A Bayesian Approach for Estimating Sizes of Fatigue Cracks near Fastener Holes

Ultrasonic in situ monitoring of metal alloys has been successfully demonstrated for determining the presence and size of fatigue damage within a stracture. Ultrasonic techniques, however, only provide an estimate of the state of the stracture at that time and do not predict the remaining fatigue life. On the other hand, a statistical crack propagation approach, which models the expected remaining life based on an assumed fatigue process, specimen geometry and material properties, allows for the fatigue life to be estimated. To maintain the safety of the stracture, this approach typically requires assuming a worst case initial flaw size. Presented here is a Bayesian estimation approach for incorporating both the measurement and modeling methodologies. An Extended Kalman Filter approximation is used to combine ultrasonic estimates of fatigue cracking with a crack propagation model. The measurement model is based upon recent work by the authors on a shear wave, angle-beam method for monitoring fastener holes, and the crack propagation model is based upon Paris's Law. Simulated and experimental results are shown to assess the performance of the estimation approach, where the resulting crack size determination is more accurate than either the ultrasonic method or the crack propagation model alone.