A new Kriging-based DoE strategy and its application to structural reliability analysis

As the numerical model of engineering structure becomes more and more complicated and time consuming, efficient structural reliability analysis is badly in need. To reduce the number of calls to the performance function and iterative times during structural reliability analysis, an innovative strategy of the design of experiments (DoE) called Isomap-Clustering strategy is proposed. According to the statistical information provided by Kriging, points with the worst uncertainty for reliability analysis are on the estimated limit state. Therefore, by combining Isomap and k-means clustering algorithm, Isomap-Clustering strategy refreshes the DoE of the Kriging model with a few representative points in the vicinity of the estimated limit state each iteration and iteratively "pushes" the estimated limit state to the real one until a stopping condition is satisfied. By employing the proposed DoE strategy and sparse polynomial-Kriging model, a structural reliability analysis method is constructed, whose stopping criterion is defined by derivation. Three examples are studied. Results show that the proposed method can lower the number of calls to the performance function and remarkably reduces the iterations of structural reliability analysis.