Abstract
In order to promote the stability of a self-propelled capsule moving in digestive tract, the target moving speed, the minimal impact force and the minimal energy consumption are considered as the optimisation objectives simultaneously. The uncertainty of small intestine environment is described by varying the external friction coefficient of capsule. Under such circumstances, NSGA-II, Monte Carlo, and Six-Sigma algorithms are combined to conduct the multi-objective optimisation of both the control and structure parameters based on reliability analysis. Compared with the passive capsules which can only move in one direction relying on small intestine peristalsis, the bi-directional motion can be fulfilled by the self-propelled capsule via adjusting its optimisation parameters. According to the obtained optimisation result, the forward motion of the capsule can achieve a large scale of moving speeds; however, it is difficult for the capsule moving backward with high speed. The reliabilities of both the energy consumption and the impact force can reach 100% via reliability optimisations; however, the reliability of the target moving speed of capsule is hard to be promoted up to 90%. Both the optimisation method and the optimisation result introduced in the paper are expected to be benefit to the improvement of the self-propelled capsule system and its application in wireless endoscope.
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The numerical data sets generated and analysed during the current study are available from the corresponding author on reasonable request.
References
Liu Y, Páez Chávez J, Zhang J, Tian J, Guo B, Prasad S (2020) The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification. Meccanica 55:1885–1902
Guo B, Ley E, Tian J, Zhang J, Liu Y, Prasad S (2020) Experimental and numerical studies of intestinal frictions for propulsive force optimisation of a vibro-impact capsule system. Nonlinear Dyn 101:65–83
Guo B, Liu Y, Birler R, Prasad S (2020) Self-propelled capsule endoscopy for small-bowel examination: proof-of-concept and model verification. Int J Mech Sci 174:105506
Zhou H, Alici G (2019) A novel magnetic anchoring system for wireless capsule endoscopes operating within the gastrointestinal tract. IEEE–ASME Trans Mech 24:1106–1116
Gao J, Zhang Z, Yan G (2020) Locomotion analysis of a clamper-based capsule robot in a compliant tube. IEEE–ASME Trans Mech 26(1):55–65
Yan Y, Liu Y, Liao M (2017) A comparative study of the vibro-impact capsule systems with one-sided and two-sided constraints. Nonlinear Dyn 89(2):1063–1087
Liao M (2020) Nonlinear dynamic behavior of impact capsule oscillator based on wireless endoscope application. J Vib Shock 39(23):279–286
Tian J, Liu Y, Chen J, Guo B, Prasad S (2021) Finite element analysis of a self-propelled capsule robot moving in the small intestine. Int J Mech Sci 206:106621
Yan Y, Liu Y, Jiang H, Peng Z, Crawford A, Williamson J, Thomson J, Kerins G, Yusupov A, Islam S (2019) Optimization and experimental verification of the vibro-impact capsule system in fluid pipeline. Proc Inst Mech Eng C 233(3):880–894
Ing J, Pavlovskaia E, Wiercigroch M, Banerjee S (2008) Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing. Physica D 310:769–775
Liao M, Liu Y, Páez Chávez J, Chong ASE, Wiercigroch M, Wiercigroch M (2018) Dynamics of vibro-impact drilling with linear and nonlinear rock. Int J Mech Sci 146:200–210
Liao M, Ing J, Páez Chávez J, Wiercigroch M (2016) Bifurcation techniques for stiffness identification of an impact oscillator. Commun Nonlinear Sci Numer Simul 41:19–31
Liao M, Ing J, Sayah M, Wiercigroch M (2016) Dynamic method of stiffness identification in impacting systems for percussive drilling applications. Mech Syst Signal Process 80:224–244
