Evidence-Theory-Based Reliability Analysis From the Perspective of Focal Element Classification Using Deep Learning Approach

Epistemic uncertainty is widespread in reliability analysis of practical engineering products. Evidence theory is regarded as a powerful model for quantifying and analyzing epistemic uncertainty. However, the heavy computational burden has severely hindered its application in practical engineering problems, which is essentially caused by the repeated extreme analysis of limit-state function (LSF). In order to address the issue, this paper proposes a novel method to solve the evidence-theory-based reliability analysis (ETRA). It transforms the conventional ETRA problem into the classification of three classes of joint focal elements (JFEs) and then solves the classification problem effectively through a deep learning approach. The core of solving an ETRA problem is to determine whether the joint focal element is located in the reliable region, failure region, or intersected with the LSF. A spatial position feature reduction and arrangement method is proposed to classify the JFEs, which can effectively reduce the feature dimension and take into account the integrity and correlation of features. The stacked autoencoders model is then constructed and updated by extracting the spatial position features of the sampled JFEs to achieve high-accuracy classification of the remaining JFEs, and the reliability interval is calculated efficiently according to the classification results. Finally, the effectiveness of the proposed method is demonstrated using several numerical examples.