An Improved Subset Sampling Method and Application in High Cycle Fatigue Reliability Assessment of a Mistuned Composite Fan Bladed Disk Assembly

Carbon fiber reinforced plastics (CFRP) are characterized by the outstanding mechanical properties. Many corporations are developing this kind of composite fan blades and apply to the next generation high-bypass-ratio turbofan engines. Stochastic sources always cause discrepancy between realizations and nominal design, e.g. raw material strength, manufacturing tolerance, defect and damage (crack), assembly, service environment, etc. The current focus of probabilistic safety design for gas turbine components have been put on efficiently evaluating the reliability index.
The objective of this study is to derive an efficient approach to evaluate the risk of a structural mistuned fan stage subject to vibration-induced high cycle fatigue (HCF). The stochastic variable is failure probability of a single composite fan blade based on corresponding probabilistic design curve in one of typical vibration modes. Since crude Monte Carlo simulation (MCS) is strongly dependent on probability of rare event, subset simulation (SS) is a remedy for this limitation by separating failure domain into a series of intermediate regions. The target probability is a product of auxiliary conditional failure probability with intermediate thresholds. However, low acceptance rate via the classical Metropolis-Hastings Markov chain Monte Carlo (MCMC) simulation leads to erroneous estimates of conditional probability. In the proposed ensemble subset sampler (ESS), Markov chain is generated by affine invariant ensemble algorithm that the acceptance rate of candidate points is increased by generating proposal samples using stretch move. Through conducting simple validation cases to compare performance with SS, the proposed method would reduce the number of limit state function evaluations and increase numerical accuracy. It is then fully integrated into composite fan blade-disk finite element (FE) model. Intermediate conditional failure probabilities are calculated with the distributed surrogate models for steady and vibratory stresses. The application further demonstrates good performance to a typical mistuning pattern for fan-disk assembly.

Keywords: Subset sampling, Ensemble sampler, Structural mistuning, High cycle fatigue, Composite fan blades.