An efficient multi-dimensional P-box propagation method via overlapping domain recognition and sample reusing

Probability-box (P-box) is increasingly employed to quantify both aleatory and epistemic uncertainties in aerospace engineering problems. However, P-box propagation, typically implemented with an inherent double-loop structure, often incurs an unaffordable computational burden, exacerbated by the expensive simulations in the aerospace system. Considering there are overlapping domains of input samples between inner loops during P-box propagation, we propose an innovative method for recognizing the overlapping domains to reuse the historical samples. For each inner loop, the multi-dimensional sampling space is first identified via the integral of probability, and then decomposed into a set of subspaces by using a rooted directed tree based on a hybrid strategy with three decomposition criteria. A sequential selection strategy, based on the maximum average distance, selects the reusable samples within each complete subspace. The applications of the proposed method are validated through three analytical case studies, as well as two engineering case studies involving a solid rocket and a space truss. The results indicate that compared with the existing double-loop Monte-Carlo and local surrogate model, the proposed method can reduce the function calls by 88∼94%. Compared with the sparse-decomposition-based polynomial chaos expansion, the proposed method can further reduce the computational cost by 56%, highlighting good potential in aerospace engineering applications.