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Deformation prediction of rock cut slope based on long short-term memory neural network

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Abstract

The cut slope graben is affected by the lithology of strata, rainfall, and man-made excavation, which is a complex geotechnical system. Deformation of a cut slope changes irregularly with time, and, if too large, the deformation causes geological disasters such as landslides. Thus, it is crucial to establish an accurate slope deformation prediction model for control and safety. We used wavelet decomposition (WD) to process the time series of slope deformation to obtain an approximate series and detailed series. Then to predict each sub-series, we used the improved particle swarm optimization (IPSO) algorithm to optimize the number of neurons in the hidden layer, the learning rate, and the number of iterations of a long short-term memory (LSTM) neural network. The prediction results were summed to obtain the final prediction. The hybrid WD-IPSO-LSTM prediction model had a mean absolute error of 0.047, 0.067, and 0.094 at 1, 3, and 6 steps, respectively. These errors were 47.19%, 49.62%, and 57.47% lower than the LSTM-alone model errors. The hybrid WD-IPSO-LSTM prediction model had greater accuracy compared with a back propagation neural network, recurrent neural network, LSTM alone, PSO-LSTM, and IPSO-LSTM in 1-step, 3-step, and 6-step prediction. In addition, our hybrid model for prediction of slope deformation was more realistic and credible compared with other models.

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References

  1. Thirugnanam H, Uhlemann S, Reghunadh R et al (2022) Review of landslide monitoring techniques with IoT integration opportunities. IEEE J Sel Top Appl Earth Observ Remote Sens 15:5317–5338. https://doi.org/10.1109/JSTARS.2022.3183684

    Article  ADS  Google Scholar 

  2. Wu LZ, Zhang LM, Zhou Y et al (2018) Theoretical analysis and model test for rainfall-induced shallow landslides in the red-bed area of Sichuan. Bull Eng Geol Environ 77:1343–1353. https://doi.org/10.1007/s10064-017-1126-0

    Article  Google Scholar 

  3. Huang FM, Yin KL, Zhang GR et al (2016) Landslide displacement prediction using discrete wavelet transform and extreme learning machine based on chaos theory. Environ Earth Sci 75:1376. https://doi.org/10.1007/s12665-016-6133-0

    Article  ADS  Google Scholar 

  4. Tutluoglu L, Oge IF, Karpuz C (2011) Two and three dimensional analysis of a slope failure in a lignite mine. Comput Geosci 37(2):232–240. https://doi.org/10.1016/j.cageo.2010.09.004

    Article  ADS  Google Scholar 

  5. Saito M (1969) Forecasting time of slope failure by tertiary creep. In: Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering. Mexico City Vol. 2, 677–683

  6. Abu Arqub O, Singh J, Alhodaly M (2023) Adaptation of kernel functions-based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations. Math Methods Appl Sci 46(7):7807–7834. https://doi.org/10.1002/mma.7228

    Article  MathSciNet  Google Scholar 

  7. Abu Arqub O, Singh J, Maayah B et al (2021) Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag-Leffler kernel differential operator. Math Methods Appl Sci. https://doi.org/10.1002/mma.7305

    Article  Google Scholar 

  8. Alshammari M, Al-Smadi M, Abu Arqub O, Alias MA et al (2020) Residual series representation algorithm for solving fuzzy duffing oscillator equations. Symmetry 12(4):572. https://doi.org/10.3390/sym12040572

    Article  ADS  Google Scholar 

  9. Abu AO (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610. https://doi.org/10.1007/s00521-015-2110-x

    Article  Google Scholar 

  10. Li WX, Qi DL, Zheng SF et al (2015) Fuzzy mathematics model and its numerical method of stability analysis on rock slope of opencast metal mine. Appl Math Model 39(7):1784–1793. https://doi.org/10.1016/j.apm.2014.10.006

    Article  MathSciNet  Google Scholar 

  11. Lu P, Rosenbaum MS (2003) Artificial neural networks and grey systems for the prediction of slope stability. Nat Hazards 30:383–398. https://doi.org/10.1023/B:NHAZ.0000007168.00673.27

    Article  Google Scholar 

  12. Wu LZ, Li SH, Huang RQ et al (2020) A new grey prediction model and its application to predicting landslide displacement. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2020.106543

    Article  PubMed  PubMed Central  Google Scholar 

  13. Tasci L, Tuncez M (2018) Monitoring of deformations in open-pit mines and prediction of deformations with the grey prediction model. J Grey Syst 30(4):152–163

