Vibration-Based Damage Assessment Using Novel Function Statistics with Multiple Time Series

摘要

Analysis of data from experiments on dynamical systems often centers on the embedding of time series data to reconstruct an atttractor. In our system, we consider output expressed as multiple time series from a circuit designed to simulate a spring-mass system in both an undamaged and a damaged state. In order to analyze differences in the reconstructed attractors between the damaged and undamaged states we employ a new version of the Continuity Statistic. This statistic was first introduced by Pecora, Carroll and Heagy. Here we use the statistic in the new setting of an embedding of multiple time series and in order to address noisy data, formulate a new null hypothesis. We show that this new continuity statistic is an appropriate tool for showing differences between reconstructed attractors in the specific case of our simulated spring-mass system in "damaged" and "undamaged" conditions.