A multi-class anomaly signal classification method for fixed-point deformation combining PSO–VMD multiscale adaptive sample entropy and ALO–SOM model
To address the challenge of identifying five predefined categories of disturbance-related abnormal signals (lightning interference, artificial blasting, power-supply failure, collapse-related events, and meteorological anomalies) in fixed-point deformation monitoring, this paper proposes an identification framework integrating parameter-optimized variational mode decomposition (VMD), multiscale entropy analysis, and an intelligent classification model. Firstly, particle swarm optimization is adopted to adaptively determine the mode number and penalty factor for VMD to realize adaptive signal decomposition. Then, an adaptive sample entropy algorithm with self-adjustable similarity thresholds is applied to extract multiscale complexity-oriented features from each decomposed modal component. Finally, the ant lion optimizer optimizes the competitive-layer topology and training hyperparameters of a self-organizing map network to build the target classifier. Comparative experiments against 18 widely-used classification models (including AdaBoost ensemble learners, generalized regression neural networks, long short-term memory networks, and gated recurrent units) are carried out on the real-world observation dataset from the Yixian seismic station. The experimental results show that the proposed framework achieves competitive classification performance for the five anomaly categories. The mean test-set accuracy over 100 independent repeated-run experiments reaches 99.62%, with a standard deviation of 0.6361. This study offers an effective technical reference for identifying deformation-related abnormal waveforms under complex observational conditions.
- Kabel M, Böhlke T, Schneider M. Efficient fixed point and Newton–Krylov solvers for FFT-based homogenization of elasticity at large deformations. Comput Mech. 2014;54(6):1497-1514. doi: 10.1007/s00466-014-1071-8
- Schirmer H. Fixed point sets of deformations of pairs of spaces. Topol Appl. 1986;23(2):193-205. doi: 10.1016/0168-8641(86)90041-6
- Shimada S, Bock Y. Crustal deformation measurements in central Japan determined by a Global Positioning System fixed-point network. J Geophys Res: Solid Earth. 1992;97(B9):12437-12455. doi: 10.1029/92JB00809
- Sun W, Okubo S, Fu G, Araya A. General formulations of global co-seismic deformations caused by an arbitrary dislocation in a spherically symmetric earth model-applicable to deformed earth surface and space-fixed point. Geophys J Int. 2009;177(3):817-833. doi: 10.1111/j.1365-246X.2009.04113.x
- Zhang Y, Wang D, Zhao Y, Shi H. Present and progress of fixed-point deformation observation. Geomatics and Information Science of Wuhan University. 2022;47(6):830-838. doi: 10.13203/j.whugis20220104
- Liu S, Pang C, Wang X, Song M. Comparison and Analysis of Multiple Entropy Feature Tests for Abnormal Signals in Fixed-Point Deformation Monitoring. International Scientific Technical and Economic Research. 2026;4(2):206-231. doi: 10.71451/istaer2622
- Peng Z, Shao Y. Deep learning seismic detection on fixed-point deformation data: A case in Tianjin, China. In: 2024 5th International Conference on Artificial Intelligence and Computer Engineering (ICAICE). 2024:598-604. doi: 10.1109/ICAICE63571.2024.10864303
- Sheng D, Yang J, Wang H, Zhao CS, Sheng C. Interference and precursor signal analysis based on random forest and improved logistic regression model. International Scientific Technical and Economic Research. 2025;3(1):8-24. doi: 10.71451/m417wa34
