We perform nonlinear system identification (NSI) on the acceleration signals that were experimentally measured at ten, almost evenly spaced positions along a cantilever beam undergoing vibro-impacts between two rigid stops with clearances. The NSI methodology is based on the correspondence between analytical and empirical slow-flow dynamics, with the first step requiring empirical mode decomposition (EMD) analysis of the measured time series leading to sets of intrinsic modal oscillators (IMOs) governing the vibro-impact dynamics at different time scales. By comparing the spatiotemporal variations of the nonlinear modal interactions (and hence the IMOs), we examine how vibro-impacts influence the low- and high-frequency modes in global and local senses. In applications of the NSI results to structural health monitoring and damage detection (SHM / DD), we calculate typical measures such as the modal assurance criterion (MAC) and the coordinate modal assurance criterion (COMAC) by extracting information about the mode shape functions from the spatiotemporal IMO solutions. Whereas the MAC provides a global aspect of damage occurrence (i.e., which modes are more affected by induced defects), the COMAC can narrow down the damage locations (i.e., where in the structure defects exist that yield low correlation values in specific modes). Finally, we discuss the use of the 2-dimensional correlation spectroscopy technique to SHM / DD, which is frequently used in optical chemistry areas. With the spatiotemporal IMOs the 2-D correlation intensity for the linear beam is proportional to the product of the two mode shape functions at the respective positions; hence any deviations from that may indicate the occurrence and locations of damage in the structure.
A Generalized Optimal Sensor Placement Technique for Structural Health Monitoring and System Identification
