Optimization of Pole Vault Parameters Using Particle Swarm Optimization and Genetic Algorithm
Ouadie El Mrimar
, Othmane Bendaou
, Bousselham Samoudi
Резюме: In the context of pole vaulting, performance primarily depends on the physical qualities of the athlete and the characteristics of the pole. Our study simplifies this complexity by modeling the athlete as a point mass and the pole as an elastic structure, called "elastica", based on a mechanical and mathematical model from a previous article by Chau et al. (2019). This approach allows us to explore more deeply the key parameters of pole vaulting and optimize performance effectively. The optimization of parameters, such as the non-dimensional elasticity deflection of the pole ( ) and the non-dimensional initial velocity of the point mass ( ), presents challenges due to the complex interaction between various variables influencing athlete performance. Currently, the focus lies in developing and integrating optimization techniques, particularly Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), to efficiently identify optimal values for parameters, and . In this research, we consider the maximum height ( ) achieved by the point mass in the dynamic modeling of pole vaulting as an objective function , focusing specifically on non-dimensional parameters, including w and . The results of PSO and GA optimization techniques were compared with a state-of-the-art approach to affirm the efficacy of the proposed method. The results obtained show that the optimized parameters, notably the initial velocity ( ) equal to 8.64 m/s and the bending stiffness (EI) equivalent to 2386.8 N.m², led to a significant improvement in maximum jump height of 6.88 m. Therefore, we recommend coaches encourage adjustments in material stiffness based on initial velocity and to implement personalized monitoring to fine-tune parameters according to individual athlete’s progress.
Series on Biomechanics, Vol.37, No.4 (2023), 93-106
Ключови думи: elasticity; genetic algorithm; optimization; particle swarm optimization; Pole vault
Литература: (click to open/close) | [1] Hubbard, M., 1980. Dynamics of the pole vault. Journal of Biomechanics 13, 11, 965-976. https://doi.org/10.1016/0021-9290(80)90168 [2] Ekevard, M., & Lundberg, B., 1995. Simulation of “smart” pole vaulting. Journal of Biomechanics 28, 9, 1079-1090. https://doi.org/10.1016/0021-9290(94)00168-4 [3] Drücker, S., Schneider, K., Ghothra, N. K., Bargmann, S., 2018. Finite element simulation of pole vaulting. Sports Engineering, 21, 2, 85-93. https://doi.org/10.1007/s12283-017-0251-0 [4] Dillman, C.J., Nelson, R.C., 1968. The mechanical energy transformations of pole vaulting with a fiberglass pole. Journal of Biomechanics 1, 3, 175–183. [5] Morlier, J., Mesnard, M., 2007. Influence of the moment exerted by the athlete on the pole in pole-vaulting performance. Journal of Biomechanics 40, 10, 2261–2267. https://doi.org/10.1016/j.jbiomech.2006.10.022 [6] Schade, F., Arampatzis, A., Brüggemann, G. P., 2006. Reproducibility of energy parameters in the pole vault. Journal of Biomechanics 39, 8, 1464-1471. https://doi.org/10.1016/j.jbiomech.2005.03.027 [7] Walker, H. S., Kirmser, P. G., 1973. Computer modeling of pole vaulting. Mechanics and Sport, 4, 131-141 [8] Dapena, J., Braff, TR., 1985. A two-dimensional simulation method for the prediction of movements in pole vaulting. Biomechanics 9B, 458-463. [9] McGinnis, P.M., 1984. Dynamic finite element analysis of a human implement system in sport: the pole vault. Ph.D.thesis, Univ. of Urbana champaign. [10] Linthorne, NP.,1994. Mathematical model of the takeoff pahse in the pole vault. Journal of Applied Biomechanics,10, 4,323-334. [11] Linthorne, N. P., Weetman, A. H. G., 2012. Effects of run-up velocity on performance, kinematics, and energy exchanges in the pole vault. IJournal of Sports Science and Medicine, 11, 2, 245. [12] Cassirame, J., Sanchez, H., Exell, T., Panoutsakopoulos, V., Theodorou, A., Homo, S.