Dynamical systems approach to fatigue damage identification

Abstract

In this paper, we present a dynamical systems approach to material damage identification. 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. A concept of phase space warping is used to develop new damage tracking feature vectors from measured time series through phase space reconstruction. These feature vectors provide critical information about the dimensionality of a damage process that was missing from an old scalar metric described in previous work. Damage identification is achieved by applying either proper orthogonal decomposition (POD) or smooth orthogonal decomposition (SOD) 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. Both damage identification methods yield a single active damage mode that shows power-law type monotonic trends, which is also consistent with a result obtained using the old scalar metric. These results are shown to be in good agreement with the Paris fatigue crack growth model during the time-period of macroscopic crack growth. Using this simple model, accurate time to failure predictions are shown well ahead of actual beam fracture. In addition, this identification scheme provides much needed insight into the dimensionality of incipient or early fatigue damage accumulation process, which is shown to be describable by only one scalar damage variable for this specific experiment.

Reconstructing slow-time dynamics from fast-time measurements

“…The next two SOCs show high sensitivity to the dramatic changes at the end of the experiment, but have clear discontinuities and considerably more noise. As in Chelidze & Liu (2005), the beam was made of carbon steel. The Paris law of macroscopic crack growth for this material stipulates a quadratic form of slow-time equation in equation (3.1).…”

“…It was also demonstrated that the algorithm can identify two-dimensional damage trajectory's phase space (Chelidze 2004;Chelidze & Liu 2005). In addition to the changes in the slow-time variables, these systems were observed to go through bifurcations in their fast-time behaviour.…”

“…Previous works (Chelidze 2004;Chelidze & Liu 2005Chelidze & Cusumano 2006) include detailed reviews of the corresponding technologies. Some of the recent developments are in the area of damage diagnosis under time-varying environmental conditions.…”

New invariant measures to track slow parameter drifts in fast dynamical systems

“…t ∈ T ⊂ R is time, overdots denote time differentiation, 0 < 1 is a small rate constant defining the time scale separation. This formulation is relevant to tracking and identifying damage processes as discussed in [5]. It is assumed that the variable φ changes slowly.…”

Robust and Dynamically Consistent Model Order Reduction for Nonlinear Dynamic Systems

“…SOD can be thought of as an extension of POD [14][15][16][17][18][19][20][21]. In addition to considering spatial (i.e., statistical) characteristics of the data set as in POD, SOD considers temporal (i.e., dynamical) characteristics of the data set as well.…”