Bayesian-informed fatigue life prediction in shallow shell structures with the dual boundary element method

This study introduces an innovative approach for statistically inferring the Equivalent Initial Flaw Size Distribution (EIFSD) in shallow shell structures with the aim of predicting fatigue life. The proposed approach integrates Bayesian inference and surrogate modelling techniques, and utilizes a long crack growth model. The EIFSD is crucial for estimating fatigue life and ensuring structural durability. To showcase the proposed methodology, a numerical example featuring a fuselage window structure under multi-axial loading, employing the Dual Boundary Element Method (DBEM) for crack growth modelling, is presented. Efficiency gains in the inference of the EIFSD are achieved through the development of surrogate models, notably a Co-Kriging model that significantly reduces computational time and outperforms a Kriging model in error reduction. The study explores two assumptions for inspection data sourcing, leading to enhanced methodological effectiveness across varying uncertainty levels. It considers the separate effects of Paris Law constants and loading conditions under increased uncertainty, presenting cases that demonstrate the Co-Kriging model's high accuracy and computational efficiency. The proposed methodology's robustness is further validated by assessing the impact of prior distribution quality on Bayesian inference, showing the method's adaptability to high uncertainty while maintaining a good level of accuracy. This study also demonstrates an approach for fatigue life estimation of structures using the inferred EIFSD. By evaluating the structure up to a critical crack length, the methodology allows for the accurate estimation of fatigue life, which, in turn, facilitates the determination of optimal inspection intervals. Notably, under conditions of high uncertainty, the method showcased a maximum difference of 1.51% in the estimated fatigue life when compared to the true EIFSD, underscoring the technique's high accuracy and reliability.