-k., Zhang, Y., 2019.Differences in approach run kinematics: successful vs. unsuccessful jums in the pole vault. International Journal of performance Analysis in sport 19, 5,794-808. [13] Liu, G., Nguang, S. K., Zhang, Y., 2011. Pole vault performance for anthropometric variability via a dynamical optimal control model. Journal of Biomechanics 44, 3, 436–441. https://doi.org/10.1016/j.jbiomech.2010.09.025 [14] Ohshima, S., Nashida, Y., Ohtsuki, A., 2010. Optimization of pole characteristic in pole vaulting using three-dimensional vaulter model. Procedia Engineering 2, 2, 3191-3196. https://doi.org/10.1016/j.proeng.2010.04.131 [15] Jahromi, A. F., Atia, A., Bhat, R. B., Xie, W., 2012. Optimizing the Pole Properties in Pole Vaulting by Using Genetic Algorithm Based on Frequency Analysis. International Journal of Sports Science and Engineering, 06, 01, 41-53. [16] El Mrimar, O., Bendaou, O. Samoudi, B., 2023. Non-linear stochastic dynamics analysis of mechanical systems using non-intrusive polynomial chaos method: application to pole vaulting. Meccanica,1-17. https://doi.org/10.1007/s11012-023-01725-7 [17] El Mrimar, O., Bendaou, O., 2022. A perturbation method for the Stochastic dynamic analysis of mechanical systems: Application to pole vaulting. 2nd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET), 1-5. [18] Ekevard, M., Lundberg, B., 1997. Influence of pole length and stiffness on the energy conversion in pole-vaulting. Journal of Biomechanics 30, 3, 259-264. https://doi.org/10.1016/S0021-9290(96)00131-5 [19] Arampatzis, A., Schade, F., Brüggemann, G. P., 2004. Effect of the pole-human body interaction on pole vaulting performance. Journal of Biomechanics, 37, 9, 1353-1360. https://doi.org/10.1016/j.jbiomech.2003.12.039 [20] Linthorne, N. P., 2000. Energy loss in the pole vault take-off and the advantage of the flexible pole. Sports Engineering 3, 4, 205-218. https://doi.org/10.1046/j.1460-2687.2000.00058.x [21] Chau, S., Mukherjee, R., 2019. Kinetic to potential energy transformation using a spring as an intermediary: Application to the pole vault problem. Journal of Applied Mechanics, Transactions ASME 86,5. https://doi.org/10.1115/1.4042576 [22] Holland, J.H., 1975. Adaptation in Natural and Artificial Systems, Ann Arbor: The University of Michigan Press. [23] Chang, T. P., 2011. Wind energy assessment incorporating particle swarm optimization method. Energy Conversion and Management 52, 3, 1630-1637. https://doi.org/10.1016/j.enconman.2010.10.024 [24] Kennedy, J., Eberhart, R., 1995. Particle Swarm optimization. In: Proceedings of ICNN’95-international Conference on Neural Networks 04, 1942-1948. [25] Athletics, W., 2021. Competitions rules, International Association of Athletics Federations (IAAF). https: //www.worldathletics.org/competitions/rules-2021 [26] Watson, L. T., Wang, C. Y., 1981. A homotopy method applied to elastica problems. International Journal of Solids and Structures 17, 1, 29-37. [27] Ashino, R., Nagase, M., Vaillancourt, R., 2000. Behind and Beyond the MATLAB ODE Suite. Computers and Mathematics with Applications, 40, 4-5, 491-512. [28] Kierzenka, J., Shampine, L. F., 2001. A bvp Solver based on Residual Control and the MATLAB PSE. ACM Transactions on Mathematical Software, 27, 3, 299-316. [29] Shampine, L., Thompson, S., 2000.Event location for ordinary differential equations. Computers & mathematics with Applications 39, 5-6, 43-54. [30] MathWorks, 2022. Global Optimization Toolbox Documentation. https://www.mathworks.com/help/gads/how-the-genetic-algorithm-works [31] Frère, J., L’Hermette, M., Slawinski, J., & Tourny-Chollet, C., 2010. Mechanics of pole vaulting: A review. Sports Biomechanics 9, 2, 123-138. https://doi.org/10.1080/14763141.2010.492430
|
|
| Дата на публикуване: 2023-11-28
(Price of one pdf file: 39.00 BGN/20.00 EUR)