Probabilistic fatigue damage prognosis using maximum entropy approach

A general framework for probabilistic fatigue damage prognosis using maximum entropy concept is proposed and developed in this paper. The fatigue damage is calculated using a physics-based crack growth model. Due to the stochastic nature of fatigue crack propagation process, uncertainties arising from the underlying physical model, parameters of the model and the response variable measurement noise are considered and integrated into this framework. Incorporating all those uncertainties, a maximum relative entropy (MRE) approach is proposed to update the statistical description of model parameters and narrow down the prognosis deviations. A Markov Chain Monte Carlo (MCMC) simulation is then employed to generate samples from updated posterior probability distributions and provide statistical information for the maximum relative entropy updating procedure. A numerical toy problem is given to demonstrate the proposed MRE prognosis methodology. Experimental data for aluminum alloys are used to validate model predictions under uncertainty. Following this, a detailed comparison between the proposed MRE approach and the classical Bayesian updating method is performed to illustrate advantages of the proposed prognosis framework.