Probabilistic measures for assessing appropriateness of robust design optimization solutions

Robust design optimization (RDO) is a popular framework for addressing uncertainties in the design of engineering systems by considering different statistical measures, typically the mean and standard deviation of the system response. RDO can lead to a wide range of different candidate designs, establishing a different compromise between these competing objectives. This work introduces a new robustness measure, termed probability of dominance, for assessing the appropriateness of each candidate design. This measure is defined as the likelihood that a particular design will outperform the rival designs within a candidate set. Furthermore, a multi-stage implementation is introduced to facilitate increased versatility/confidence in the decision-making process by considering the comparison among smaller subsets within the initial larger set of candidate designs. For enhancing the robustness in these comparisons the impact of prediction errors, introduced to address potential differences between the real (i.e. as built) system and the numerical model adopted for it, is also addressed. This extends to proper modeling of the influence of the prediction error, including selection of its probability model, as well as evaluation of its impact on the probability of dominance and on the RDO formulation itself. Two illustrative examples are presented, the first considering the design of a tuned mass damper (TMD) for vibration mitigation of harmonic excitations and the second a topology optimization problem for minimum compliance. Extensive comparisons are presented in these two examples and the discussions demonstrate the power of the proposed approach for assessing the designs’ robustness.