Fatigue crack growth assessment method subject to model uncertainty

Fatigue crack growth (FCG) is an important degradation process of many critical mechanical equipment. Probabilistic FCG models are often used to account for the variability among FCG process conditions. In the well-known model of Yang and Manning, a deterministic FCG model is randomized by multiplying the crack growth rate with a random multiplier assumed to obey a lognormal distribution and unknown parameters are jointly estimated through Maximum likelihood estimation. By so doing, the modeling error due to inappropriate choice of the deterministic FCG model and that due to unsuitable assignment of the probability distribution of the random multiplier cannot be distinguished. Besides, the model uncertainty of the random multiplier is not explicitly considered. In this paper, a two-step least-square estimation method is proposed, which estimates the unknown parameters in the deterministic FCG model at first, and generates a sample set for the estimation of the random multiplier considering model uncertainty by way of Bayesian model selection. In Bayesian model selection, three types of Bayes factor are considered to select the appropriate candidate model and a simulation experiment is carried out to guide their selection. The effectiveness and feasibility of the proposed method are illustrated through two case studies using the real FCG datasets.