Characteristic lengths and distancesâ fast and robust features for nonlinear time series
Date of Original Version
Estimation of most of the metrics used to characterize dynamical systemsâTM output require fairly long time series (e.g., Lyapunov Exponents, Fractal Dimensions), or substantial computational resources (e.g., phase space warping metrics, sensitivity vector fields). In many practical applications, when there is abundance of data (e.g., in Atomic Force Microscopy) fast and simple features are needed, and when there is sparsity of data (e.g., in many Structural Health Monitoring situations) robust features are needed. Here, we propose a new class of features based on Birkhoff Ergodic Theorem, which are fast to calculate and do not require large data or computational resources. Applications of these metrics, in conjunction with the smooth orthogonal decomposition, to identifying underlying processes causing nonstationarity both in simulations and actual experiments are demonstrated. Copyright © 2012 by ASME.
Proceedings of the ASME Design Engineering Technical Conference
PARTS A AND B
Nguyen, Son Hai, and David Chelidze. "Characteristic lengths and distancesâ fast and robust features for nonlinear time series." Proceedings of the ASME Design Engineering Technical Conference 1, PARTS A AND B (2012): 615-621. doi:10.1115/DETC2012-71281.