Research on Stick-Slip Vibration Suppression Method of Drill String Based on Machine Learning Optimization
Ariticle ID:
1677
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Abstract
During the drilling process, stick-slip vibration of the drill string is mainly caused by the nonlinear friction generated by the contact between the drill bit and the rock. To eliminate the fatigue wear of downhole drilling tools caused by stick-slip vibrations, the Fractional-Order Proportional-Integral-Derivative (FOPID) controller is used to suppress stick-slip vibrations in the drill string. Although the FOPID controller can effectively suppress the drill string stick-slip vibration, its structure is flexible and parameter setting is complicated, so it needs to use the corresponding machine learning algorithm for parameter optimization. Based on the principle of torsional vibration, a simplified model of multi-degree-of-freedom drill string is established and its block diagram is designed. The continuous nonlinear friction generated by cutting rock is described by the LuGre friction model. The adaptive learning strategy of genetic algorithm (GA), particle swarm optimization (PSO) and particle swarm optimization improved (IPSO) by arithmetic optimization (AOA) is used to optimize and adjust the controller parameters, and the drill string stick-slip vibration is suppressed to the greatest extent. The results show that: When slight drill string stick-slip vibration occurs, the FOPID controller optimized by machine learning algorithm has a good effect on suppressing drill string stick-slip vibration. However, the FOPID controller cannot get the drill string system which has fallen into serious stick-slip vibration (stuck pipe) out of trouble, and the machine learning algorithm is required to mark a large amount of data on adjacent Wells to train the model. Set a reasonable range of drilling parameters (weight on bit/drive torque) in advance to avoid severe stick-slip vibration (stuck pipe) in the drill string system.
References
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International Conference and Exhibition, Lagos, Nigeria. https://doi.org/10.2118/184381-MS
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on PID control. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,
234(1), 82–94. https://doi.org/10.1177/1464419319876397
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uncertainty in drill strings containing torsional vibration tool using sliding-mode cont-rol. Proceedings of the
Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 235(4), 653–667. https://doi.
org/10.1177/14644193211045273
6. Depouhon, A., Detournay, E. (2014). Instability regimes and self-excited vibrations in deep drilling systems.
Journal of Sound and Vibration, 333(7), 2019–2039. https://doi.org/10.1016/j.jsv.2013.11.011
7. Navarro-Lopez, E. M., Cortes, D. (2007). Avoiding harmful oscillations in a drill string through dynamical
analysis. Journal of Sound and Vibration, 307(1/2), 152–171. https://doi.org/10.1016/j.jsv.2007.06.035
8. Richard, T., Germay, C., Detournay, E. (2004). Self-excited stick-slip oscillations of drill bits. Comptes Rendus
Mécanique, 332(8), 619–626. https://doi.org/10.1016/j.crme.2004.04.004
9. Khulief, Y. A. (2010). Control engineering and stick-slip vibration in drilling. Journal of Petroleum Science and
Engineering, 72(3–4), 199–211. https://doi.org/10.1016/j.petrol.2010.06.008
SV, 2023, vol.57 115
10. Smit, A. T. (1999). Using of optimal control techniques to dampen torsional drill strings vibrations, vol. 1999,
pp. 20–45. Netherlands: University of Twente. https://doi.org/10.3990/1.9789036513529
11. Canudas-De-Wit, C., Rubio, F. R., Corchero, M. A. (2008). DOSKIL: A new mechanism for controlling stick-slip
oscillations in oil well drill strings. IEEE Transactions on Control Systems Technology, 16(6), 1171–1191. https://
doi.org/10.1109/TCST.2008.918365
12. Tucker, R. W., Wang, C. (1999). On the effective control of torsional vibrations of drill string systems. Journal of
Sound and Vibration, 224(1), 101–122. https://doi.org/10.1006/jsvi.1999.2115
13. Yousefi, S., Arefi, M. M. (2020). Online optimization of fractional order PID controllers for stick-slip vibration
suppression in drilling systems using a deep reinforcement learning approach. Journal of Petroleum Science
and Engineering, 185, 106655.
14. Karkoub, M., Abdel-Magid, Y. L., Balachandran, B. (2009). Drill-string torsional vibration suppres- sion using GA
optimized controllers. Journal of Canadian Petroleum Technology, 48(12), 32–38. https://doi.org/10.2118/
09-12-32
15. Navarro-López, E. M., Cortés, D. (2007). Sliding-mode control of a multi-DOF oilwell drill string with stick-slip
oscillations. American Control Conference, pp. 3837–3842. IEEE, New York, NY, USA. https://doi.org/10.1109/
ACC.2007.4282769
16. Tavakkoli-Moghaddam, R., Mohaghegh, M., Aghayari, R. (2020). A new fractional order PID controller for
suppression of stick-slip vibrations in drilling systems: A combination of particle swarm optimization and
bacterial foraging algorithm. Journal of Petroleum Science and Engineering, 185, 106536.
