Robust Optimization of Structural Risks Under Epistemic Uncertainties

Abstract eng:
Risk optimization involves minimization of total expected costs, which include expected costs of failure, evaluated from nominal failure probabilities. Failure probabilities reflect the analyst's degree of belief in the structure's performance, and are said to be nominal because they are evaluated from imperfect and/or incomplete mechanical, mathematical and probabilistic models. Hence, epistemic uncertainties are likely to compromise results of risk optimization. In this paper, the concept of robustness is employed in order to find risk optimization solutions which are less sensitive to epistemic uncertainties. The investigation is based on an elementary but fundamental structural (load-resistance) reliability problem. Intrinsic or aleatoric uncertainties, which can be quantified probabilistically and modeled as random variables, are incorporated in the underlying structural reliability problem. Epistemic uncertainties that can only be quantified possibilistically are modeled as fuzzy variables, based on subjective judgment. Risk optimization is made robust with respect to the whole fuzzy portfolio of epistemic uncertainties. It is shown in the paper that the robust formulation leads to optimal structural configurations which are more conservative, present higher nominal costs but which are less sensitive to epistemic uncertainties, in comparison to the non-robust optimum structures. This is especially true for larger levels of intrinsic uncertainties (in the underlying reliability problem) and for greater costs of failure. An application example, involving optimization of partial safety factors for the codified design of steel beams under bending, is also presented.

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