ON THE ROBUSTNESS OF STRUCTURAL RISK OPTIMIZATION WITH RESPECT TO EPISTEMIC UNCERTAINTIES

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 involves the minimization of total expected costs, which include expected costs of failure. 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. Hence, model uncertainty and other types of epistemic uncertainties are likely to compromise the 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 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 stochastic processes, 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. These include uncertainties in random load and resistance variables, in the nominal (calculated) 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. An application example, involving optimization of partial safety factors for the codified design of steel beams under bending, is also presented. In general, results obtained herein show 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. The essential result of robust optimization is also shown to be insensitive to reasonable variations of expert confidence: the robust solution is more conservative and more expensive, but also less sensitive to epistemic uncertainties. The more pessimistic the expert, the more conservative is the robust solution he gets, in comparison to the nominal, non-robust solution.