17. Lyu, M., Shen, S. (2014). The simulation and analysis of drill string stick-slip vibration. Journal of Southwest
Petroleum University: Science & Technology Edition, 36(6), 150–159. https://doi.org/10.11885/j.issn.
1674-5086.2013.02.22.02
18. Fu, M., Li, J., Wu, Y., S, S., A, Z. et al. (2019). State feedback and torque feed forward combined control system for
suppressing drill-strings stick-slip vibration. Journal of Mechanical Engineering, 55(14), 1–10. https://doi.org/10.
3901/JME.2019.14.001
19. Zhang, Q., Xu, S. (2020). Suppression of stick-slip vibration of drill string by fractional-order PID control. China
Petroleum Machinery, 48(3), 44–50. https://doi.org/10.16082/j.cnki.issn.1001-4578.2020.03.008
20. Gad, S., Metered, H., Bassuiny, A., Abdel Ghany, A. M. (2017). Multi-objective genetic algorithm fracti-onalorder pid controller for semi-active magnetorheologically damped seat suspension. Journal of Vibration and
Control, 23(8), 1248–1266. https://doi.org/10.1177/1077546315591620
21. Mohaghegh, M., Tavakkoli-Moghaddam, R., Khorasani, K. (2020). A novel multi-objective optimization
algorithm based on the pareto dominance and reinforcement learning for the stick-slip vibration control
problem. Journal of Petroleum Science and Engineering, 191, 107213.
22. Muftah, M. N., Faudzi, A. A. M., Sahlan, S., Shouran, M. (2022). Modeling and fuzzy FOPID controller tuned by
PSO for pneumatic positioning system. Energies, 15(10), 3757. https://doi.org/10.3390/en15103757
23. Mohamed, M. E. A., Guo, Y. (2019). Separately excited DC motor speed tracking control using adaptive neurofuzzy inference system based on genetic algorithm particle swarm optimization and fuzzy auto-tuning PID. IOP
Conference Series: Earth and Environmental Science, vol. 300, no. 4, 042114. IOP Publishing, San Francisco,
USA.
24. Castro, F., Bernardes, N. D., Cuadros, M., Almeida, G. M. (2016). Comparison of fractional and integer PID
controllers tuned by genetic algorithm. IEEE Transactions on Industrial Electronics, 63(3), 1821–1830. https://
doi.org/10.1109/INDUSCON.2016.7874389
25. Ahmadi, A., Bahmani, M. (2019). A hybrid machine learning approach for real-time optimization of the drilling
process to mitigate stick-slip vibrations. Journal of Petroleum Science and Engineering, 178, 300–310.
26. Pérez-Aracil, J., Camacho-Gómez, C., Pereira, E., Vaziri, V., Aphale, S. S. et al. (2021). Eliminating stick-slip
vibrations in drill-strings with a dual-loop control strategy optimised by the CRO-SL algorithm. Mathematics,
9(13), 1526. https://doi.org/10.3390/math9131526
27. Khulief, Y. A., Al-Sulaiman, F. A., Bashmal, S. (2007). Vibration analysis of drill strings with self-excited stickslip oscillations. Journal of Sound and Vibration, 299(3), 540–558. https://doi.org/10.1016/j.jsv.2006.06.035
116 SV, 2023, vol.57
28. Lin, Y. Q., Wang, Y. H. (1991). Stick-slip vibration of the drill strings. Journal of Manufacturing Science and
Engineering, 113(1), 38–43. https://doi.org/10.1016/j.jsv.2006.06.065
29. Lopez, E. N., Navarro-Lopez, E. M., Suarez, R. (2004). Modelling and analysis of stick-slip behavior in a drill
string under dry frictions. Congreso de la AMCA 2004: Congress of the Mexican Association of Computational
Mechanics, pp. 1–10. Mexico City, Mexico. https://doi.org/10.1016/j.jsv.2014.08.001
30. Wit, C., Olsson, H., Åström, K. J., Lischinsky, P. (1995). A new model for control of systems with friction. IEEE
Transactions on Control Systems Technology, 3(3), 419–425. https://doi.org/10.1109/9.376054
31. Derbal, M., Gharib, M., Refaat, S. S., Palazzolo, A., Sassi, S. (2021). Fractional-order controllers for stick-slip
vibration mitigation in oil well drill-strings. Journal of Low Frequency Noise, Vibration and Active Control,
40(3), 1571–1584. https://doi.org/10.1177/1461348420984040
32. Kanagaraj, N., Jha, V. N. (2021). Design of an enhanced fractional order PID controller for a class of second-order
system. COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic
Engineering, 40(3), 579–592. https://doi.org/10.1108/COMPEL-08-2020-0267
33. Chen, M., Gao, Y. (2019). Parameter tuning of fractional order PID controller based on deep reinforcement
learning for drilling systems. ISA Transactions, 96, 450–457.
