Structural analysis with alternative uncertainty models: From data to safety measures

• Use of super-ellipsoids and contours of Nataf’s pdfs for convex function modeling.
• Unified conceptual framework to characterize safety of uncertain structures.
• Treatment of mixed uncertainty models in characterizing structural safety.

When adequate empirical data on uncertain variables is lacking, non-probabilistic approaches to quantify uncertainties become appropriate. This study discusses such situations in the context of structural safety assessment. The problem of developing convex function and fuzzy set models for uncertain variables based on limited data and subsequent application in structural safety assessment is considered. Strategies to develop convex set models for limited data based on super-ellipsoids with minimum volume and Nataf’s transformation based method are proposed. These models are shown to be fairly general (for instance, approximations to interval based models emerge as special cases). Furthermore, the proposed convex functions are mapped to a unit multi-dimensional sphere. This enables the evaluation of a unified measure of safety, defined as the shortest distance from the origin to the limit surface in the transformed standard space, akin to the notion used in defining the Hasofer–Lind reliability index. Also discussed are issues related to safety assessment when mixed uncertainty modeling approach is used. Illustrative examples include safety assessment of an inelastic frame with uncertain properties.