An adaptive extreme learning machine based on an active learning method for structural reliability analysis

The metamodel-assisted reliability method opens a promising way to achieve efficient structural reliability assessment for structures with expensive-to-evaluate simulations. The advances in machine learning promote the development of the metamodel technique over the last decades. In this study, an active learning reliability method is presented by the combination of the extreme learning machine(ELM) and an efficient sequential sampling method with the framework of the Bayesian optimization theory. To determine the hyperparameters of ELM automatically, an adaptive extreme learning machine is introduced to approximate the performance function for reliability analysis. Furthermore, a novel active learning function inspired by the ensemble learning strategy is established to select the next best sample for approximation model refinement. Correspondingly, an effective stopping criterion on the cross-validation technique is built to terminate the active learning process timely. Four problems including numerical examples and practical engineering structures are analyzed. The test results show that the proposed method provides a satisfactory failure probability estimation with fewer performance function evaluations for these different reliability problems.