A novel hybrid model for predicting the bearing capacity of piles
Abstract
Due to the uncertainty of soil condition and pile design characteristics, it is always a challenge for geotechnical engineers to accurately determine the bearing capacity of piles. The main objective of this study is to propose a hybrid model coupling least squares support vector machine (LSSVM) with an improved particle swarm optimization (IPSO) algorithm for the prediction of bearing capacity of piles. The improved PSO algorithm was used to optimize the LSSVM hyperparameters. The performance of the IPSO-LSSVM model was compared with seven artificial intelligence models, namely adaptive neuro-fuzzy inference system (ANFIS), M5 model tree (M5MT), multivariate adaptive regression splines (MARS), gene expression programming (GEP), random forest (RF), regression tree (RT) and a stacked ensemble model. Six statistical indices (e.g., coefficient of determination (R2), mean absolute error (MAE), root mean squared error (RMSE), relative root mean squared error (RRMSE), BIAS and discrepancy ratio (DR)) were used to evaluate the performance of the models. The R2, MAE, RMSE, RRMSE and BIAS values of the IPSO-LSSVM model were 1, 4.27 kN, 6.164 kN, 0.005 and 0, respectively, for the training datasets and 0.9977, 22 kN, 36.03 kN, 0.0275 and –11, respectively, for the testing datasets. Compared with the ANFIS, MARS, GEP, M5MT, RF, RT and the stacked ensemble models, the proposed IPSO-LSSVM model shows high accuracy and robustness on the test datasets. In addition, the sensitivity, uncertainty, reliability and resilience of the IPSO-LSSVM model were also analyzed in this study.
First published online 22 October 2024
Keyword : bearing capacity, pile, adaptive neuro-fuzzy inference system, least squares support vector machine, stacked ensemble model
How to Cite
Tao, L., & Xue, X. (2024). A novel hybrid model for predicting the bearing capacity of piles. Journal of Civil Engineering and Management, 1-14. https://doi.org/10.3846/jcem.2024.21886
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Baghban, A., Kashiwao, T., Bahadori, M., Ahmad, Z., & Bahadori, A. (2016a). Estimation of natural gases water content using adaptive neuro-fuzzy inference system. Petroleum Science and Technology, 34(10), 891–897. https://doi.org/10.1080/10916466.2016.1176039
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Baghban, A., Abbasi, P., & Rostami, P. (2016c). Modeling of viscosity for mixtures of Athabasca bitumen and heavy n-alkane with LSSVM algorithm. Petroleum Science and Technology, 34(20), 1698–1704. https://doi.org/10.1080/10916466.2016.1219748
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Bemani, A., Baghban, A., Mosavi, A., & Shahab, S. (2020a). Estimating CO2-Brine diffusivity using hybrid models of ANFIS and evolutionary algorithms. Engineering Applications of Computational Fluid Mechanics, 14(1), 818–834. https://doi.org/10.1080/19942060.2020.1774422
Bemani, A., Baghban, A., Mohammadi, & Amir H. (2020b). An insight into the modeling of sulfur content of sour gases in supercritical region. Journal of Petroleum Science and Engineering, 184, Article 106459. https://doi.org/10.1016/j.petrol.2019.106459
Bemani, A., Baghban, A., Shamshirband, S., Mosavi, A., Csiba, P., & Varkonyi-Koczy, A. R. (2020c). Applying ANN, ANFIS, and LSSVM models for estimation of acid solvent solubility in supercritical CO2. Computers, Materials & Continua, 63(3), 1175–1204. https://doi.org/10.32604/cmc.2020.07723
Benbouras, M. A., Petrişor. A.-I., Zedira, H., Ghelani, L., & Lefilef, L. (2021). Forecasting the bearing capacity of the driven piles using advanced machine-learning techniques. Applied Sciences, 11(22), Article 10908. https://doi.org/10.3390/app112210908
Breiman, L., Friedman, J. H., Olshen, B. A., & Stone, C. (1984). Classification and regression trees. Biometrics, 40, Article 874. https://doi.org/10.2307/2530946
Chiu, S. L. (1994). Fuzzy model identification based on cluster estimation. Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 2(3), 267–278. https://doi.org/10.3233/IFS-1994-2306
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Ferreira, C. (2001). Gene expression programming: a new adaptive algorithm for solving problems. Complex Systems, 13(2), 87–129. https://doi.org/10.48550/arXiv.cs/0102027
Friedman, J. H. (1991). Multivariate adaptive regression splines. The Annals of Statistics, 19(1), 1–67. https://doi.org/10.1214/aos/1176347963
