Non-Linear Stability Analysis of Real Signals from Nuclear Power Plants (Boiling Water Reactors) Based on Noise Assisted Empirical Mode Decomposition Variants and the Shannon Entropy

Abstract

There are currently around 78 nuclear power plants (NPPs) in the world based on Boiling Water Reactors (BWRs). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature.Entropy 2017, 19, 359 2 of 33 operates at a low mass flow and at high nominal power. Another current trend is to increase the size of the core, which causes a weaker special coupling in the neutron field which increases the susceptibility of the reactor to experiencing unstable oscillations. In summary, all current tendencies related to reactor design enhance the regions where the reactor should not be operated (reactor operation at low flow and high power).Also, the DR often jumps discontinuously from the well stable to the far-unstable region [7]. The BWR stability is of primary interest from the point of view of BWR operation, due to the fact, that the stability margin may be strongly reduced during plant maneuvering and transients [8]. According to these issues, the DR might not be a reliable monitoring index after all, under certain operating conditions. Besides, in regular operating conditions, the need for stationary signals might be a handicap for DR estimation. Thus, it is relevant to explore new alternative methodologies and indexes adapted to accommodate for non-stationary and non-linear BWR signal behavior.In [9] a short time Fourier transform based technique was explored to study the time dependence of the natural frequency when the BWR signal is non-stationary. Later, the wavelet theory was applied to explore new alternatives for transient instability analysis [10,11]. However, in general BWR signals are non-stationary and non-linear, thus Fourier-based or wavelet-based approaches might lead to a biased stability analysis. Several methods for non-linear BWR stability analysis have been applied before [12,13], to study BWR signals containing stationary and non-stationary segments. In this work, the Shannon Entropy (SE) was applied, to infer whether it can be used as a novel stability parameter for BWRs. The SE is a concept that was developed by Claude E. Shannon [14] to study a discrete source through the information content of this source. The SE is a statistical index that quantifies the complexity of a signal. In this case, the BWR stability issue is assessed quantifying the complexity of BWR si...

Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems

“…The fixed-time neural network adaptive controller is present for nonlinear high-order systems. Based on the fixed-time adaptive technology, the strict-feedback high-order system has fixed-time Lyapunov stability based on Lyapunov stability theory [36][37][38]. The convergence time of the system can be accurately calculated, and the settling time does not rely on the initial situation.…”