基于 GRA-BP 模型预测排球扣球落地的 vGRF

vGRF based on GRA-BP model for predicting volleyball dunk landings

摘要

目的 建立灰色关联度分析（grey relational analysis，GRA）和 BP 神经网络（BP neural network）的耦合数学模型来预测排球运动员扣球落地的垂直地面反作用力（vertical ground reaction force，vGRF）从而来代替三维测力台。 方法 选取北京体育大学 20 名二级排球运动员，采取两步助跑方式进行排球扣球动作演示，通过运动捕捉系统和三维测力台同步采集运动学和动力学数据。采用 OpenSim 计算排球运动员在进行两步助跑扣球落地时的运动学数据。采用 GRA 来筛选关联度低于 0.98 的运动学指标，采用均方根误差、平均绝对百分比误差和平均绝对误差、R 作为 GRA-BP 模型的评价指标，使用肯德尔 W 系数评价预测 vGRF 与测量 vGRF 之间的一致性。 结果 GRA 结果显示骨盆前后倾角度、骨盆左右倾角度、骨盆旋转角度等 13 个运动学数据关联度高于 0.98。训练集中预测值与测量值间均方根误差为 0.271 BW，平均绝对百分比误差为 4%，平均绝对误差为 0.17 BW，R = 0.999；验证集中预测值与测量值间均方根误差为 0.235 BW、平均绝对百分比误差为 3.9%，平均绝对误差为 0.14 BW，R = 0.998；测试集中预测值与测量值间均方根误差为 0.224 BW，平均绝对百分比误差为 3.6%，平均绝对误差为 0.14 BW，R = 0.998；肯德尔 W 系数为 0.945，P≤0.001。 结论 本研究所建立的 GRA-BP 模型可提高排球运动员扣球落地 vGRF 测量的准确性，缩短测量时间。

Abstract

Objective To establish a coupled mathematical model of grey relation analysis (GRA) and BP neural networks to predict the vertical ground reaction force (vGRF) of a volleyball player's dunked ball to the ground to replace a three-dimensional force measuring table. Methods Twenty volleyball players from Beijing Sport University were selected to demonstrate the volleyball dunking action with two-step running, and their kinematics and dynamics data were simultaneously collected by the motion capture system and the 3D force measuring table. Opensim was used to calculate the kinematic data of the volleyball players' two-step running dunks. GRA was used to screen kinematic indicators with correlations lower than 0.98. Root mean square error, mean absolute percentage error, mean absolute error, and R were used as the evaluation indexes of the GRA-BP model, and Kendall's W coefficient was used to evaluate the consistency between predicted vGRF and measured vGRF. Results The GRA results showed 13 kinematic data correlations of anterior-posterior pelvic tilt angle, left-right pelvic tilt angle, and pelvic rotation angle were all higher than 0.98. The R_RMSE between predicted and measured values in the training set was 0.271 BW, the R_MAPE was 4%, the R_MAE was 0.17 BW, and the R was 0.999. The R_RMSE between predicted and measured values in the validation set was 0.235 BW, R_MAPE was 3.9%, R_MAE was 0.14 BW, and R was 0.998. Between predicted and measured values in the test set, the R_RMSE was 0.224 BW, R_MAPE was 3.6%, R_MAE was 0.14 BW, and R was 0.998; the coefficient of Kendall's W was 0.945 (P≤0.001). Conclusion The GRA-BP model established by this study can be significantly improved. GRA-BP model can significantly improve the accuracy of vGRF of volleyball players' dunk landing and significantly shorten the measurement time.

关键词

垂直地面反作用力 / 灰色关联度分析 / 神经网络 / 排球扣球 / OpenSim

Key words

vertical ground reaction force / grey relational analysis / neural network / volleyball spike / OpenSim

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基金资助

国家体育总局科技服务项目(BSU20240236)

专用风洞及气动减阻装备研发项目(2020YFF0304601)