CVaR Formulation of Reliability-Based Design Problems Considering the Risk of Extreme Failure Events

The reliability-based design optimization (RBDO) considers uncertainties under probability constraints. The probability constraint ensures a minimum level of safety, but it does not account for the risks beyond the level and potentially catastrophic accidents caused by those extreme risks. Accordingly, the optimum design based on the conventional RBDO formulation may either lead to bearing high uncontrollable risks or difficult to optimize. To capture these uncertainties and extreme risks, the risk measure of conditional-value-at-risk (CVaR), which is a coherent and adverse measure of risk, should be integrated into the RBDO formulation. This paper aims at proposing an efficient and robust reliability-based design formulation for engineering systems, which takes the advantages of the CVaR measure to manage system risks intelligently. The developed formulation helps the reliability-based design to obtain a conservative final design and control the design with extreme risks automatically. Numerical experiments demonstrate that the proposed RBDO formulation achieves a more conservative optimum design controlling extreme risks compared with the conventional RBDO formulation.