    Google Scholar 

  14. Li L, Qiang Y, Li S et al (2018) Research on slope deformation prediction based on fractional-order calculus gray model. Adv Civ Eng 1:1–9. https://doi.org/10.1155/2018/9526216

    Article  ADS  Google Scholar 

  15. Jia L, Li Y, Xie YP (2013) Slope deformation prediction based on chaotic-svm. Appl Mech Mater. https://doi.org/10.4028/www.scientific.net/AMM.353-356.673

    Article  Google Scholar 

  16. Li X, Jiang C, Xu R et al (2021) Combining forecast of landslide displacement based on chaos theory. Arab J Geosci 14:202. https://doi.org/10.1007/s12517-021-06514-8

    Article  Google Scholar 

  17. Stahlke D, Wackerbauer R (2011) Length scale of interaction in spatiotemporal chaos. Phys Rev E Stat Nonlinear Soft Matter Phys 83(4):204–207

    Article  Google Scholar 

  18. Zhang X, Zhu C, He M et al (2022) Failure mechanism and long short-term memory neural network model for landslide risk prediction. Remote Sens 14(1):166. https://doi.org/10.3390/rs14010166

    Article  ADS  Google Scholar 

  19. Daviran M, Shamekhi M, Ghezelbash R et al (2023) Landslide susceptibility prediction using artificial neural networks, SVMs and random forest: hyperparameters tuning by genetic optimization algorithm. Int J Environ Sci Technol 20:259–276. https://doi.org/10.1007/s13762-022-04491-3

    Article  CAS  Google Scholar 

  20. Wang H, Long G, Liao J et al (2021) A new hybrid method for establishing point forecasting, interval forecasting, and probabilistic forecasting of landslide displacement. Nat Hazards. https://doi.org/10.21203/rs.3.rs-839771/v1

    Article  Google Scholar 

  21. Wang S, Zhang Z, Ren Y et al (2019) UAV photogrammetry and AFSA-Elman neural network in slopes displacement monitoring and forecasting. KSCE J Civ Eng. https://doi.org/10.1007/s12205-020-1697-3

    Article  Google Scholar 

  22. Xu F, Xu WX, Wang K (2010) Prediction of displacement time series based on support vector machines-Markov chain. Appl Mech Mater 580–583:436–439. https://doi.org/10.4028/www.scientific.net/AMM.580-583.436

    Article  Google Scholar 

  23. Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36(4):7535–7543. https://doi.org/10.1016/j.eswa.2008.09.066

    Article  Google Scholar 

  24. Dong JQ, Wang BX, Yan XX et al (2022) Prediction of undisturbed clay rebound index based on soil microstructure parameters and PSO-SVM model. KSCE J Civ Eng 26:2097–2111. https://doi.org/10.1007/s12205-022-1031-3

    Article  Google Scholar 

  25. Eshtay M, Faris H, Obeid N (2019) Metaheuristic-based extreme learning machines: a review of design formulations and applications. Int J Mach Learn Cybern 10(6):1543–1561. https://doi.org/10.1007/s13042-018-0833-6

    Article  Google Scholar 

  26. Li ZW, He YC, Ya L et al (2021) A hybrid grey wolf optimizer for solving the product knapsack problem. Int J Mach Learn Cybern 12:201–222. https://doi.org/10.1007/s13042-020-01165-9

    Article  Google Scholar 

  27. SK PK, Sumithra MG, Saranya N (2019) Particle Swarm Optimization (PSO) with fuzzy c means (PSO-FCM)–based segmentation and machine learning classifier for leaf diseases prediction. Concurr Comput Pract Exp. https://doi.org/10.1002/cpe.5312

    Article  Google Scholar 

  28. Saha S, Arya RK (2021) Adaptive virtual anchor node based underwater localization using improved shortest path algorithm and particle swarm optimization (PSO) technique. Concurr Comput Pract Exp. https://doi.org/10.1002/cpe.6552

    Article  Google Scholar 

  29. Su HZ, Li X, Yang B et al (2018) Wavelet support vector machine-based prediction model of dam deformation. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2018.03.022

    Article  Google Scholar 

  30. Bao G, Liu Y, Xu R (2022) Short-term electricity price forecasting based on empirical mode decomposition and deep neural network. Int J Artif Intell Tools. https://doi.org/10.1142/S021821302240019X

