Reliability analysis of underground tunnel by a novel adaptive Kriging based metamodeling approach

An adaptive Kriging based metamodeling approach for tunnel reliability analysis strategy is proposed with due consideration to accuracy and efficiency. Based on a preliminary design of experiments (DOE), an initial Kriging model is constructed. Subsequently, a reduced space is built from the Monte Carlo Simulation (MCS) points located near the limit state surface. The MCS points closer to the existing training points are removed from the reduced space to avoid clustering. Finally, the MCS point having the highest joint probability density value is selected from the reduced space. The inclusion of such a point in the DOE is expected to improve the prediction accuracy of a maximum number of neighbouring points. The selection of new training points and updating the Kriging model iteratively is continued until no point is left in the reduced space. The estimated failure probability is considered final if its coefficient of variation is less than a predefined threshold; otherwise a new set of MCS samples are considered for further iterations. The effectiveness of the proposed algorithm is demonstrated by three tunnel reliability analysis problems and noted to be quite efficient and superior over the AK-MCS method in most of the cases.