AI-driven triple-optimization based on ant colony optimization for minimizing deformation energy in three-dimensional analysis of bottom-hole assemblies

  • Qinfeng DI ,
  • Dakun LUO ,
  • Heyuan YANG ,
  • Tianxin LI ,
  • Wenchang WANG ,
  • Feng CHEN ,
  • H. ZHANG
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  • 1.Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China
    2.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
    3.School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China
    4.School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200444, China
    5.Itasca Consulting Group, Minneapolis 55401, MN, U. S. A.
Wenchang WANG, E-mail: wangwenchang1982@163.com

Received date: 2025-11-12

  Revised date: 2026-03-26

  Online published: 2026-06-18

Supported by

Project supported by the National Natural Science Foundation of China (Nos.?52174003, 52574006, and 52374008) and Subproject of the National Science and Technology Major Project of China (No.?2024ZD1401805)

Copyright

© Shanghai University 2026

Abstract

An accurate analysis of the three-dimensional (3D) deformed configuration of a bottom-hole assembly (BHA) is critical for predicting and controlling well paths in directional drilling. Among the various numerical approaches, the weighted residual method exhibits superior performance owing to its semi-analytical nature, enabling high accuracy in handling diverse boundary conditions. In previous studies, the weighted residual method has been coupled with a dual optimization process to determine the 3D deformation and tangency point of the BHA. However, its applicability is limited by the conventional treatment of contact interactions between the BHA and wellbore wall. Specifically, stabilizer-wellbore contacts are regarded as predefined boundary conditions, rather than solving these contact positions as unknown variables consistent with actual downhole conditions. This limitation reduces modeling fidelity in complex downhole environments. To address this limitation, this study enhances the optimization-based weighted residual method by introducing ant colony optimization (ACO) to solve the 3D contact problem. In the proposed framework, the bending energy of the deformed BHA is conceptualized as “food”, while the contact positions and orientations of stabilizers are assigned a measure of “taste”. Through this metaphor, the ACO algorithm employs artificial “ants” to explore the optimal stabilizer locations and orientations that minimize the BHA bending energy, thereby refining the computed 3D deformation. The simulation results demonstrate that integrating ACO into the previously established dual optimization framework enables the effective determination of the contact configuration between the BHA and wellbore wall. As a result, the overall accuracy of the 3D BHA deformation analysis is significantly improved. In one representative case study, the bending energy of the BHA is reduced by 55.6% compared with that obtained from the original dual-optimization method.

Cite this article

Qinfeng DI , Dakun LUO , Heyuan YANG , Tianxin LI , Wenchang WANG , Feng CHEN , H. ZHANG . AI-driven triple-optimization based on ant colony optimization for minimizing deformation energy in three-dimensional analysis of bottom-hole assemblies[J]. Applied Mathematics and Mechanics, 2026 , 47(6) : 1417 -1432 . DOI: 10.1007/s10483-026-3399-9

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