    Article  Google Scholar 

  31. Zhao N, Sun H, Li QQ et al (2022) Research on application of time series forecast model mWDLNet based on wavelet decomposition. J Chin Comput Syst. https://doi.org/10.20009/j.cnki.21-1106/TP.2020-0912. (in Chinese)

    Article  Google Scholar 

  32. Wu X, Qian JS, Huang CH et al (2014) Short-term coalmine gas concentration prediction based on wavelet transform and extreme learning machine. Math Probl Eng. https://doi.org/10.1155/2014/858260

    Article  Google Scholar 

  33. Ehteram M, Salih SQ, Yaseen ZM (2020) Efficiency evaluation of reverse osmosis desalination plant using hybridized multilayer perceptron with particle swarm optimization. Environ Sci Pollut Res 27:15278–15291. https://doi.org/10.1007/s11356-020-08023-9

    Article  CAS  Google Scholar 

  34. Shukla SK, Koley E, Ghosh S (2019) A hybrid wavelet-APSO-ANN-based protection scheme for six-phase transmission line with real-time validation. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3400-x

    Article  Google Scholar 

  35. Clerc M (2002) The swarm and queen: towards a deterministic and adaptive particle swarm optimization. In: Congress on Evolutionary Computation-cec. https://doi.org/10.1109/CEC.1999.785513

  36. Zhang XJ (2019) Study on safety evaluation of highway slope based on online monitoring system. Chang'an University. https://kns.cnki.net/KCMS/detail/detail.aspx?dbname=CMFD202001&filename=1019628384.nh. (in Chinese)

  37. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735

    Article  CAS  PubMed  Google Scholar 

  38. Chen CC, Zhang Q, Kashani MH et al (2022) Forecast of rainfall distribution based on fixed sliding window long short-term memory. Eng Appl Comput Fluid Mech 16(1):248–261. https://doi.org/10.1080/19942060.2021.2009374

    Article  Google Scholar 

  39. Wang WC, Yj Du, Chau KW et al (2021) An ensemble hybrid forecasting model for annual runoff based on sample entropy, secondary decomposition, and long short-term memory neural network. Water Resour Manag 35:4695–4726. https://doi.org/10.1007/s11269-021-02920-5

    Article  Google Scholar 

  40. Wang KG, Band SS, Ameri R et al (2022) Performance improvement of machine learning models via wavelet theory in estimating monthly river streamflow. Eng Appl Comput Fluid Mech 16(1):1833–1848. https://doi.org/10.1080/19942060.2022.2119281

    Article  Google Scholar 

  41. Ali Ghorbani M, Kazempour R, Chau K et al (2018) Forecasting pan evaporation with an integrated artificial neural network quantum-behaved particle swarm optimization model: a case study in Talesh, Northern Iran. Eng Appl Comput Fluid Mech 12(1):724–737. https://doi.org/10.1080/19942060.2018.1517052

    Article  Google Scholar 

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Acknowledgements

This research was funded by the Graduate Science and Technology Innovation program of Chongqing University of Science and Technology (YKJCX2220646). The authors thank AiMi Academic Services (www.aimieditor.com) for English language editing and review services.

Funding

The Graduate Science and Technology Innovation program of Chongqing University of Science and Technology (YKJCX2220646).

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Chongqing University of Science and Technology, Chongqing, 401331, China

    Sichang Wang, Tian-le Lyu, Naqing Luo & Pengcheng Chang

  2. Chongqing Key Laboratory of Energy Engineering Mechanics & Disaster Prevention and Mitigation, Chongqing, 401331, China

    Sichang Wang

  3. Chongqing Ruode Technology Co., LTD, Chongqing, 401331, China

    Naqing Luo

  4. Chongqing Institute of Safety Production Science Co. LTD, Chongqing, 401331, China

    Pengcheng Chang

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  1. Sichang Wang
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Contributions

SW: Conceptualization, Methodology,Supervision. T-lL: Software, Validation,Data curation, Writing-Original draft preparation. NL: Resources,Investigation,Data Curation. PC: Writing- Reviewing and Editing.

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Correspondence to Sichang Wang.

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Wang, S., Lyu, Tl., Luo, N. et al. Deformation prediction of rock cut slope based on long short-term memory neural network. Int. J. Mach. Learn. & Cyber. 15, 795–805 (2024). https://doi.org/10.1007/s13042-023-01939-x

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