Analysis of Local State Space Models for Feature Extraction in Structural Health Monitoring

Error metrics based on nonlinear dynamical predictive models has been implemented earlier to determine discrepancies or nonstationarity in time series caused by external sources, such as noise or filtering. The structural health monitoring (SHM) field has adapted various forms of such prediction error metrics for damage detection. This process usually requires randomly selecting a number of fiducial points on a reconstructed attractor, tracking their time evolutions, and then comparing them to a corresponding set (in a general sense) of points on another attractor. Such an approach has been successful, but it is a process that is globally averaged over the whole data set. However, changes to dynamics resulting from processes such as damage may only noticeably affect small regions within state space if the damage manifests itself locally in time and/or space. In such a case, a generalized selection of points covering the entire attractor may not be able to identify that a dynamical change has taken place. This work examines local dynamics and local dynamical stability and how these concepts relate to prediction error for similarly local regions in phase space. Further, this work considers whether computing features such as prediction error in these local regions can improve the ability to detect changes, including in the presence of additive noise on the output. This work considers a Lorenz-driven three-degree-of-freedom oscillator subject to both simulated linear and nonlinear damage scenarios in the presence of noise, as well as an experimental frame structure subject to bolt preload loss.