Robust, Risk and Robust Risk Optimization under Uncertainties
Andre Beck1; Wellison Gomes2; Rafael Lopez2; Leandro Miguel2
1 University of São Paulo; 2 UFSC
doi:10.20906/CPS/USM-2016-0038
Resumo
Robust optimization aims at producing designs which are less sensitive to uncertainties. Risk optimization looks for designs with optimal balance between performance and safety. This paper explores the similarities and differences between these formulations. The strong similitude between robust and risk-based optimizations has not been thoroughly explored before. In this paper, it is shown that the alpha factors, which lead to the compromise solutions in robust optimization, are equivalent to the costs of failure in risk-based optimization. Moreover, it is shown that the robust objective function is often non-convex, with results being given by (often arbitrary) design constraints. In some sense, the usual robust objective function lacks objectiveness, with results becoming largely dependent on arbitrary normalizing constants. On the other hand, when there is a critical limit to performance, which characterizes system failure, and when costs of failure can be defined, the risk-based optimization yields consistent results; no normalizing constants needed. The paper also addresses a combined formulation, the robust risk optimization. In this formulation, the objective, intrinsic uncertainties, which can be modelled in terms of probabilities, are considered in the risk optimization problem. The subjective, epistemic uncertainties are described by fuzzy variables, leading to a fuzzy risk optimization problem. The robust risk optimization is obtained by making the risk optimization problem less sensitive to the fuzzy epistemic uncertainties. The design of a concrete gravity dam is addressed for illustration purposes.
Palavras-chave: Structural optimization; optimum design; robust optimization; risk optimization; reliability analysis; epistemic uncertainties