Optimization of Pacing Strategies for Cycling Time Trials Using a Smooth 6-Parameter Endurance Model
Optimization of Pacing Strategies for Cycling Time Trials Using a Smooth 6-Parameter Endurance Model
复制标题
使用平滑 6 参数耐力模型优化自行车计时赛的起搏策略
DOI：
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发表时间：
2012
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通讯作者：
Thorsten Dahmen
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作者：
Thorsten Dahmen
计算最佳的起搏策略，骑自行车时间试验可以制定为一个最佳的控制问题，其中的机械模型和生理耐力模型形成的动态系统和时间，以完成的轨道是最小化。我们回顾了使用3参数临界功率模型计算最佳起搏策略的方法，并将其修改为平滑的6参数耐力模型。由于它的3个额外的参数，它是更灵活的建模生理动力学适当。此外，我们证明，该模型具有良好的数值特性，可以消除纯数学的解决方案，计算近似的最佳起搏的原始3参数临界功率模型。一个建立的简化的3参数临界功率模型被认为是比较数值计算的最佳起搏策略的人工轨道上连续变化的斜率受到这些变量的3参数临界功率模型。结果表明，最佳蹬踏功率受原始模型表现出不切实际的大的变化，这是平滑的简化模型。6参数耐力模型原来是一个灵活的模型，表现出中间的变化，在最佳蹬踏功率，而数值表现良好。在这方面的贡献所使用的方法是可扩展的，并可用于计算最佳起搏策略结合更复杂的生理模型。
Computing the optimal pacing strategy for cycling time trials can be formulated as an optimal control problem, where a mechanical model and a physiological endurance model form the dynamical system and time to complete the track is to be minimized. We review approaches that use the 3-parameter critical power model to compute optimal pacing strategies and modify it to become a smooth 6-parameter endurance model. Due to its 3 additional parameters, it is more flexible to model the physiological dynamics appropriately. Besides, we demonstrate that this model has favourable numerical properties that allow to eliminate purely mathematical workarounds to compute an approximate optimal pacing for the original 3- parameter critical power model. An established simplification of the 3-parameter critical power model is considered for a comparison of numerically computed optimal pacing strategies on an artificial track with continuously varying slope subject to these variants of the 3-parameter critical power model. It is shown, that the optimal pedalling power subject to the original model exhibits unrealistically large variations, which are smoothed heavily by the simplified model. The 6-parameter endurance model turns out to be a flexible model, that exhibits intermediate variations in the optimal pedalling power, while being numerically well behaved. The methods used in this contribution are extensible and can be used for the computation of optimal pacing strategies in conjunction with more sophisticated physiological models.