Modelling Plate Penetration in Bekker Soil Model Using Machine Learning for Off-Road Vehicles

Articles in Press

Document Type : Research Article- En

Authors

• A. Nazari Chamki
• A. Mardani
• A. Hosainpour

Department of Mechanical Engineering of Biosystems, Faculty of Agriculture, Urmia University, Urmia, Iran

https://doi.org/10.22067/jam.2025.93736.1386

Abstract

The study of soil behaviour in wheel interaction is complex due to the wheel's geometry and the varying soil conditions. Traditional measurements of soil parameters, such as the Bevameter and the cone penetrometer, are time-consuming and labour-intensive. This research presents a machine learning-based approach to predict soil sinkage in plate penetration tests, providing a suitable alternative to conventional methods. A soil bin with controlled experimental conditions was used to collect data, which was measured by a load cell and a magnetic encoder at a constant penetration rate of 4 mm s^-1. Two main machine learning models were selected; XGBoost and CatBoost. Hybrid versions of these models were developed using the Shrike Bird Optimisation Algorithm (SBOA). The results showed that the hybrid models outperformed the base models. The SBOA-CatBoost hybrid model achieved the highest accuracy on the training data with a coefficient of determination of 0.99, a mean square error of 2.81, and a mean absolute error of 0.79. The findings of this study highlight the potential of machine learning as a cost-effective and efficient alternative to traditional methods for measuring soil parameters. Further research is recommended to validate these models in different soil types and conditions.

