Probabilistic inference of fatigue damage propagation with limited and partial information

A general method of probabilistic fatigue damage prognostics using limited and partial information is developed. Limited and partial information refers to measurable data that are not enough or cannot directly be used to statistically identify model parameter using traditional regression analysis. In the proposed method, the prior probability distribution of model parameters is derived based on the principle of maximum entropy (MaxEnt) using the limited and partial information as constraints. The posterior distribution is formulated using the principle of maximum relative entropy (MRE) to perform probability updating when new information is available and reduces uncertainty in prognosis results. It is shown that the posterior distribution is equivalent to a Bayesian posterior when the new information used for updating is point measurements. A numerical quadrature interpolating method is used to calculate the asymptotic approximation for the prior distribution. Once the prior is obtained, subsequent measurement data are used to perform updating using Markov chain Monte Carlo (MCMC) simulations. Fatigue crack prognosis problems with experimental data are presented for demonstration and validation.