Injuries to the lower extremity joints are often debilitating, particularly for professional athletes. Understanding the onset of stressful conditions on these joints is therefore important in order to ensure prevention of injuries as well as individualised training for enhanced athletic performance. We study the biomechanical joint angles from the hip, knee and ankle for runners who are experiencing fatigue. The data is cyclic in nature and densely collected by body worn sensors, which makes it ideal to work with in the functional data analysis (FDA) framework. We develop a new method for multiple change point detection for functional data, which improves the state of the art with respect to at least two novel aspects. First, the curves are compared with respect to their maximum absolute deviation, which leads to a better interpretation of local changes in the functional data compared to classical $L^2$-approaches. Secondly, as slight aberrations are to be often expected in a human movement data, our method will not detect arbitrarily small changes but hunts for relevant changes, where maximum absolute deviation between the curves exceeds a specified threshold, say $\Delta >0$. We recover multiple changes in a long functional time series of biomechanical knee angle data, which are larger than the desired threshold $\Delta$, allowing us to identify changes purely due to fatigue. In this work, we analyse data from both controlled indoor as well as from an uncontrolled outdoor (marathon) setting.

翻译：下肢关节损伤常常令人丧失能力，尤其对职业运动员而言。因此，了解这些关节的受力状态出现的时间点对于预防损伤以及制定个性化训练以提升运动表现至关重要。我们研究了疲劳状态下跑步者的髋、膝、踝关节的生物力学角度数据。这些数据具有周期性特征，并通过人体佩戴的传感器密集采集，非常适合在功能数据分析框架下处理。我们开发了一种新的功能数据多变点检测方法，该方法至少在两个创新方面改进了现有技术。首先，曲线之间的比较基于其最大绝对偏差，与经典的 $L^2$ 方法相比，这能更好地解释功能数据中的局部变化。其次，由于人体运动数据中常存在微小偏差，我们的方法不会检测任意小的变化，而是寻找相关变化，即曲线之间的最大绝对偏差超过某个指定阈值（如 $\Delta > 0$）的情况。我们从生物力学膝关节角度数据的长功能时间序列中恢复了多个大于所需阈值 $\Delta$ 的变化，从而能够识别纯粹由疲劳引起的变化。在本研究中，我们分析了来自受控室内环境以及非受控室外环境（马拉松）两种场景下的数据。