A Deep Learning-Enhanced Active Sampling Approach to Evidential Uncertainty Propagation

Abstract Evidence theory offers a flexible framework for characterizing both aleatory and epistemic uncertainties. However, uncertainty propagation under the evidence theory framework is computationally tedious due to the combinatorial explosion of input focal elements and frequent evaluations of the system response function for extremum analysis. To address these issues, this article proposes an active sampling approach that accurately and efficiently constructs a metamodel of the system response function, thereby reducing the frequency of system response evaluations. The proposed metamodeling strategy effectively balances exploration, exploitation, and robustness, while also establishing an optimal maximin distance strategy to generate well-distributed candidate sample points. Additionally, an artificial neural network (ANN) model is introduced to replace the extremum calculation of evidential variables. In constructing the ANN model, a centroid-based farthest point sampling method is developed to select training focal elements, with joint focal elements of inputs and response focal elements serving as input and output features of the ANN model, respectively. Furthermore, multiple stopping criteria based on the Hartley measure and Jousselme distance are applied to the iterative training process to ensure the convergence. Numerical and engineering case studies demonstrate that the proposed method achieves high accuracy and efficiency when handling engineering applications with large number of focal elements and high nonlinearity features.