A comparison of different failure assessment methodologies applied to the NESC-1 test

Predictions for a 75x205mm surface semi-elliptic defect in the NESC-1 spinning cylinder test have been made using BS PD 6493:1991, the R6 procedure, non-linear cracked body finite element analysis techniques and the local approach to fracture. All the techniques agree in predicting ductile tearing near the inner surface of the cylinder followed by cleavage initiation. However they differ in the amount of ductile tearing, and the exact location and time of any cleavage event. The amount of ductile tearing decreases with increasing sophistication in the analysis, due to the drop in peak crack driving force and more explicit consideration of constraint effects. The local approach predicts a high probability of cleavage in both HAZ and base material after 190s, while the other predictions suggest that cleavage is unlikely in the HAZ due to constraint loss, but likely in the underlying base material. The timing of this event varies from ∼150s for R6 predictions to ∼250-300s using non-linear cracked body analysis.

Auxiliary particle implementation of the probability hypothesis density filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.