Publications

Gaspar, B., Teixeira, A.P. and Guedes Soares, C. (2015), “A study on a stopping criterion for active refinement algorithms in Kriging surrogate models”, Safety and Reliability of Complex Engineered Systems, Podofilini et al (Eds.), Taylor & Francis Group, London, UK, pp. 1219-1227

The use of surrogate models for time-consuming implicit limit state functions (e.g. requiring a finite element analysis (FEA)) has been a common approach to cope with the computational cost in the context of structural reliability analysis. Well established and efficient methods to compute small failure probabilities such as the first-order reliability method (FORM) or the Monte Carlo based simulation methods with variance reduction techniques can then be applied at low computational cost. Among the presently available surrogate models for these applications (e.g. Bucher & Most 2008, Sudret 2012), the use of Kriging models (also known as Gaussian process models) has emerged recently due to their interesting features for structural reliability analysis, such as the interpolation capability, large flexibility or local adaptability and the prediction uncertainty measure (e.g. Echard et al. 2011, Gaspar et al. 2014). In particular, the prediction uncertainty measure has been explored in the development of efficient adaptive surrogate models based on active refinement algorithms, which provide an active control of the accuracy of the surrogate model and the corresponding failure probability predictions (e.g. Echard et al. 2011, Dubourg et al. 2013). Typically, such algorithms use learning functions (e.g. U-function proposed by Echard et al. (2011)) to identify the best points of a Monte Carlo sample that will iteratively enrich the sample of support points that define the Kriging surrogate model. Although such active refinement algorithms lead to quite accurate surrogate models and failure probability predictions, the stopping criteria that have been adopted are in some cases too conservative for practical applications, as the iterative enrichment of the surrogate model proceeds without significant gains in terms of failure probability accuracy (e.g. Echard et al. 2011). This problem tends to be more significant in larger dimensional spaces of random variables, which is typically the case in practical applications. This paper presents a study of an alternative stopping criterion for such active refinement algorithms that exploits the stabilization of the failure probability prediction during the iterative enrichment of the surrogate model. The alternative stopping criterion will contribute to a more efficient implementation of the presently available adaptive Kriging surrogate models.

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