To enhance the quantitative analysis and optimization of standing long jump performance, this study proposed a computational method integrating biomechanical constraints, graph neural networks, and random forest regression. A human pose estimation model based on HRNet-GCN-Transformer was constructed to extract spatiotemporal coordinates of 33 key joints from video sequences. Based on this, a feasible domain constraint system for parameters such as take-off angle and arm swing amplitude was established according to projectile motion equations and human kinematic characteristics. Furthermore, a random forest regression model was designed to quantify the nonlinear mapping between posture parameters and jump performance, and a gradient-based constrained optimization algorithm was employed to search for optimal posture parameters within biomechanically plausible ranges. Experimental results showed that the method achieved a performance prediction accuracy of $ R^2 = 0.892 $ and $ MAE = 0.05 \, \text{m} $, with a theoretical performance improvement of approximately $ 17.9% $ after optimization. This study provided a computable and interpretable mathematical model for data-driven human motion analysis and personalized training recommendations.
Citation: Yonggang Su, Tingting Xu, Ziqi Guo. Biomechanically constrained optimization of standing long jump performance using graph neural networks and random forest regression[J]. AIMS Mathematics, 2026, 11(9): 29234-29255. doi: 10.3934/math.20261162
To enhance the quantitative analysis and optimization of standing long jump performance, this study proposed a computational method integrating biomechanical constraints, graph neural networks, and random forest regression. A human pose estimation model based on HRNet-GCN-Transformer was constructed to extract spatiotemporal coordinates of 33 key joints from video sequences. Based on this, a feasible domain constraint system for parameters such as take-off angle and arm swing amplitude was established according to projectile motion equations and human kinematic characteristics. Furthermore, a random forest regression model was designed to quantify the nonlinear mapping between posture parameters and jump performance, and a gradient-based constrained optimization algorithm was employed to search for optimal posture parameters within biomechanically plausible ranges. Experimental results showed that the method achieved a performance prediction accuracy of $ R^2 = 0.892 $ and $ MAE = 0.05 \, \text{m} $, with a theoretical performance improvement of approximately $ 17.9% $ after optimization. This study provided a computable and interpretable mathematical model for data-driven human motion analysis and personalized training recommendations.
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Yonggang Su, Tingting Xu, Ziqi Guo. Biomechanically constrained optimization of standing long jump performance using graph neural networks and random forest regression[J]. AIMS Mathematics, 2026, 11(9): 29234-29255. doi: 10.3934/math.20261162
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