Liao M, Wiercigroch M, Sayah M, Ing J (2021) Experimental verification of the percussive drilling model. Mech Syst Signal Process 146:107067
Guo B, Chávez JP, Liu Y, Liu C (2021) Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts. Commun Nonlinear Sci Numer Simul 102:105909
Guo SPB, Liu Y (2019) Modelling of capsule–intestine contact for a self-propelled capsule robot via experimental and numerical investigation. Nonlinear Dyn 98:3155–3167
Liu Y, Páez Chávez J, Zhang BGSPJ, Tian J (2020) The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification. Meccanica 55:1885–1902
Jiang Z, Xu J (2017) Analysis of worm-like locomotion driven by the sine-squared strain wave in a linear viscous medium. Mech Res Commun 85:33–44
Zhan X, Xu J, Fang H (2018) A vibration-driven planar locomotion robot-shell. Robotica 36(9):1402–1420
Zhang Q, Fang H, Xu J (2021) Yoshimura–Origami based earthworm-like robot with 3-dimensional locomotion capability. Front Robot AI 8:056012
Van der Velden A (2010) Isight design optimization methodologies. In: ASM handbook. ASM International, Materials Park
Chen X, Yu X, Ji B (2010) Study of crankshaft strength based on Isight platform and DOE methods. IEEE Comput Soc 3(3):548–551
Yin B, Xu D, An Y, Chen Y (2008) Aerodynamic optimization of 3D wing based on Isight. Appl Math Mech 29(5):603–610
Koch PN, Evans JP, Powell D (2002) Interdigitation for effective design space exploration using Isight. Struct Multidiscip Optim 23(2):111–126
Baril C, Yacout S, Clement B (2011) Design for Six Sigma through collaborative multi-objective optimization. Comput Ind Eng 60(1):43–55
Asafuddoula M, Singh HK, Ray T (2015) Six-Sigma robust design optimization using a many-objective decomposition-based evolutionary algorithm. IEEE Trans Evol Comput 19(4):490–507
Shirazi B, Fazlollahtabar H, Mahdavi I (2010) A six sigma based multi-objective optimization for machine grouping control in flexible cellular manufacturing systems with guide-path flexibility. Adv Eng Softw 41(6):865–873
Ray HSKAT, Asafuddoula M (2015) An approach to identify six-sigma robust solutions of multi/many-objective engineering design optimization problems. J Mech Des 137(5):051404
Zhang KCYWX, Lu Z (2020) A novel reliability sensitivity analysis method based on directional sampling and Monte Carlo simulation. Proc Inst Mech Eng O 234(4):622–635
Zhou L, Cai G, Yang J, Jia L (2010) Monte Carlo simulation based on FTA in reliability analysis of door system. In: International conference on computer and automation engineering, Singapore, Singapore
Li F, Brown RE, Freeman LAA (2003) A linear contribution factor model of distribution reliability indices and its applications in Monte Carlo simulation and sensitivity analysis. IEEE Trans Power Syst 18(3):1213–1215
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Yusoff Y, Ngadiman M, Zain A (2011) Overview of NSGA-II for optimizing machining process parameters. Procedia Eng 15:3978–3983
Diao B, Zhang X, Fang H, Xu J (2021) Bi-objective optimization for improving the locomotion performance of the vibration-driven robot. Arch Appl Mech 91(5):2073–2088
Zhan X, Xu J, Fang H (2020) In-plane gait planning for earthworm-like metameric robots using genetic algorithm. Bioinspir Biomim 15:056012
Acknowledgements
Dr. Maolin Liao would like to acknowledge the financial support from Beijing Municipal Natural Science Foundation (No. 3204049), and from Interdisciplinary Research Project for Young Teachers of USTB (Fundamental Research Funds for the Central Universities) (No. FRF-IDRY-19-006).
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Zhu, J., Liao, M., Zheng, Y. et al. Multi-objective optimisation based on reliability analysis of a self-propelled capsule system. Meccanica 58, 397–419 (2023). https://doi.org/10.1007/s11012-022-01519-3
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DOI: https://doi.org/10.1007/s11012-022-01519-3