An efficient strategy for computing interval expectations of risk

In order to minimize risks it is of paramount importance to take into account the effects of uncertainties from the design stage. In fact, the knowledge about the behaviour of complex systems and future conditions is always incomplete. Risk-based optimization is a powerful and well-recognized tool for identification of the optimal (robust) design with a systematic consideration of uncertainty. More specifically, this approach looks for the best design solution, whilst minimizing the risk, thus considering the effects of uncertainties giving a measure of safety levels. However, traditional optimization procedures come out with a punctual (single) optimum that rarely can be translated in engineering solutions, leaving little or no room for manufacturing and operating tolerances. The optimization shall be given an even more rational connotation for treating the uncertainties that comprises set-wise quantities. Solution is found by means of interval analysis even if it introduces further computational costs that are herein addressed developing tailored numerical strategies. In this paper an efficient method that allows to break down the computational costs of risk and uncertainty analyses considering intervals is presented. The method, implemented in an open source computational framework, is based on a very efficient Monte Carlo technique. Numerical results are delivered showing the applicability and efficiency of the proposed approach.