An enhanced active learning Kriging model for evidence theory-based reliability analysis

Evidence theory-based reliability analysis (ETRA) is investigated in this paper. To estimate the plausibility (Pl) and belief (Bel) measures of failure probability, the active learning method based on Kriging model for ETRA (ALK-ETRA) has been proposed. However, ALK-ETRA pays too much attention to rightly predicting the signs of performance function at points throughout the uncertain space. To minimize the waste of training points, an enhanced version of ALK-ETRA (En-ALK-ETRA) is proposed in this paper. Pl or Bel is determined by the sign associated with an individual joint focal element (JFE) rather than a single point. Based on this idea, a brand-new learning function and a novel stopping condition are proposed in En-ALK-ETRA. Aided by the new learning function, the most dangerous JFE in which the lower (or upper) bound of performance function has the largest probability of wrong sign prediction is identified. The added training point is chosen from the most dangerous JFE and thus the convergence speed of learning process is accelerated. In the new stopping condition, the number of JFEs where the minimum (or maximum) of performance function with wrong sign predictions is explicitly deduced and thus the error of ETRA can be estimated. The error of ETRA is real-time monitored and thus the learning process is timely terminated without accuracy sacrifice. The performance of the proposed method is demonstrated by six case studies.