Enhanced damage tracking via state variable normalization

by Liu, Yuging.

Two trackers based on a general dynamical systems approach to data analysis are presented. These trackers allow one to monitor slowly drifting variables responsible for nonstationarity in the fast subsystem of a hierarchical system. Both of these methods are based on the general idea of phase space warping, which illustrates a small distortion in the fast subsystem’s phase space caused by the drift of the slow subsystem. This distortion leads to a short time reference model prediction error, based on which the tracker is developed. However, this error has unwanted fluctuations from the variability of fast states. The trackers in this research are used to remove, via different approaches, these unwanted fluctuations so that the useful information about the slowly drifting variables can be obtained. The first approach uses the theoretical solution of the short time reference model prediction error and normalizes the error with aspect to the fast state. This method shows that there exists an affine map between the error vector space and the slow subsystem space and we are able to give real-time estimation of the current slow variable state and identify the governing slow evolution model. The second apiii proach assembles a multivariate tracking matrix and applies a multivariate analysis technique on this matrix to obtain the variances of slow subsystem. This multivariate tracking matrix version of the procedure, based on principal component analysis, is applied to the study of vector tracking with scalar observation. The basic theory is presented, and the issues associated with its implementation in a practical algorithm are discussed. Firstly, a numerical experiment of a spring-mass system was studied with the first tracker to illustrate the concepts which can be hardly explained in physical experiment. Then these two trackers were applied to the study of an Euler-Bernoulli beam-string oscillator experiment in which nonstationarity was provided by a battery powered electromagnetic restoring force. The complete discharge of the battery models the “damage” propagation to complete failure in the experimental system. iv