Uniform confidence bands for joint angles across different fatigue phases

TL;DR

This paper introduces a method to create uniform confidence bands for mean joint angles in functional time series, helping analyze fatigue effects on athletes' joint flexibility during running.

Contribution

It extends change point detection to provide confidence bands for segments with significant jumps, aiding biomechanical analysis of fatigue-related joint motion.

Findings

Confidence bands for joint angles under fatigue

Application to athlete's lower-extremity joint analysis

Enhanced understanding of fatigue's impact on ROM

Abstract

We develop uniform confidence bands for the mean function of stationary time series as a post-hoc analysis of multiple change point detection in functional time series. In particular, the methodology in this work provides bands for those segments where the jump size exceeds a certain threshold $\Delta$. In \cite{bastian2024multiplechangepointdetection} such exceedences of $\Delta$ were related to fatigue states of a running athlete. The extension to confidence bands stems from an interest in understanding the range of motion (ROM) of lower-extremity joints of running athletes under fatiguing conditions. From a biomechanical perspective, ROM serves as a proxy for joint flexibility under varying fatigue states, offering individualized insights into potentially problematic movement patterns. The new methodology provides a valuable tool for understanding the dynamic behavior of joint motion and its relationship to fatigue.