34. Xue, D., Zhao, C., Chen, Y. (2006). A modified approximation method of fractional order system.
2006 International Conference on Mechatronics and Automation (ICMA 2006), vol. 3, pp. 1043–1048. IEEE,
Luoyang, China. https://doi.org/10.1109/ICMA.2006.257697
35. Abiyev, R. (2014). Design of fractional order controllers using genetic algorithms. British Journal of Mathematics
& Computer Science, 4(18), 2594–2602. https://doi.org/10.9734/BJMCS/2014/10447
36. Pour, M. S., Parsa, S. (2019). Stick-slip vibration suppression in drilling systems using a new method based on a
fuzzy fractional order PID controller optimized by a genetic algorithm. Journal of Petroleum Science and
Engineering, 180, 521–535.
37. Srinivas, M., Patnaik, L. M. (1994). Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE
Transactions on Systems,Man,and Cybernetics, 24(4), 656–667. https://doi.org/10.1109/21.286374
38. Chen, C., Hu, L., Ma, Y., Zhang, Y., Li, Y. (2016). Improved genetic algorithm for optimal fractional order PID
controller. Journal of Xi’an Technological University, 36(6), 510–516. https://doi.org/10.1081/CEH-200044273
39. Zhang, X., Zhong, C. Q. (2018). Fractional order PIλDμ controller design based on quantum particle swarm
optimization. Control Engineering of China, 25(3), 493–498. https://doi.org/10.14107/j.cnki.kzgc.1001-9669.
2018.03.067
40. Abualigah, L., Diabat, A., Mirjalili, S., Faris, H., Aljarah, I. (2021). The arithmetic optimization algorithm.
Computer Methods in Applied Mechanics and Engineering, 376, 113610. https://doi.org/10.1016/j.cma.2021.
113610
41. Teng, X., Di, Q. F., Li, N., Chen, F., Zhou, B. (2017). Measurement and analysis of stick-slip characteristics of drill
string in ultra-deep wells. Petroleum Drilling Techniques, 45(2), 32–39. https://doi.org/10.11911/syztjs
7(3), 168–174. https://doi.org/10.2118/23606-PA
2. Feng, M., Chen, B., He, X. (2019). A review of stick-lip vibration control in oilwell drilling. IEEE Access, 7,
156158–156173.
3. Asgharzadeh, A., Bello, O., Baptista, N. R. P., Carvajal, C. A. P., Oppelt, J. (2016). Qualitative analysis of drill
string torsional vibration preventive measures: Present status and future possible solution. SPE Nigeria Annual
International Conference and Exhibition, Lagos, Nigeria. https://doi.org/10.2118/184381-MS
4. Tian, J., Zhou, Y., Yang, L., Hu, S. (2020). Analysis of stick-slip reduction for a new torsional vibration tool based
on PID control. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,
234(1), 82–94. https://doi.org/10.1177/1464419319876397
5. Tian, J., Wang, J., Zhou, S., Yang, Y., Dai, L. (2021). Study of stick-slip suppression and robustness to parametric
uncertainty in drill strings containing torsional vibration tool using sliding-mode cont-rol. Proceedings of the
Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 235(4), 653–667. https://doi.
