Ensemble of surrogates combining Kriging and Artificial Neural Networks for reliability analysis with local goodness measurement

In engineering problems, reliability assessment is often computationally expensive. Surrogate models with active learning approaches are commonly used to solve this problem. Kriging is one of the most popular surrogate models used in this domain. Recently, artificial neural networks (ANN) have also attracted a lot of interest for structural reliability assessment due to their powerful capability. Many active learning approaches have been developed based on Kriging models and ANN. But selecting an appropriate model or technique for a reliability assessment problem with limited knowledge of the limit state function remains a challenging task. Ensemble of surrogates seems to be a good approach to tackle this challenge. In this work, two active learning approaches are proposed to combine Kriging and ANN models for reliability analysis. One is the local best surrogate (LBS) approach and the other is the local weighted average surrogate (LWAS) approach. Cross-validation and Jackknife techniques are used to estimate prediction errors of the surrogate models. In addition, two methods are proposed to locally measure the goodness of the surrogate models and calculate the prediction errors of the ensemble of surrogates. The surrogate models are updated by selecting the new sample points that have large prediction errors and are close to the limit state. The efficiency and accuracy of the proposed approaches are demonstrated by 4 representative examples and two finite element problems. The results show that the proposed methods can be effective in evaluating the reliability of high dimension and rare event problems with less computational costs than the single typical surrogate model with active learning approaches (e.g. AK-MCS). Moreover, compared with the ensemble of surrogate models based on global goodness measurement, the proposed approaches also outperform in most cases. Finally, it should be mentioned that the proposed approaches are not only suitable for the combination of Kriging and ANN but also can be extended to other multiple surrogate models including support vector machine, polynomial chaos expansion, and so on.