Dynamical systems approach to material damage diagnosis
Date of Original Version
In this paper, a dynamical systems approach to material damage identification is presented. This methodology does not depend on knowledge of the particular damage physics of material fatigue. Instead, it provides experimental means to determine what are practically observable and observed facts of damage accumulation, thus making it possible to develop or experimentally verify appropriate damage evolution laws. The procedure implicitly uses the fact that the system undergoing fatigue damage accumulation possesses time scale separation, where damage accumulation occurs on a much slower time scale than the observable dynamics of a system. Damage tracking is achieved using a two-time-scale modeling strategy based on phase space reconstruction. Fast-time oscillation data is collected and used to estimate a damage tracking function by calculating the short time reference model prediction error. Tracking metrics based on these estimates are used as feature vectors. Damage identification is achieved either by applying proper orthogonal decomposition or optimal tracking methods to these vectors. The method is experimentally validated using an elasto-magnetic system, in which a harmonically forced cantilever beam in a nonlinear magnetic field accumulates fatigue damage. The damage tracking results were virtually identical for both identification schemes. In both cases tracking data showed power-law type monotonic trends. These results were in good agreement with the Paris fatigue crack growth model during the time-period of macroscopic crack growth. In addition, the tracking provides much needed insight into the incipient or early damage accumulation process, where only one scalar damage variable is needed to describe the incipient or early damage accumulation process.
Proceedings of the ASME Design Engineering Technical Conference
Chelidze, David. "Dynamical systems approach to material damage diagnosis." Proceedings of the ASME Design Engineering Technical Conference 5 B, (2003): 1263-1270. doi:10.1115/detc2003/vib-48452.