Permutation Entropy and Ordinal Patterns as a Resilience Indicator

Orlando Duran, Luca Fumagalli, Adolfo Arata

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Resilience quantification in production systems is essential for making informed decisions. This paper introduces a novel resilience indicator derived from time-series data of system availability. The proposed approach involves symbolic time-series analysis where the availability data is discretized into symbolic sequences. Each symbol in the sequence represents a range of availability values. Using these symbolic sequences, we apply permutation entropy based on ordinal patterns to assess system complexity and resiliency. The methodology is exemplified through a case study involving two production systems with different availability profiles. The symbolic sequences are generated based on predefined thresholds and labeled as 'High,' 'Medium,' and 'Low' availability. Unique ordinal patterns are identified, and their frequencies are calculated to derive the permutation entropy for each system. Special emphasis is placed on dramatic performance declines and spikes, with these events weighted differently in the entropy calculations. Our results indicate that the proposed resilience indicator is computationally efficient and robust to noise and variability, making it ideal for realtime analysis of large datasets. Comparative entropy values provide insights into the relative resilience of the systems under study. The system with lower entropy demonstrated greater regularity and, by extension, higher resilience. This innovative approach promises a new avenue for quantifying resilience in complex systems. Future work will focus on empirical validation in various applications and continuous refinement of the underlying algorithm.

Original languageEnglish
Title of host publication2023 7th International Conference on System Reliability and Safety, ICSRS 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages384-388
Number of pages5
ISBN (Electronic)9798350306057
DOIs
StatePublished - 2023
Event7th International Conference on System Reliability and Safety, ICSRS 2023 - Bologna, Italy
Duration: 22 Nov 202324 Nov 2023

Publication series

Name2023 7th International Conference on System Reliability and Safety, ICSRS 2023

Conference

Conference7th International Conference on System Reliability and Safety, ICSRS 2023
Country/TerritoryItaly
CityBologna
Period22/11/2324/11/23

Keywords

  • availability
  • permutation entropy
  • resilience
  • symbolic time series analysis (STSA)

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