Dynamical Assessment of Structural Damage Using the Continuity Statistic

Recent works by Nichols et al. (Nichols, J.M., Todd, M.D., Seaver, M. and Virgin, L.N. (2003). Use of chaotic excitation and attractor property analysis in structural health monitoring. Phys Rev E, 67(016209)) and Pecora et al. (Todd, M.D., Nichols, J.M., Pecora, L.M. and Virgin, L.N. (2001). Vibration-based damage assessment utilizing state-space geometry changes: Local attractor variance ratio. Smart Materials and Structures, 10, 1000-1008.) have shown that steady-state dynamic analysis of structural health exhibits advantages over transient vibrational analysis. A geometric representation of system dynamics can be used to extract information about a structure’s response to sustained excitation. Analysis of various features of the geometric representation can be used to describe the degree to which the dynamics have been altered by damage. Here, the feature we employ is the ‘‘continuity test,’’ a statistical test first described by Pecora et al. (Pecora, L.M., Carroll, T.L. and Heagy, J.F. (1997). Statistics for continuity and differentiability: an application to attractor reconstruction from time-series. Fields Institute Communications, 11). This test measures the probability that a continuous function exists from one geometric object to another. In this implementation, we formulate a new null hypothesis which serves to make the test less sensitive to noise in the data than the original test. Using experimental data from an excited three-story aluminum frame structure with multiple sensors at the joints, we show that the continuity test can be used not only to detect, but also in some cases to localize damage to particular joints in the frame structure.