Adaptive Kriging Metamodel with Error Stability-Based Stopping Criterion for Reliability Analysis of Underground Tunnel

Reliability analysis of tunnel involves complex implicit limit-state functions (LSFs). The direct Monte Carlo simulation (MCS) based reliability analysis of tunnel becomes costly as it involves expensive numerical simulation models to evaluate the related implicit LSFs. The surrogate model-based analysis is a viable alternative to the direct MCS approach, as it replaces the original complex LSFs with suitable metamodels. Thereby and reduces the computation cost. The Kriging metamodel is noted to be highly effective in this regard. Furthermore, the Kriging model can predict the uncertainty of prediction utilising. An efficient adaptative Kriging-based metamodeling approach based on the max–min learning function in the reduced sample space and error stability-based stopping criteria is proposed in the present study. A uniform design sampling approach is used to generate the initial Kriging model. Thereafter, the learning process is initiated from a reduced sample space. The convergence is defined by stopping criteria based on error stability. The effectiveness of the proposed adaptive Kriging-based metamodeling approach is numerically demonstrated by comparing the present reliability results with the active learning Kriging-based reliability results in terms of accuracy and efficiency.