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Adams-Bashforth-Moulton method with Savitzky-Golay filter to reduce reactivity fluctuations

Die Adams-Basforth-Moulton-Methode mit Savitzky-Golay-Filter zur Reduzierung von Reaktivitätsschwankungen
D. Suescún-Díaz, D. A. Rasero Causil and J. H. Figueroa-Jimenez
From the journal Kerntechnik

Abstract

In this paper we present a new method of calculating reactivity with fluctuation reduction. First we propose the generalized predictor and corrector using the fourth order Adams-Basforth-Moulton (ABM) for the numerical solution of the point kinetic equations for the calculation of reactivity, without using the history of nuclear power. Due to the nature of point kinetic equations, we use modifiers of the different predictors to increase precision in the approximation obtained. Secondly, we use the filter known as Savitzky-Golay (SG), which permits the reduction of the fluctuation in reactivity. It is known that the SG filter smoothing without diminishing the value of the nuclear power, irrespective of its form; this guarantees the reduction of Gaussian random noise levels, which is distributed around the average value of the nuclear power of up to σ = 0.1, with a time step h = 0.01 s. This formulation uses the Gram polynomial approximation, with a degree d = 2 the results show better values in the maximum difference in reactivity in comparison with that reported in literature.

Kurzfassung

In diesem Beitrag wird eine neue Methode zur Reduzierung von Reaktivitätsschwankungen vorgestellt. Zuerst wird ein generalisiertes Prädiktor-Korrektor-Verfahren vorgeschlagen unter Verwendung der Adams-Basforth-Moulton (ABM)-Methode vierter Ordnung für die numerische Lösung der punktkinetischen Gleichung zur Berechnung der Reaktivität. Wegen der Natur punktkinetischer Gleichungen wurden Modifier der verschiedenen Prädiktoren verwendet, um die Genauigkeit der erhaltenen Näherungen zu erhöhen. Dann wurden mit Hilfe eines Savitzky-Golay (SG)-Filters die Reaktivitätsschwankungen reduziert. Es ist bekannt, dass SG-Filter die Leistungswerte glätten ohne diese zu verkleinern. Dadurch werden die Gaussschen Rauschlevel der Leistungswerte reduziert um bis zu σ = 0.1, mit einem Zeitschritt von h = 0.01 s. Diese Formulierung verwendet die Gram Näherung. Die Ergebnisse zeigen bessere Werte der maximalen Differenz in der Reaktivität im Vergleich zu den Literaturwerten.


* Corresponding author: E-mail address: (Daniel Suescún-Díaz)

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Received: 2017-08-26
Published Online: 2017-12-09
Published in Print: 2017-12-18

© 2017, Carl Hanser Verlag, München