org/10.1177/14644193211045273
6. Depouhon, A., Detournay, E. (2014). Instability regimes and self-excited vibrations in deep drilling systems.
Journal of Sound and Vibration, 333(7), 2019–2039. https://doi.org/10.1016/j.jsv.2013.11.011
7. Navarro-Lopez, E. M., Cortes, D. (2007). Avoiding harmful oscillations in a drill string through dynamical
analysis. Journal of Sound and Vibration, 307(1/2), 152–171. https://doi.org/10.1016/j.jsv.2007.06.035
8. Richard, T., Germay, C., Detournay, E. (2004). Self-excited stick-slip oscillations of drill bits. Comptes Rendus
Mécanique, 332(8), 619–626. https://doi.org/10.1016/j.crme.2004.04.004
9. Khulief, Y. A. (2010). Control engineering and stick-slip vibration in drilling. Journal of Petroleum Science and
Engineering, 72(3–4), 199–211. https://doi.org/10.1016/j.petrol.2010.06.008
SV, 2023, vol.57 115
10. Smit, A. T. (1999). Using of optimal control techniques to dampen torsional drill strings vibrations, vol. 1999,
pp. 20–45. Netherlands: University of Twente. https://doi.org/10.3990/1.9789036513529
11. Canudas-De-Wit, C., Rubio, F. R., Corchero, M. A. (2008). DOSKIL: A new mechanism for controlling stick-slip
oscillations in oil well drill strings. IEEE Transactions on Control Systems Technology, 16(6), 1171–1191. https://
doi.org/10.1109/TCST.2008.918365
12. Tucker, R. W., Wang, C. (1999). On the effective control of torsional vibrations of drill string systems. Journal of
Sound and Vibration, 224(1), 101–122. https://doi.org/10.1006/jsvi.1999.2115
13. Yousefi, S., Arefi, M. M. (2020). Online optimization of fractional order PID controllers for stick-slip vibration
suppression in drilling systems using a deep reinforcement learning approach. Journal of Petroleum Science
and Engineering, 185, 106655.
14. Karkoub, M., Abdel-Magid, Y. L., Balachandran, B. (2009). Drill-string torsional vibration suppres- sion using GA
optimized controllers. Journal of Canadian Petroleum Technology, 48(12), 32–38. https://doi.org/10.2118/
09-12-32
15. Navarro-López, E. M., Cortés, D. (2007). Sliding-mode control of a multi-DOF oilwell drill string with stick-slip
oscillations. American Control Conference, pp. 3837–3842. IEEE, New York, NY, USA. https://doi.org/10.1109/
ACC.2007.4282769
16. Tavakkoli-Moghaddam, R., Mohaghegh, M., Aghayari, R. (2020). A new fractional order PID controller for
suppression of stick-slip vibrations in drilling systems: A combination of particle swarm optimization and
bacterial foraging algorithm. Journal of Petroleum Science and Engineering, 185, 106536.
17. Lyu, M., Shen, S. (2014). The simulation and analysis of drill string stick-slip vibration. Journal of Southwest
Petroleum University: Science & Technology Edition, 36(6), 150–159. https://doi.org/10.11885/j.issn.
1674-5086.2013.02.22.02
18. Fu, M., Li, J., Wu, Y., S, S., A, Z. et al. (2019). State feedback and torque feed forward combined control system for
suppressing drill-strings stick-slip vibration. Journal of Mechanical Engineering, 55(14), 1–10. https://doi.org/10.
3901/JME.2019.14.001
19. Zhang, Q., Xu, S. (2020). Suppression of stick-slip vibration of drill string by fractional-order PID control. China
Petroleum Machinery, 48(3), 44–50. https://doi.org/10.16082/j.cnki.issn.1001-4578.2020.03.008
20. Gad, S., Metered, H., Bassuiny, A., Abdel Ghany, A. M. (2017). Multi-objective genetic algorithm fracti-onalorder pid controller for semi-active magnetorheologically damped seat suspension. Journal of Vibration and
Control, 23(8), 1248–1266. https://doi.org/10.1177/1077546315591620
21. Mohaghegh, M., Tavakkoli-Moghaddam, R., Khorasani, K. (2020). A novel multi-objective optimization
algorithm based on the pareto dominance and reinforcement learning for the stick-slip vibration control
problem. Journal of Petroleum Science and Engineering, 191, 107213.
22. Muftah, M. N., Faudzi, A. A. M., Sahlan, S., Shouran, M. (2022). Modeling and fuzzy FOPID controller tuned by
PSO for pneumatic positioning system. Energies, 15(10), 3757. https://doi.org/10.3390/en15103757
23. Mohamed, M. E. A., Guo, Y. (2019). Separately excited DC motor speed tracking control using adaptive neurofuzzy inference system based on genetic algorithm particle swarm optimization and fuzzy auto-tuning PID. IOP
Conference Series: Earth and Environmental Science, vol. 300, no. 4, 042114. IOP Publishing, San Francisco,
USA.
24. Castro, F., Bernardes, N. D., Cuadros, M., Almeida, G. M. (2016). Comparison of fractional and integer PID
controllers tuned by genetic algorithm. IEEE Transactions on Industrial Electronics, 63(3), 1821–1830. https://
doi.org/10.1109/INDUSCON.2016.7874389
25. Ahmadi, A., Bahmani, M. (2019). A hybrid machine learning approach for real-time optimization of the drilling
process to mitigate stick-slip vibrations. Journal of Petroleum Science and Engineering, 178, 300–310.
