A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds
提出一种基于场景优化的设计方法，利用数据直接优化可靠性和风险，无需概率模型，并给出失效概率的上下界证书，可处理异常值并权衡不同要求的可靠性。
Reliability-based design approaches via scenario optimization are driven by data thereby eliminating the need for creating a probabilistic model of the uncertain parameters. A scenario approach not only yields a reliability-based design that is optimal for the existing data, but also a probabilistic certificate of its correctness against future data drawn from the same source. In this article, we seek designs that minimize not only the failure probability but also the risk measured by the expected severity of requirement violations. The resulting risk-based solution is equipped with a probabilistic certificate of correctness that depends on both the amount of data available and the complexity of the design architecture. This certificate is comprised of an upper and lower bound on the probability of exceeding a value-at-risk (quantile) level. A reliability interval can be easily derived by selecting a specific quantile value and it is mathematically guaranteed for any reliability constraints having a convex dependency on the decision variable, and an arbitrary dependency on the uncertain parameters. Furthermore, the proposed approach enables the analyst to mitigate the effect of outliers in the data set and to trade-off the reliability of competing requirements.