Stability analysis by means of information entropy: Assessment of a novel method against natural circulation experimental data

Abstract

In this paper, a method based on the Information Entropy (IE) is developed to evaluate the equilibrium stability of a given dynamic system. While for analytical/semi-analytical approaches the definition of stability is formally rigorous (e.g., thanks to the tools provided by the linear analysis), the process of identifying stable and unstable behaviours can be subject to a certain degree of arbitrariness in case of experimental and/or numerical transients. Generally speaking, the classification is based on the time dependent behaviour of the signals recorded during a transient of the system. These signals can be characterised by oscillations with non-decreasing amplitude or can converge to a steady-state value. In the first case, the system experiences an unstable operating condition, in the latter one, the operating condition is stable. For this reason, the key issue is the determination of a well-defined threshold in order to separate converging and oscillating signals. To this purpose, the proposed method evaluates the convergence of a transient by computing the IE associated with a selected signal, and adopts as convergence threshold the IE related to a constant amplitude sinusoid, which represents the condition for the onset of the instability.In this work, the developed methodology, which can be applied in general to any kind of signal, is assessed against the data obtained from the L2 single-phase Natural Circulation Loop (NCL) (University of Genoa, DIME-Tec Labs), for which the IE is also adopted to evaluate the system stability map. Satisfactory results are achieved not only for the identification of stable and unstable transients, but also for the stability map, which is in agreement with the predictions achievable with other methodologies (e.g., semi-analytical linear analysis) developed by the authors (Pini et al., 2016; Cammi et al., 2016a; Luzzi et al., 2017).