Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking: Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking

Victoria Smith Hussain, Mark L. Spano, Thurmon E. Lockhart

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number20200311
JournalJournal of the Royal Society Interface
Volume17
Issue number168
DOIs
StatePublished - Jul 1 2020

Keywords

  • Lyapunov exponents
  • gait
  • local dynamic stability
  • phase space reconstruction

ASJC Scopus subject areas

  • Biotechnology
  • Biophysics
  • Bioengineering
  • Biomaterials
  • Biochemistry
  • Biomedical Engineering

Fingerprint Dive into the research topics of 'Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking: Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking'. Together they form a unique fingerprint.

  • Cite this