Reliability Analysis of Shell Structures Under Small Failure Probabilities Using Adaptive Multi-fidelity Sampling

Reliability analysis of complex engineering structures faces significant computational challenges, particularly when estimating small failure probabilities that are critical for aerospace safety requirements. The high computational cost of evaluating limit state functions through numerical methods such as finite element or boundary element analysis often makes direct Monte Carlo simulation prohibitive. This study employs the Global-Error Active Learning Function (GEALF) method, which strategically selects training points to maintain accuracy while substantially reducing computational demands. The approach is further enhanced through multi-fidelity modelling, using low-fidelity models for global exploration and reserving computational expensive high fidelity evaluations for critical regions near the limit state. The methodology is demonstrated through two examples. First, a two-dimensional analytical multimodal function validates the approach against Monte Carlo simulation, achieving errors below 1.32% with only 36 high-fidelity and 75 low-fidelity evaluations compared to the benchmark 108 Monte Carlo samples. Second, a shallow shell structure under cabin pressure is analysed and the stress intensity factor was evaluated using the Dual Boundary Element method. The multi-fidelity approach requires approximately 35 high-fidelity and 80 low-fidelity evaluations, compared to the 267 training points needed for traditional Kriging-based Monte Carlo simulation. This shows a computational cost reduction of around 60% in terms of numbers of high-fidelity calls. While relative errors increase for very small failure probabilities (reaching 5.43% at ~ 10-⁶), the accuracy remains within acceptable level.