Permutation Entropy: An Ordinal Pattern-Based Resilience Indicator for Industrial Equipment

In a highly dynamic and complex environment where risks and uncertainties are inevitable, the ability of a system to quickly recover from disturbances and maintain optimal performance is crucial for ensuring operational continuity and efficiency. In this context, resilience has become an increasingly important topic in the field of engineering and the management of productive systems. However, there is no single quantitative indicator of resilience that allows for the measurement of this characteristic in a productive system. This study proposes the use of permutation entropy of ordinal patterns in time series as an indicator of resilience in industrial equipment and systems. Based on the definition of resilience, the developed method enables precise and efficient assessment of a system's ability to withstand and recover from disturbances. The methodology includes the identification of ordinal patterns and their analysis through the calculation of a permutation entropy indicator to characterize the dynamics of industrial systems. Case studies are presented and the results are compared with other resilience models existing in the literature, aiming to demonstrate the effectiveness of the proposed approach. The results are promising and highlight a highly applicable and simple indicator for resilience in industrial systems.