Non-probabilistic uncertainty quantification and response analysis of structures with a bounded field model

A general framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions is developed in this study. By using a non-probabilistic series expansion (NPSE) method similar as the Expansion Optimal Linear Estimator (EOLE), the bounded field uncertainties with certain spatial correlation characteristic are modeled with a reduced set of uncertain-but-bounded coefficients. Further, it is shown that these coefficients are bounded by a multi-ellipsoid convex model. The gradient-based mathematical programming algorithm combined with an efficient adjoint variable sensitivity scheme is then employed to evaluate the upper and lower bounds of structural performance. The proposed method allows spatially varying uncertainties as well as their dependencies to be described in a non-probabilistic framework, which ensures the objectivity and accuracy of representations of bounded field uncertainties. Moreover, it provides an efficient way to evaluate the variation range of structural performance with a significant reduction of computational cost compared to direct treatments. Numerical examples regarding the performance bound evaluation of structures with bounded field uncertainties are presented to illustrate the validity and applicability of this method.