Unknown-but-bounded uncertainty propagation in spacecraft structural system: Interval reduced basis method and its integrated framework

Uncertainty propagation analysis is a key issue for the safety and optimal design of spacecraft structures. This paper proposes an interval reduced basis method (IRBM) for predicting static response of spacecraft structures with unknown-but-bounded uncertainties. Meanwhile, an integrated framework on the basis of IRBM is established by coupling the current finite element codes, which lays the foundation for development of an easy-to-use interval finite element software. In this paper, the novel idea is to approximate the static response using a linear combination of interval basis vectors with undetermined coefficients. The reduced order equations for computing the undetermined coefficients are derived based on Galerkin scheme. For the second-order approximation in IRBM, the static response is easily converted into a family of quadratic programming problems subject to box constraints. The difference of convex functions algorithm is employed to solve these quadratic programming problems. The proposed method can improve the accuracy of the traditional first-order approximation and perform the efficient computation of the second-order approximation of the structural response. Two numerical examples are presented to show the good performance of the proposed method. And an engineering example is performed for its application.