes and reaction rates in order to prepare one-group cross sections necessary for the fuel depletion analysis. BGCore, on the other hand, uses a multi-group (MG) approach for generation of one group cross-sections. This coupling approach significantly reduces the code execution time without compromising the accuracy of the results. Substantial reduction in the BGCore code execution time allows consideration of problems with much higher degree of complexity, such as introduction of thermal hydraulic (TH) feedback into the calculation scheme. Recently, a simplified TH feedback module, THERMO, was developed and integrated into the BGCore system. To demonstrate the capabilities of the upgraded BGCore system, a coupled neutronic TH analysis of a full PWR core was performed. The BGCore results were compared with those of the state of the art 3D deterministic nodal diffusion code DYN3D (Grundmann et al.; 2000). Very good agreement in major core operational parameters including k-eff eigenvalue, axial and radial power profiles, and temperature distributions between the BGCore and DYN3D results was observed. This agreement confirms the consistency of the implementation of the TH feedback module. Although the upgraded BGCore system is capable of performing both, depletion and TH analyses, the calculations in this study were performed for the beginning of cycle state with pre-generated fuel compositions. © 2011 Published by Elsevier B.V.

Efficient generation of one-group cross sections for coupled Monte Carlo depletion calculations

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main drawback of Monte Carlo-based systems is a long calculation time imposing significant restrictions on the complexity and amount of design-oriented calculations. This paper presents an alternative approach to interfacing the Monte Carlo and depletion modules aimed at addressing this problem. The main idea is to calculate the one-group cross sections for all relevant isotopes required by the depletion module in a separate module external to Monte Carlo calculations. Thus, the Monte Carlo module will produce the criticality and neutron spectrum only, without tallying of the individual isotope reaction rates. The onegroup cross section for all isotopes will be generated in a separate module by collapsing a universal multigroup (MG) cross-section library using the Monte Carlo calculated flux. Here, the term "universal" means that a single MG cross-section set will be applicable for all reactor systems and is independent of reactor characteristics such as a neutron spectrum; fuel composition; and fuel cell, assembly, and core geometries. This approach was originally proposed by Haeck et al. and implemented in the ALEPH code. Implementation of the proposed approach to Monte Carlo burnup interfacing was carried out through the BGCORE system. One-group cross sections generated by the BGCORE system were compared with those tallied directly by the MCNP code. Analysis of this comparison was carried out and led to the conclusion that in order to achieve the accuracy required for a reliable core and fuel cycle analysis, accounting for the background cross section (σ0) in the unresolved resonance energy region is essential. An extension of the one-group cross-section generation model was implemented and tested by tabulating and interpolating by a simplified σ0 model. A significant improvement of the one-group cross-section accuracy was demonstrated.

Monitoring and preventing numerical oscillations in 3D simulations with coupled Monte Carlo codes

Previous studies have reported that different schemes for coupling Monte Carlo (MC) neutron transport with burnup and thermal hydraulic feedbacks may potentially be numerically unstable. This issue can be resolved by application of implicit methods, such as the stochastic implicit mid-point (SIMP) methods. In order to assure numerical stability, the new methods do require additional computational effort. The instability issue however, is problem-dependent and does not necessarily occur in all cases. Therefore, blind application of the unconditionally stable coupling schemes, and thus incurring extra computational costs, may not always be necessary. In this paper, we attempt to develop an intelligent diagnostic mechanism, which will monitor numerical stability of the calculations and, if necessary, switch from simple and fast coupling scheme to more computationally expensive but unconditionally stable one. To illustrate this diagnostic mechanism, we performed a coupled burnup and TH analysis of a single BWR fuel assembly. The results indicate that the developed algorithm can be easily implemented in any MC based code for monitoring of numerical instabilities. The proposed monitoring method has negligible impact on the calculation time even for realistic 3D multi-region full core calculations. © 2014 Elsevier Ltd. All rights reserved.

Monte Carlo filtering and smoothing with application to time-varying spectral estimation

We develop methods for performing filtering and smoothing in non-linear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

Bayesian model selection for time series using Markov chain Monte Carlo

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

An overview of sequential Monte Carlo methods for parameter estimation in general state-space models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, are numerical techniques based on Importance Sampling for solving the optimal state estimation problem. The task of calibrating the state-space model is an important problem frequently faced by practitioners and the observed data may be used to estimate the parameters of the model. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed for this task accompanied with a discussion of their advantages and limitations.