A dynamical systems approach to damage evolution tracking, part 1: Description and experimental application

In this two-part paper we present a novel method for tracking a slowly evolving hidden damage process responsible for nonstationarity in a fast dynamical system. The development of the method and its application to an electromechanical experiment is the core of Part 1. In Part 2, a mathematical model of the experimental system is developed and used to validate the experimental results. In addition, an analytical connection is established between the tracking method and the physics of the system based on the idea of averaging and the slow flow equations for the hidden process. The tracking method developed in this study uses a nonlinear, two-time-scale modeling strategy based on the delay reconstruction of a system’s phase space. The method treats damage-induced nonstationarity as evolving in a hierarchical dynamical system containing a fast, directly observable subsystem coupled to a slow, hidden subsystem. The utility of the method is demonstrated by tracking battery discharge in a vibrating beam system with a battery-powered electromagnetic restoring force. Applications to systems with evolving material damage are also discussed.