Probabilistic Maintenance-Free Operating Period via Bayesian Filter with Markov Chain Monte Carlo (MCMC) Simulations and Subset Simulation

This paper presents a probabilistic approach via Bayesian-filter (BF) with Markov chain Monte Carlo (MCMC) simulations and subset simulation (SS), to determine the probabilistic maintenance-free operating period (MFOP) for probabilistic lifing assessment of aircraft fatigue critical components. State transition function representing virtual damage growth of a component and measurement function representing the SHM measurements of the component are defined. State transition function is described by a typical Paris equation for fatigue crack propagation. Measurement functions are assumed in this study, which describe the relationship between the damage features derived from SHM signals and the damage sizes. Damage tolerance (DT) and risk-based methodologies are used for fracture-based reliability assessment. Random samples for posterior joint probability density function of initial flaw size and crack growth rate are generated with information obtained through structural health monitoring (SHM) systems. Subset simulation (SS) is used in conjunction with MCMC in order to determine the small probability of failure with high efficiency. The results have shown that the MCMC-SS combined methodology is two orders of magnitude more efficient than that of MCMC alone.