Coupled fuzzy-interval model and method for structural response analysis with non-probabilistic hybrid uncertainties

In many engineering practices with uncertainty, the non-probabilistic methods play an increasing important role. To overcome the limitation of traditional single-uncertainty modeling methods in handling coupled uncertain problems, this paper develops a more general hybrid uncertainty analysis framework. The non-probabilistic hybrid uncertainties are expressed as coupled fuzzy-interval variables, where the bounds of interval are interpreted as fuzzy sets instead of deterministic values. By means of the cut-set strategy and decomposition theorem in fuzzy set theory, the hybrid uncertain problem is transformed into a series of dual-interval problems. The conservative and radical extreme-value predictions in different variable subspaces are adopted to characterize the coupled uncertainty in output response. To further improve the computational efficiency of extreme-value prediction, an adaptive response surface model using radial basis function is proposed, where the potential global optimum points are introduced as the new sample points in the sequential sampling process. Finally, the effectiveness of the proposed method on dealing with non-probabilistic hybrid uncertainties is validated by two examples. (c) 2020 Elsevier B.V. All rights reserved.