Bayesian prediction and probabilistic model of fatigue cracks in steel structures

Fatigue cracks commonly occur in bridges, and their propagation is a random process. In addition, their propagation will cause deterioration of structural performance. In the future, the prediction of the deterioration of structural performance should be based on the current status followed by the update of bridge performances in accordance to field observations. In this study, a probabilistic model of fatigue crack growth in steel structures under fatigue loading was first proposed based on the linear elastic fracture mechanics (LEFM) and the on Paris semi-empirical formulation for fatigue crack growth. Accordingly, the Bayesian updating method and Markov Chain Monte Carlo (MCMC) simulations were then employed to build the method for updating the parameters in the fatigue crack growth model based on the data obtained from field observations, thus allowing the real time prediction of the structural life and structural performance degradation trajectory at a specific future period. The proposed method was used for simulating test combinations of the existing test data of fatigue crack growth. Analysed results showed that the predicted steel structural performance degradation trajectory updated by test data was similar to the real structural performance degradation trajectory. After one update, the mean absolute error between the predicted and the actual degradation trajectory of the steel structure was 0.0159 in, the root-mean-square-error was 0.0173 in, and the mean absolute percentage error was 1.3175%. After two updates of the steel structure degradation trajectory, the outcome was shown to be closer to the real degradation trajectory. The mean absolute error was only 0.0117 in, the root-mean-square-error was 0.0128, and the average absolute percentage error was 0.9670%. The results indicate that the present method can be used to update the random parameters in the fatigue crack growth model, and to effectively predict the variation of steel structural performance degradation trajectory and structural time-dependent reliability.