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Determination of Limit Cycles Using Both the Slope of Correlation Integral and Dominant Lyapunov Methods

Rogelio Castillo, Gustavo Alonso, Javier C. Palacios

Nuclear Technology

Volume 145 / Number 2 / February 2004 / Pages 139-149


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A method for nonlinear analysis of instabilities in boiling water reactors (BWRs) is presented. Both the Dominant Lyapunov Exponent method and the Slope of the Correlation Integral (SOCI) method are used to analyze the average power reactor monitor (APRM) signals from a BWR. The main advantage of using the two methods in a complementary manner is that doing so results in an enhancement of the capability to analyze noisy systems, such as the APRM signals in a BWR. Previously, such nonlinear analysis had been performed using independently either the Dominant Lyapunov Exponent Method or the SOCI method. These two methods are sensitive to noise in a signal and normally require large amounts of data for a reliable analysis.

This proposed system for nonlinear analysis is composed first of a home-developed computer program called "SLOPE," which is based on the SOCI method. Then, the signal analysis is also performed by the "LENNS" code, which is used to obtain the dominant Lyapunov exponent. Since only the dominant Lyapunov exponent is computed, there is no need to acquire large amounts of data; thus, computational processing time is greatly reduced, even in the case of noisy data.

The system was used to analyze BWR signals containing stationary and nonstationary limit cycles. It was found that this method satisfactorily calculates the limit cycles, extracting useful information from noisy signals.

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