Inverse problems in structural safety analysis with combined probabilistic and non-probabilistic uncertainty models

Abstract

In problems of structural safety analysis, depending upon the nature and extent of availability of empirical data, uncertainties could be quantified by using probabilistic and/or non-probabilistic models. The options for non-probabilistic representations include intervals, convex functions, and (or) fuzzy variable models. We consider a few inverse problems of structural safety analysis aimed at the determination of system parameters to ensure a target level of safety and/or to minimize a cost function for problems involving combined probabilistic and non-probabilistic uncertainty modeling. The treatment of this problem calls for combining methods of uncertainty analysis with finite element structural modeling and numerical optimization tools. Development of load and resistance factor design format, in problems with combined uncertainty models, is also presented. We employ super-ellipsoid based convex function models for representing non-probabilistic uncertainties. The target safety levels are taken to be specified in terms of indices defined in standard space of uncertain variables involving standard normal random variables and/or unit hyper-spheres. A class of problems amenable for exact solutions is identified and a general procedure for dealing with more general problems involving nonlinear performance functions is developed. Illustrations include studies on inelastic frame with uncertain properties. Accompanying supplementary material contains additional illustrations.