Probabilistic fatigue damage prognosis using maximum entropy approach

A general framework for probabilistic fatigue damage prognosis using maximum entropy concept is proposed in this paper. The fatigue damage is calculated using a physics-based crack growth model. Due to the stochastic nature of crack growth process, uncertainties arising from the underlying physical model, parameters of the model, and the measurement noise are considered and integrated into this framework. A maximum relative entropy (MRE) approach is proposed to update the prognosis result and confidence bounds incorporating various types of uncertainties from measuring, modeling, and maintenance. Markov Chain Monte Carlo (MCMC) sampling is employed to generate the posterior probability distribution of model parameters and provide statistical information for the maximum relative entropy updating procedure. Numerical examples are used 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 classical Bayesian updating method is performed to illustrate advantages of the proposed MRE approach.