Predictive Modeling for Fatigue Crack Propagation via Linearizing Time Transformations

Summary

Engineering structures operating under cyclic loading are subject to fatigue damage accumulation, which leads to the initiation and subsequent growth of fatigue cracks. Predictive modeling of fatigue crack growth is important for the prevention of catastrophic failures commonly associated with aging air-transport fleets, critical aerospace components, and other large engineering structures such as hydroelectric dams and off-shore oil rigs. In this article, we demonstrate how a training sample of few experimental units from the underlying fatigue crack growth process can be effectively used to predict the crack propagation of an unit under use into the future, given its early growth history. Aspects of the process that represent population (macro) growth characteristics are integrated in a semiparametric time transformation model, which linearizes the functional relationship between average crack length and the number of load cycles. On the transformed time scale, individual (micro) growth characteristics are effectively accounted by a linear model fitted to whatever initial crack-growth data might be available for the particular specimen of interest. The prediction results for an experimental data set are quite appealing.