Non-linear boiling water reactor stability with Shannon Entropy

Highlights: • Non-linear Shannon Entropy (SE) is explored to study BWR instability. • The SE as a stability indicator was validated with artificial signals. • The SE was compared with Decay Ratio (Linear method) and Lyapunov exponents (Non-linear method). • Methodology based on the SE can be applied to develop an online stability monitor. - Abstract: The most common indicator currently used to assess boiling water reactor (BWR) instability is the Decay Ratio (DR), which is an indicator that assumes stationarity and linearity of BWR signals. However, it is well known that BWRs are complex dynamical systems that may exhibit chaotic behavior when an instability event occurs, jeopardizing the DR validity and reliability when the reactor is working at a specific operating point. Thus, it is required to study new stability indicators that satisfy as much as possible this complex dynamics of BWR systems. With this latter fundamental idea in mind, in this work, the non-linear Shannon Entropy (SE) is explored to study BWR instability. The SE measures the uncertainty of BWR signals to appraise for system stability, a low SE estimation indicates a predictable BWR operation (stable behavior) whereas a high SE estimation indicates an unpredictable BWR operation (unstable behavior). The SE estimation was validated with artificial signals from a non-linear Reduced Order Model (ROM), that represents qualitatively the dynamic behavior of a BWR system. The result comparison proves that the SE satisfies the BWR complex dynamics whereas the DR does not during the chaotic behavior. The SE was also compared with the Largest Lyapunov Exponent (LLE), which represents adequately the chaotic behavior of a BWR but, from the practical point of view, it cannot be applied to an online stability monitor, while the methodology presented in this work based on the SE, is a good candidate.