Time Series Analysis of Monte Carlo Fission Sources—I: Dominance Ratio Computation

Ueki, Taro; Brown, Forrest B.; Parsons, Donald Kent; Warsa, James S.

doi:10.13182/nse03-95

Cited by 27 publications

(35 citation statements)

References 11 publications

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“…4,6,11,12) Each of these works has its own formalism; however, all of them arrived at the formula below: e e ðmþ1Þ ¼ A 0ẽ e ðmÞ þ" " ðmþ1Þ ;…”

Section: Noise Propagation and Autoregressive Moving Average Reprmentioning

confidence: 99%

“…(3), (5), and (6). This work was rediscovered and successfully applied to dominance ratio computation 4) and the confidence interval estimation of keffective eigenvalue. 9) These works are reviewed with a new interpretation of the observation matrix associated with Eq.…”

Section: Noise Propagation and Autoregressive Moving Average Reprmentioning

confidence: 99%

“…This theoretically justifies the application of ARMA(p,p À 1) fitting to nearly all linear tallies of interest in MC reactor core calculation because ARMA(p,p À 1) representation was previously derived for the fluctuation of fission source distribution of collision estimator type and its linear response. 4) The argument based on the eigenmodes of fluctuation and the solution form of linear difference equation for lag autocovariances dictate that ARMA(3,2) fitting is generally the lowest order fitting that must be taken into account. Numerical results from the continuous energy calculation of a three-dimensional PWR whole core model with top and bottom structures 3) show that ARMA(3,2) fitting is promising; the real standard deviation ( R ) estimation by ARMA(3,2) fitting yielded 78-100% of the reference value of R at tally cells where the sample standard deviation formula for uncorrelated data yielded 21-38% of R .…”

Section: Conclusion and Future Research Directionmentioning

confidence: 99%

“…3) For theoretical justification, ARMA representation was examined and formally shown to be valid for track length tallies as was previously derived for the fission source fluctuation of a collision estimator type. 4) In MC calculation for nuclear criticality and reactor core, there are two actively investigated approaches to the estimation of real standard deviation. The first approach is the direct computation of covariances along with the use of associated formulae among them.…”

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confidence: 99%

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Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

Ueki

2010

Journal of Nuclear Science and Technology

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Time series methodology has been studied to assess the feasibility of statistical error estimation in the continuous space and energy Monte Carlo calculation of the three-dimensional whole reactor core. The noise propagation was examined and the fluctuation of track length tallies for local fission rate and power has been formally shown to be represented by the autoregressive moving average process of orders p and, where p is an integer larger than or equal to two. Therefore, ARMA(p,p À 1) fitting was applied to the real standard deviation estimation of the power of fuel assemblies at particular heights. Numerical results indicate that straightforward ARMA(3,2) fitting is promising, but a stability issue must be resolved toward the incorporation in the distributed version of production Monte Carlo codes. The same numerical results reveal that the average performance of ARMA(3,2) fitting is equivalent to that of the batch method with a batch size larger than 100 and smaller than 200 cycles for a 1,100 MWe pressurized water reactor.

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“…4,6,11,12) Each of these works has its own formalism; however, all of them arrived at the formula below: e e ðmþ1Þ ¼ A 0ẽ e ðmÞ þ" " ðmþ1Þ ;…”

Section: Noise Propagation and Autoregressive Moving Average Reprmentioning

confidence: 99%

Section: Noise Propagation and Autoregressive Moving Average Reprmentioning

confidence: 99%

Section: Conclusion and Future Research Directionmentioning

confidence: 99%

mentioning

confidence: 99%

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Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

Ueki

2010

Journal of Nuclear Science and Technology

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“…Accurate determination of the dominance ratio from Monte Carlo calculations has been the subject of considerable study in recent years. [1][2][3][4][5] For many applications it is only necessary that the dominance ratio be an end result of the Monte Carlo calculation. There are some applications, however, in which an evolving estimate of the dominance ratio obtained 'on-the-fly' during the calculation may be useful.…”

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confidence: 99%

On-the-Fly Monte Carlo Dominance Ratio Calculation Using the Noise Propagation Matrix

Sutton

Romano

Nease

2011

Progress in Nuclear Science and Technology

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Two Monte-Carlo-based methods for computing the dominance ratio in reactor calculations are the Fission Matrix Method (FMM) and the Coarse Mesh Projection Method (CMPM). The FMM allows an estimate of the dominance ratio to be computed before the fission source has converged, but requires a fine mesh-and hence considerable computational resources-for sufficient accuracy. Conversely, the CMPM gives very accurate results on a coarse mesh with very little computational effort, but can be used only after the fission source has converged. In this paper we describe a new method called the Noise Propagation Matrix Method (NPMM) that has the same coarse-mesh accuracy properties as the CMPM while also permitting an 'on-the-fly' estimation of the dominance ratio during fission source convergence. Like the CMPM, the NPMM uses the noise propagation matrix (NPM) in determining the dominance ratio. The two methods differ, however, in how the matrix is used to obtain the dominance ratio. A new derivation of the equations used to compute the NPM in a Monte Carlo calculation is presented that eliminates an approximation made in an earlier work on the CMPM. It is shown that by using the improved expression for the NPM, the dominance ratio can be found directly and simply as the largest-modulus eigenvalue of the matrix-thereby eliminating the more complicated time-series-analysis method used by the CMPM. Results for several problems are presented that demonstrate the validity of the method.

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Particle clustering in Monte Carlo criticality simulations

Dumonteil

Malvagi

Zoia

et al. 2014

Annals of Nuclear Energy

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Time Series Analysis of Monte Carlo Fission Sources—I: Dominance Ratio Computation

Cited by 27 publications

References 11 publications

Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

On-the-Fly Monte Carlo Dominance Ratio Calculation Using the Noise Propagation Matrix

Particle clustering in Monte Carlo criticality simulations

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