Keywords: structural reliability, risk, robust optimization, uncertainties, random variables, fuzzy variables.

In the context of structural design, risk optimization allows one to find a proper point of balance between the concurrent goals of economy and safety. Risk optimization allows the designer to find the optimum level of safety for a structure, in order to minimize the total expected costs. Expected costs of failure are evaluated from nominal failure probabilities, which reflect the analyst's degree of belief in the structure's performance. Such failure probabilities are said to be nominal because they are evaluated from imperfect and/or incomplete mechanical, mathematical and probabilistic models. Model uncertainty and other types of epistemic uncertainties are likely to affect the solution of risk optimization problems.

In this paper, the concept of robust optimization is used in order to derive a solution to risk optimization problems which is less sensitive to epistemic uncertainties. The investigation is based on a simple but illustrative problem, which is built from an elementary but fundamental structural (load-resistance) reliability problem. Intrinsic or aleatoric uncertainties, which can be quantified probabilistically and modeled as random variables or processes, are incorporated in the underlying structural reliability problem. Epistemic and other uncertainties that can only be quantified possibilistically are modeled as fuzzy variables, based on subjective judgment. These include uncertainties in the load and resistance random variable parameters (e.g. the coefficient of variation (c.o.v.)), in the calculated (nominal) failure probabilities and in the nominal costs of failure. The risk optimization problem is made robust with respect to the whole fuzzy portfolio of epistemic uncertainties. Two levels of uncertainty (c.o.v.=0.1 and 0.3) and two different costs of failure are considered.

In general, the results obtained herein show that the robust formulation leads to optimal structural configurations which are more conservative, present higher costs but which are less sensitive to epistemic uncertainties, in comparison with the non-robust structures. This is especially true for higher levels of intrinsic uncertainties (in the underlying reliability problem) and for higher costs of failure. In a practical extension of the present investigation, the formulation presented herein will be applied in the optimization of partial safety factors for codified structural design.

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