The Lyapunov exponent (LyE) is a trending measure for characterizing gait stability. Previous studies have shown that data length has an effect on the resultant LyE, but the origin of why it changes is unknown. This study investigates if data length affects the choice of time delay and embedding dimension when reconstructing the phase space, which is a requirement for calculating the LyE. The effect of three different preprocessing methods on reconstructing the gait attractor was also investigated. Lumbar accelerometer data were collected from 10 healthy subjects walking on a treadmill at their preferred walking speed for 30 min. Our results show that time delay was not sensitive to the amount of data used during calculation. However, the embedding dimension had a minimum data requirement of 200 or 300 gait cycles, depending on the preprocessing method used, to determine the steady-state value of the embedding dimension. This study also found that preprocessing the data using a fixed number of strides or a fixed number of data points had significantly different values for time delay compared to a time series that used a fixed number of normalized gait cycles, which have a fixed number of data points per stride. Thus, comparing LyE values should match the method of calculation using either a fixed number of strides or a fixed number of data points.

中文翻译：

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步行中计算李亚普诺夫指数时数据长度对时延和嵌入维数的影响

李亚普诺夫指数 (LyE) 是表征步态稳定性的趋势指标。先前的研究表明，数据长度对所得 LyE 有影响，但其变化的根源尚不清楚。本研究调查了数据长度是否会影响重建相空间时时间延迟和嵌入维数的选择，这是计算 LyE 的要求。还研究了三种不同预处理方法对重建步态吸引子的影响。腰椎加速计数据收集自 10 名健康受试者以他们喜欢的步行速度在跑步机上行走 30 分钟。我们的结果表明，时间延迟对计算过程中使用的数据量并不敏感。然而，嵌入维度的最小数据要求为 200 或 300 个步态周期，具体取决于所使用的预处理方法，以确定嵌入维度的稳态值。这项研究还发现，与使用固定数量的标准化步态周期（具有固定数量的数据）的时间序列相比，使用固定步数或固定数量的数据点预处理数据具有显着不同的时间延迟值每步点数。因此，比较 LyE 值应与使用固定步幅数或固定数据点数的计算方法相匹配。