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

Sirui Liu; Cong Pang; Xin Wang; Meiping Song

doi:10.71451/ISTAER2622

Authors

Sirui Liu Institute of Seismology, China Earthquake Administration Author https://orcid.org/0009-0002-0524-4947
Cong Pang Institute of Seismology, China Earthquake Administration, Wuhan, Hubei, China and Wuhan Gravitation and Solid Earth Tides, National Observation and Research Station, Wuhan, Hubei, China Author https://orcid.org/0009-0001-8579-7527
Xin Wang Shenyang Earthquake Monitoring Center, Liaoning Earthquake Administration, Shenyang, Liaoning, China Author https://orcid.org/0009-0002-8056-182X
Meiping Song Datong Earthquake Monitoring Center, Shanxi Earthquake Administration, Datong, Shanxi, China Author https://orcid.org/0009-0000-9529-9778

DOI:

https://doi.org/10.71451/ISTAER2622

Keywords:

Sample entropy; Fuzzy entropy; Distribution entropy; Permutation entropy; Adaptive weighted multi-scale fusion entropy

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.

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