Adaptive Kriging with biased randomisation for reliability analysis of complex limit state functions

Abstract

The present paper researches an innovative approach in the application of meta-modelling for reliability analysis. It consists in the usage of a priori knowledge about the problem being analysed in order to improve the meta-modelling numerical efficiency, in the present case, when calculating the probability of failure. A kriging model is applied to surrogate the failure surface. Its implementation uses an iterative active learning procedure that progressively improves the accuracy of the surrogate prediction of failure. The uncertainty characteristics of the Kriging model are applied in order to establish a notion of improvement in the surrogate characterization of the failure surface. A biased randomisation is applied in order to improve the active learning algorithm. Biased randomisation consists in weighting the search function such that the algorithm prioritizes points in the Design of Experiments that are more important for the problem analysed. Such approach is of high interest for highly non-linear failure functions that may enclose multiple regions in the space of variables that contribute to failure. Since meta-modelling reduces the number of evaluations of the limit-state function, the approach is also of relevance for complex problems that are costly to evaluate. Two examples of application are presented to ilustrate the usage of biased randomisation in the active Kriging approaches. The results show that the number of evaluations of the limit-state function, and consequently the numerical effort demanded for analysis, can be reduced with the approach implemented. It is shown that simple a priori information about the limit-state function and problem analysed may be applied to improve the numerical efficiency of the reliability analysis with active learning techniques.