- Chen F, Diao F, Haghighi MH, et al. Mechanism and implications of the post-seismic deformation following the 2021 Mw 7.4 Maduo (Tibet) earthquake. Geophys J Int. 2024;237(1):203-216. doi: 10.1093/gji/ggae034
- Doan NP, Nguyen BP, Park SS. Seismic deformation analysis of earth dams subject to liquefaction using UBCSAND2 model. Soil Dyn Earthq Eng. 2023;172:108003. doi: 10.1016/j.soildyn.2023.108003
- Guo ZM, Wang ZY, Lei Y, Li YM. High-speed railway signal processing based on a combination of VMD and KSVD. Appl Geophys. 2025:1-16. doi: 10.1007/s11770-025-1223-y
- Kohler M, Puzrin AM. Mechanism of co-seismic deformation of the slow-moving La Sorbella landslide in Italy revealed by MPM analysis. J Geophys Res Earth Surf. 2022;127(7). doi: 10.1029/2022JF006618
- Zhang S, Jia P, Hou B, Hao M. Vertical deformation before and after the 2022 Menyuan Ms6.9 earthquake and analysis of earthquake precursors. Geod Geodyn. 2023;14(6):582-588. doi: 10.1016/j.geog.2023.03.005
- Zhao S, McClusky S, Cummins PR, Miller MS. Co-seismic and post-seismic deformation associated with the 2018 Lombok, Indonesia, earthquake sequence, inferred from InSAR and seismic data analysis. Remote Sens Environ. 2024;304:114063. doi: 10.1016/j.rse.2024.114063
- Kulshrestha A, Chang L, Stein A. Use of LSTM for sinkhole-related anomaly detection and classification of InSAR deformation time series. IEEE J Sel Top Appl Earth Obs Remote Sens. 2022;15:4559-4570. doi: 10.1109/JSTARS.2022.3180994
- Maes K, Salens W, Feremans G, Segher K, Francois S. Anomaly detection in long-term tunnel deformation monitoring. Eng Struct. 2022;250:113383. doi: 10.1016/j.engstruct.2021.113383
- Zhang J, Tang H, Zhou B, Wen T, Zhang S. A new early warning criterion for landslides movement assessment: Deformation Standardized Anomaly Index. Bull Eng Geol Environ. 2024;83(5):205. doi: 10.1007/s10064-024-03672-3
- Milillo P, Sacco G, Di Martire D, Hua H. Neural network pattern recognition experiments toward a fully automatic detection of anomalies in InSAR time series of surface deformation. Front Earth Sci. 2022;9:728643. doi: 10.3389/feart.2021.728643
- Zhang T, Zhang W, Cao D, Yi Y, Wu X. A new deep learning neural network model for the identification of InSAR anomalous deformation areas. Remote Sens. 2022;14(11):2690. doi: 10.3390/rs14112690
- You H, Hua L, Su T. Power Transformer Fault Diagnosis and Prediction Based on Deep Learning. Journal of Digital Frontier. 2026;1(1):144-184. doi: 10.67541/jdf2606
- Wang W. Design Scheme Style Feature Extraction and Machine Learning Classification Algorithm Construction. International Scientific Technical and Economic Research. 2026;4(3):1-21. doi: 10.67541/istaer2623
- Castillo-Villamor L, Hardy A, Bunting P, et al. The Earth Observation-based Anomaly Detection (EOAD) system: a simple, scalable approach to mapping in-field and farm-scale anomalies using widely available satellite imagery. Int J Appl Earth Obs Geoinf. 2021;104:102535. doi: 10.1016/j.jag.2021.102535
- Liu C, Pan J, Wang J. An LSTM-based anomaly detection model for the deformation of concrete dams. Struct Health Monit. 2024;23(3):1914-1925. doi: 10.1177/14759217231199569
- Wibowo A, Purnama SR, Pratama C, Heliani LS, Sahara DP, Wibowo ST. Anomaly detection on displacement rates and deformation pattern features using tree-based algorithm in Japan and Indonesia. Geod Geodyn. 2023;14(2):150-162. doi: 10.1016/j.geog.2022.07.003
- Ma X, Lin Z, Jiao L, et al. Phase identification with VMD and HT combined method for an active seismic source experiment. Measurement. 2022;201:111689. doi: 10.1016/j.measurement.2022.111689
