Comparison and Analysis of Multiple Entropy Feature Tests for Abnormal Signals in Fixed-Point Deformation Monitoring

Sirui Liu1 , Cong Pang1,2 , Xin Wang3 , Meiping Song4
1 Institute of Seismology, China Earthquake Administration, Wuhan, Hubei, China
2 Wuhan Gravitation and Solid Earth Tides, National Observation and Research Station, Wuhan, Hubei, China
3 Shenyang Earthquake Monitoring Center, Liaoning Earthquake Administration, Shenyang, Liaoning, China
4 Datong Earthquake Monitoring Center, Shanxi Earthquake Administration, Datong, Shanxi, China
International Scientific Technical and Economic Research 2026, Vol. 4, No. 2, pp. 206-231
DOI: 10.71451/ISTAER2622
Received: 26 March 2026; Revised: 23 April 2026; Accepted: 28 April 2026; Published: 29 May 2026
Abstract

Fixed-point deformation monitoring is essential for geological hazard early warning, and identifying abnormal signals remains a key challenge. To evaluate the effectiveness of five entropy methods for this purpose, a quantitative comparison was conducted. Abnormal deformation data were preprocessed to extract sample entropy (SE), fuzzy entropy (FE), distribution entropy (DE), permutation entropy (PE), and adaptive weighted multi-scale fusion entropy (AWM-FE). Their ability to distinguish abnormal signals was compared using the T-test, followed by the Kruskal Wallis test and post hoc multiple comparisons. Simulation experiments showed that AWM-FE exhibited stable, reliable performance and was well-suited for complex field environments with multi-scale analysis needs. Real deformation data analysis revealed that SE had an average T-test p-value of 0.0016, indicating significant distinction across six category pairs, while DE achieved an F-value of 74.7205 in ANOVA, reflecting the largest overall inter-group variation. This study provides a reference for feature selection in identifying abnormal signals in fixed-point deformation observations.

Keywords
Sample entropy Fuzzy entropy Distribution entropy Permutation entropy Adaptive weighted multi-scale fusion entropy
Funding

This work was supported by the Open Fund of Wuhan Gravitation and Solid Earth Tides, National Observation and Research Station, No. WHYWZ202406; Earthquake Monitoring and Early Warning Task No. CEA-JCYJ-202601025; Research grants from National Institute of Natural Hazards, Ministry of Emergency Management of China (Grant Number: ZDJ2024-31, ZDJ2025-58).

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© 2026 The Author(s). Published by Sichuan Knowledgeable Intelligent Sciences. This is an open access article under the CC BY 4.0 license.

How to cite: Liu, S., Pang, C., Wang, X., & Song, M. (2026). Comparison and Analysis of Multiple Entropy Feature Tests for Abnormal Signals in Fixed-Point Deformation Monitoring. International Scientific Technical and Economic Research, 4(2), 206-231. https://doi.org/10.71451/ISTAER2622