A modified parallelepiped model for non-probabilistic uncertainty quantification and propagation analysis

摘要

As a typical convex model, the parallelepiped plays an important role in the non-probabilistic uncertainty quantification with simultaneous dependent and independent variables. To overcome the complexity of the conventional geometric design-based method, this paper proposes a more efficient sample-driven procedure to construct the explicit mathematical expression of parallelepiped model. Instead of the geometric characteristics of minimum-volume parallelepiped, the statistical characteristics of available samples are employed to directly evaluate the marginal intervals and correlation coefficients of uncertain variables. Especially for the inconstant uncertainty problem with dispersed samples, a sub-parallelepiped modeling method is further presented by means of the sample clustering analysis, which can effectively decrease the invalid domains in uncertainty quantification. Besides, in order to improve the computing efficiency of uncertainty propagation analysis under the parallelepiped model, the radial basis function-based surrogate model is introduced as an approximation of the original time-consuming computational model. Finally, two numerical examples verify the effectiveness of the proposed model and method. (C) 2020 Elsevier B.V. All rights reserved.