Keywords

• Bevameter
• CatBoost
• SBOA
• Soil bin
• Terramechanics
• XGBoost

Main Subjects

• Modeling

References

1. Ani, O. A., Uzoejinwa, B. B., Ezeama, A. O., Onwualu, A. P., Ugwu, S. N., & Ohagwu, C. J. (2018). Overview of soil-machine interaction studies in soil bins. Soil and Tillage Research, 175, 13-27. https://doi.org/10.1016/j.still.2017.08.002
2. Bekker, M. G. (1969). Off-Road Locomotion. Ordnance, 53(292), 416-418. Retrieved from http://www.jstor.org/stable/45361962
3. Bentéjac, C., Csörgő, A., & Martínez-Muñoz, G. (2021). A comparative analysis of gradient boosting algorithms. Artificial Intelligence Review, 54(3), 1937-1967. https://doi.org/10.1007/s10462-020-09896-5
4. Brunskill, C., Patel, N., Gouache, T. P., Scott, G. P., Saaj, C. M., Matthews, M., & Cui, L. (2011). Characterisation of martian soil simulants for the ExoMars rover testbed. Journal of Terramechanics, 48(6), 419-438. https://doi.org/10.1016/j.jterra.2011.10.001
5. Carman, K. (2002). Compaction characteristics of towed wheels on clay loam in a soil bin. Soil and Tillage Research, 65(1), 37-43.
6. Chou, C. C., Zhu, F., Skelton, P., Wagner, C., & Yang, K. (2011). Numerical simulations of tyre/soil interaction using geomaterial properties characterised with a new calibration method. International Journal of Vehicle Safety, 5(4), 287-306. https://doi.org/10.1504/IJVS.2011.045784
7. De Janosi, P. E. (1959). Factors influencing the demand for new automobiles. Journal of Marketing, 23(4), 412-418. https://doi.org/10.1177/002224295902300408
8. Golanbari, Behzad, & Mardani, A. (2023). Analytical Traction Force Model Development for Soil-Tire Interaction: Incorporating Dynamic Contact Area and Parameter Analysis Using Taguchi Method. Biomechanism and Bioenergy Research, 2(2), 56-64. https://doi.org/22103/bbr.2023.22356.1059
9. Golanbari, B., & Mardani, A. (2024). An analytical model for stress estimation at the soil-tire interface using the dynamic contact length. Journal of Terramechanics, 111, 1-7. https://doi.org/10.1016/j.jterra.2023.08.006
10. Golanbari, B., Mardani, A., Farhadi, N., & Nazari Chamki, A. (2025). Applications of machine learning in predicting rut depth in off-road environments. Scientific Reports, 15(1), 5486. https://doi.org/10.1038/s41598-025-90054-8
11. Golanbari, B., Mardani, A., Farhadi, N., & Reina, G. (2024). Machine learning applications in off-road vehicles interaction with terrain: An overview. Journal of Terramechanics, 116, 101003. https://doi.org/10.1016/j.jterra.2024.101003
12. Golanbari, B., Mardani, A., Hosainpour, A., & Taghavifar, H. (2023). Modeling Soil Deformation for Off-Road Vehicles Using Deep Learning Optimized by Grey Wolf Algorithm. Journal of Agricultural Machinery, 14(1), 69-82. https://doi.org/10.22067/jam.2023.84339.1188
13. Golanbari, B., Mardani, A., Hosainpour, A., & Taghavifar, H. (2025). Predicting terrain deformation patterns in off-road vehicle-soil interactions using TRR algorithm. Journal of Terramechanics, 117, 101021. https://doi.org/10.1016/j.jterra.2024.101021
14. Huang, Z.-K., Zhang, D.-M., & Xie, X.-C. (2022). A practical ANN model for predicting the excavation-induced tunnel horizontal displacement in soft soils. Underground Space, 7(2), 278-293. https://doi.org/10.1016/j.undsp.2021.07.009
15. Kim, J.-T., Im, D.-U., Choi, H.-J., Oh, J.-W., & Park, Y.-J. (2021). Development and performance evaluation of a bevameter for measuring soil strength. Sensors, 21(4), 1541. https://doi.org/10.3390/s21041541
16. Laughery, S., Gerhart, G., & Muench, P. (2000). Evaluating Vehicle Mobility Using Bekker’s Equations. Tacom Research Development and Engineering Center Warren Mi.
17. Mardani, A., & Golanbari, B. (2024). Indoor measurement and analysis on soil-traction device interaction using a soil bin. Scientific Reports, 14(1), 10077. https://doi.org/10.1038/s41598-024-59800-2
18. Mason, G. L., Salmon, J. E., McLeod, S., Jayakumar, P., Cole, M. P., & Smith, W. (2020). An overview of methods to convert cone index to bevameter parameters. Journal of Terramechanics, 87, 1-9. https://doi.org/10.1016/j.jterra.2019.10.001
19. Negrut, D., Hu, W., Li, P., Unjhawala, H. M., & Serban, R. (2023). Calibration of an expeditious terramechanics model using a higher-fidelity model, Bayesian inference, and a virtual bevameter test. https://doi.org/10.1002/rob.22276
20. Rashidi, M., & Gholami, M. (2010). Prediction of soil sinkage by multiple loadings using the finite element method.
21. Taghavifar, H., & Mardani, A. (2014a). Effect of velocity, wheel load and multipass on soil compaction. Journal of the Saudi Society of Agricultural Sciences, 13(1), 57-66. https://doi.org/10.1016/j.jssas.2013.01.004
22. Taghavifar, H., & Mardani, A. (2014b). Wavelet neural network applied for prognostication of contact pressure between soil and driving wheel. Information Processing in Agriculture, 1(1), 51-56. https://doi.org/10.1016/j.inpa.2014.05.002
23. Taghavifar, H., & Mardani, A. (2017). Off-road vehicle dynamics. Studies in Systems, Decision and Control, 70, 37. https://doi.org/10.1007/978-3-319-42520-7
24. Taghavifar, H., Mardani, A., & Karim-Maslak, H. (2014). Multi-criteria optimization model to investigate the energy waste of off-road vehicles utilizing soil bin facility. Energy, 73, 762-770. https://doi.org/10.1016/j.energy.2014.06.081
25. Thornton, B., Pesheck, E., & Jayakumar, P. (2023). A Combined Simple/Complex Terramechanics Representation Part 1: Using Machine Learning to Identify DEM Soil Properties From Bevameter Test Data. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 87387, p. V010T10A019). American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2023-117123
26. Van, N. N., Matsuo, T., Koumoto, T., & Inaba, S. (2008). Experimental device for measuring sandy soil sinkage parameters. Bulletin of the Faculty of Agriculture Saga University, 93(1), 91-99.
27. Wong, J. Y. (1989). Terramechanics and off-road vehicles.