Moon Jeongin, Ahn Jooeun
Department of Physical Education, Seoul National University, Seoul, Republic of Korea.
Soft Robot Research Center, Seoul National University, Seoul, Republic of Korea.
R Soc Open Sci. 2025 Aug 13;12(8):250106. doi: 10.1098/rsos.250106. eCollection 2025 Aug.
Floquet multiplier (FM) is a commonly used metric for evaluating gait orbital stability in biomechanics. However, variability of human gait and noise from various sources can induce significant bias and variance in the estimation of FM. Furthermore, FM is employed in gait analysis without standardized protocols, leading to highly case-dependent outcomes. To address these challenges, we quantify the effects of sampling conditions on the accuracy and consistency of FM estimations. We recruited 20 healthy participants and conducted five trials of 10 minutes of walking per participant. Using individualized Jacobian matrices calculated from the walking experiments, we synthesized multiple sets of virtual time series with varying lengths and trial counts. Using stochastic linear models, we simulated the error dynamics depending on the sampling methods. The bias and variance of FM estimates decreased as the time series lengthened, achieving a strong correlation with the true value after 140 strides for 14-dimensional state vector. Our results further suggest that partitioning a long time series into appropriately sized segments can yield more reliable FM estimates, reducing both bias and variance in FM estimations.
弗洛凯乘数（FM）是生物力学中评估步态轨道稳定性常用的指标。然而，人类步态的变异性以及来自各种来源的噪声会在FM估计中引起显著的偏差和方差。此外，FM在步态分析中的应用没有标准化协议，导致结果高度依赖具体案例。为应对这些挑战，我们量化了采样条件对FM估计准确性和一致性的影响。我们招募了20名健康参与者，每位参与者进行了5次每次10分钟的步行试验。利用从步行实验中计算出的个性化雅可比矩阵，我们合成了多组长度和试验次数不同的虚拟时间序列。使用随机线性模型，我们根据采样方法模拟了误差动态。随着时间序列延长，FM估计的偏差和方差减小，对于14维状态向量，在140步之后与真实值实现了强相关性。我们的结果进一步表明，将长时时间序列划分为大小合适的段可以产生更可靠的FM估计，减少FM估计中的偏差和方差。
