Trans-dimensional MCMC for fatigue prognosis model determination, updating, and averaging

In this paper, a general Bayesian framework for fatigue model determination, updating and averaging using trans-dimensional Markov Chain Monte Carlo (MCMC) simulations is presented. Uncertainties introduced by model choice, mechanism modeling, model parameter, and response measures are systematically included. Additional response measures are used to update the model probabilities and the parameter distributions associated with each of the models simultaneously via one trans-dimensional MCMC simulation in the general state space. The averaging of model predictions can readily be performed using the simulation samples. The results of Bayes factors serve as a reference for model comparisons and determinations. To improve the simulation efficiency, we incorporate a new algorithm to construct the dimension matching densities and bijection functions. A fatigue crack growth example with experimental data is presented for methodology demonstration and validation.