Haratipour, P., Baghban, A., Mohammadi, A. H., Nazhad, S. H. H., & Bahadori, A. (2017). On the estimation of viscosities and densities of CO2-loaded MDEA, MDEA+AMP, MDEA+DIPA, MDEA+MEA, and MDEA+DEA aqueous solutions. Journal of Molecular Liquids, 242, 146–159. https://doi.org/10.1016/j.moliq.2017.06.123
Homaei, F., & Najafzadeh, M. (2020). A reliability-based probabilistic evaluation of the wave-induced scour depth around marine structure piles. Ocean Engineering, 196, Article 106818. https://doi.org/10.1016/j.oceaneng.2019.106818
Homaei, F., & Najafzadeh, M. (2022). Failure analysis of scouring at pile groups exposed to steady-state flow: On the assessment of reliability-based probabilistic methodology. Ocean Engineering, 266(Part 3), Article 112707. https://doi.org/10.1016/j.oceaneng.2022.112707
Kalinli, A., Acar, M. C., & Gunduz, Z. (2011). New approaches to determine the ultimate bearing capacity of shallow foundations based on artificial nerual networks and ant colony optimization. Engineering Geology, 117(1–2), 29–38. https://doi.org/10.1016/j.enggeo.2010.10.002
Kardani, M. N., Baghban, A., Sasanipour, J., Mohammadi, Amir, H., & Habibzadeh, S. (2018). Group contribution methods for estimating CO2 absorption capacities of imidazolium and ammonium-based polyionic liquids. Journal of Cleaner Production, 203, 601–618. https://doi.org/10.1016/j.jclepro.2018.08.127
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Lin, H. M., Chang, S. K., Wu, S. K., & Juang, C. H. (2009). Neural network-based model for assessing failure potential of highway slopes in the Alishan, Taiwan Area: Pre- and post earthquake investigation. Engineering Geology, 104(3–4), 280–289. https://doi.org/10.1016/j.enggeo.2008.11.007
Luo, R. P., Yang, M., & Li, W. C. (2018). Normalized settlement of piled raft in homogeneous clay. Computers and Geotechnics, 103, 165–178. https://doi.org/10.1016/j.compgeo.2018.07.023
Mercer, J. (1909). Functions of positive and negative type, and their connection with the theory of integral equations. Proceedings of the Royal Society A, 209, 415–446. https://doi.org/10.1098/rspa.1909.0075
Momeni, E., Nazir, R., Armaghani, D. J., & Maizir, H. (2014). Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN. Measurement, 57, 122–131. https://doi.org/10.1016/j.measurement.2014.08.007
Murlidhar, B. R., Sinha, R. K., Mohamad, E. T., Sonkar, R., & Khorami, M. (2020). The effects of particle swarm optimisation and genetic algorithm on ANN results in predicting pile bearing capacity. International Journal of Hydromechatronics, 3(1), 69–87. https://doi.org/10.1504/IJHM.2020.105484
Najafzadeh, M. (2015). Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions. Ocean Engineering, 99, 85–94. https://doi.org/10.1016/j.oceaneng.2015.01.014
Najafzadeh, M., & Azamathulla, H. M. (2013a). Group method of data handling to predict scour depth around bridge piers. Neural Computing and Applications, 23, 2107–2112. https://doi.org/10.1007/s00521-012-1160-6
Najafzadeh, M., & Azamathulla, H. M. (2013b). Neuro-fuzzy GMDH to predict the scour pile groups due to waves. Journal of Computing in Civil Engineering, 29(5), Article 04014068. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000376
Najafzadeh, M., & Barani, G.-A. (2011). Comparison of group method of data handling based genetic programming and back propagation system to predict scour depth around bridge piers. Scientia Iranica, 18(6), 1207–1213. https://doi.org/10.1016/j.scient.2011.11.017
Najafzadeh, M., & Oliveto, G. (2021). More reliable predictions of clear-water scour depth at pile groups by robust artificial intelligence techniques while preserving physical consistency. Soft Computing, 25, 5723–5746. https://doi.org/10.1007/s00500-020-05567-3
Najafzadeh, M., & Mahmoudi-Rad, M. (2024). New empirical equations to assess energy efficiency of flow-dissipating vortex dropshaft. Engineering Applications of Artificial Intelligence, 131, Article 107759. https://doi.org/10.1016/j.engappai.2023.107759
Najafzadeh, M., Barani, G.-A., & Azamathulla, H. M. (2013). GMDH to predict scour depth around a pier in cohesive soils. Applied Ocean Research, 40, 35–41. https://doi.org/10.1016/j.apor.2012.12.004
Najafzadeh, M., Etemad-Shahidi, A., & Lim, S. Y. (2016). Scour prediction in long contractions using ANFIS and SVM. Ocean Engineering, 111, 128–135. https://doi.org/10.1016/j.oceaneng.2015.10.053
Nejad, F. P., & Jaksa, M. B. (2017). Load-settlement behavior modeling of single piles using artificial neural networks and CPT data. Computers and Geotechnics, 89, 9–21. https://doi.org/10.1016/j.compgeo.2017.04.003
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