- Ou B, Zhang C, Xu B, et al. Innovative approach to dam deformation analysis: integration of VMD, fractal theory, and WOA-DELM. Struct Control Health Monit. 2024;(1):1710019. doi: 10.1155/2024/1710019
- Zhiyao L, Yong D, Denghua L. Coupling VMD and MSSA denoising for dam deformation prediction. Structures. 2023;58:105503. doi: 10.1016/j.istruc.2023.105503
- Zhou J, Zhang Y, Wang H, Yang J, Li P, Wang J. SABO-optimized VMD for seismic damage assessment of frame structures considering soil–structure interaction. Buildings. 2025;15(11):1822. doi: 10.3390/buildings15111822
- Bo Y, Guo X, Liu Q, Pan Y, Zhang L, Lu Y. Prediction of tunnel deformation using PSO variant integrated with XGBoost and its TBM jamming application. Tunn Undergr Space Technol. 2024;150:105842. doi: 10.1016/j.tust.2024.105842
- Li Q, Cheng F, Zhang X. Numerical simulation and deformation prediction of deep pit based on PSO-BP neural network inversion of soil parameters. Sensors. 2024;24(10):2959. doi: 10.3390/s24102959
- Li X, Jia C, Zhu X, Zhao H, Gao J. Investigation on the deformation mechanism of the full-section tunnel excavation in the complex geological environment based on the PSO-BP neural network. Environ Earth Sci. 2023;82(13):326. doi: 10.1007/s12665-023-10963-7
- Cui S, Jia J, Pang X, Wen J, Shi Y, Zeng J. A data-driven method with sample entropy and CEEMDAN for short-term performance degradation prediction of dynamic hydrogen fuel cells. Int J Hydrogen Energy 2024;83:916-932. doi: 10.1016/j.ijhydene.2024.08.123
- You H, Hua L, Su T. Economic Dispatch Optimization of Microgrid Based on an Improved Particle Swarm Optimization Algorithm. International Scientific Technical and Economic Research. 2026;4(3):90-124. doi: 10.67541/istaer2627
- Delgado-Bonal A, Marshak A. Approximate entropy and sample entropy: a comprehensive tutorial. Entropy. 2019;21(6):541. doi: 10.3390/e21060541
- Bigdeli A, Maghsoudi A, Ghezelbash R. Application of self-organizing map (SOM) and K-means clustering algorithms for portraying geochemical anomaly patterns in Moalleman district, NE Iran. J Geochem Explor. 2022;233:106923. doi: 10.1016/j.gexplo.2021.106923
- Rahman ATMS, Kono Y, Hosono T. Self-organizing map improves understanding on the hydrochemical processes in aquifer systems. Sci Total Environ 2022;846:157281. doi: 10.1016/j.scitotenv.2022.157281
- Roeva O, Zoteva D, Roeva G, Lyubenova V. An efficient hybrid of an ant lion optimizer and genetic algorithm for a model parameter identification problem. Mathematics. 2023;11(6):1292. doi: 10.3390/math11061292
- Mirjalili S. The ant lion optimizer. Adv Eng SoftwAdv Eng Softw. 2015;83:80-98. doi: 10.1016/j.advengsoft.2015.01.010
- Vu Hong Son P, Soulisa FV. A Hybrid Ant Lion Optimizer (ALO) Algorithm for Construction Site Layout Optimization. J Soft Comput Civ Eng. 2023;7(4):50-71. doi: 10.22115/scce.2023.365303.1540
- Wang A, Pang C, Chen G, Li C, Zhao T. Optimization of the SOM neural network model using CEEMDAN distribution entropy and ALO for seismic and blasting identification. J Seism Explor. 2025;34(2):28-43. doi: 10.36922/JSE025280033
- Zosso D, Dragomiretskiy K, Bertozzi AL, Weiss PS. Two-Dimensional Compact Variational Mode Decomposition. J Math Imaging Vis. 2017;58(2):294-320. doi: 10.1007/s10851-017-0710-z
- Richman JS, Moorman JR. Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol - Heart Circ Physiol. 2000;278(6):H2039-H2049. doi: 10.1152/ajpheart.2000.278.6.H2039
- Akbari MA, Zare M, Azizipanah-Abarghooee R, Mirjalili S, Deriche M. The cheetah optimizer: a nature-inspired metaheuristic algorithm for large-scale optimization problems. Sci Rep. 2022;12(1):10953. doi: 10.1038/s41598-022-14338-z43
