The adaptive weight learning function for reliability analysis and its application to multiple active learning methods

Abstract In engineering, evaluating the failure probability of structures with complex performance functions is a challenging task. Some active learning methods based on the Kriging model gain considerable attention for structural reliability analysis. The existing learning functions offer new learning criterions to select sample points, but the probability density function (PDF) of sample points is ignored in some learning functions. To decrease selecting sample points in low PDF regions, this study presents a new adaptive weight learning function (WLF). The learning function WLF constituted by the adaptive orient function and the joint PDF can be applicable to multiple learning functions. Depending on the importance degree of candidate sample points, the sample points can be assigned different weight by learning function WLF. When the leaning function WLF is applicated to the existing active learning methods, the sample point with a higher PDF in neighborhood of the limit state function (LSF) can be given a larger weight to preferentially select into design of experiments (DoE). Therefore, the learning function WLF can help the multiple learning functions to select informative sample points with high PDF, which can further improve the efficiency of these learning functions. Four examples are used to illustrate the accuracy and efficiency as well as the suitability of the learning function WLF.