26. Pérez-Aracil, J., Camacho-Gómez, C., Pereira, E., Vaziri, V., Aphale, S. S. et al. (2021). Eliminating stick-slip
vibrations in drill-strings with a dual-loop control strategy optimised by the CRO-SL algorithm. Mathematics,
9(13), 1526. https://doi.org/10.3390/math9131526
27. Khulief, Y. A., Al-Sulaiman, F. A., Bashmal, S. (2007). Vibration analysis of drill strings with self-excited stickslip oscillations. Journal of Sound and Vibration, 299(3), 540–558. https://doi.org/10.1016/j.jsv.2006.06.035
116 SV, 2023, vol.57
28. Lin, Y. Q., Wang, Y. H. (1991). Stick-slip vibration of the drill strings. Journal of Manufacturing Science and
Engineering, 113(1), 38–43. https://doi.org/10.1016/j.jsv.2006.06.065
29. Lopez, E. N., Navarro-Lopez, E. M., Suarez, R. (2004). Modelling and analysis of stick-slip behavior in a drill
string under dry frictions. Congreso de la AMCA 2004: Congress of the Mexican Association of Computational
Mechanics, pp. 1–10. Mexico City, Mexico. https://doi.org/10.1016/j.jsv.2014.08.001
30. Wit, C., Olsson, H., Åström, K. J., Lischinsky, P. (1995). A new model for control of systems with friction. IEEE
Transactions on Control Systems Technology, 3(3), 419–425. https://doi.org/10.1109/9.376054
31. Derbal, M., Gharib, M., Refaat, S. S., Palazzolo, A., Sassi, S. (2021). Fractional-order controllers for stick-slip
vibration mitigation in oil well drill-strings. Journal of Low Frequency Noise, Vibration and Active Control,
40(3), 1571–1584. https://doi.org/10.1177/1461348420984040
32. Kanagaraj, N., Jha, V. N. (2021). Design of an enhanced fractional order PID controller for a class of second-order
system. COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic
Engineering, 40(3), 579–592. https://doi.org/10.1108/COMPEL-08-2020-0267
33. Chen, M., Gao, Y. (2019). Parameter tuning of fractional order PID controller based on deep reinforcement
learning for drilling systems. ISA Transactions, 96, 450–457.
34. Xue, D., Zhao, C., Chen, Y. (2006). A modified approximation method of fractional order system.
2006 International Conference on Mechatronics and Automation (ICMA 2006), vol. 3, pp. 1043–1048. IEEE,
Luoyang, China. https://doi.org/10.1109/ICMA.2006.257697
35. Abiyev, R. (2014). Design of fractional order controllers using genetic algorithms. British Journal of Mathematics
& Computer Science, 4(18), 2594–2602. https://doi.org/10.9734/BJMCS/2014/10447
36. Pour, M. S., Parsa, S. (2019). Stick-slip vibration suppression in drilling systems using a new method based on a
fuzzy fractional order PID controller optimized by a genetic algorithm. Journal of Petroleum Science and
Engineering, 180, 521–535.
37. Srinivas, M., Patnaik, L. M. (1994). Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE
Transactions on Systems,Man,and Cybernetics, 24(4), 656–667. https://doi.org/10.1109/21.286374
38. Chen, C., Hu, L., Ma, Y., Zhang, Y., Li, Y. (2016). Improved genetic algorithm for optimal fractional order PID
controller. Journal of Xi’an Technological University, 36(6), 510–516. https://doi.org/10.1081/CEH-200044273
39. Zhang, X., Zhong, C. Q. (2018). Fractional order PIλDμ controller design based on quantum particle swarm
optimization. Control Engineering of China, 25(3), 493–498. https://doi.org/10.14107/j.cnki.kzgc.1001-9669.
2018.03.067
40. Abualigah, L., Diabat, A., Mirjalili, S., Faris, H., Aljarah, I. (2021). The arithmetic optimization algorithm.
Computer Methods in Applied Mechanics and Engineering, 376, 113610. https://doi.org/10.1016/j.cma.2021.
113610
41. Teng, X., Di, Q. F., Li, N., Chen, F., Zhou, B. (2017). Measurement and analysis of stick-slip characteristics of drill
string in ultra-deep wells. Petroleum Drilling Techniques, 45(2), 32–39. https://doi.org/10.11911/syztjs
Published
2024-09-01
How to Cite
Su, K. (2024). Research on Stick-Slip Vibration Suppression Method of Drill String Based on Machine Learning Optimization. Sound & Vibration, 58(1). Retrieved from https://ojs.acad-pub.com/index.php/SV/article/view/1677
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