Abstract
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.
Highlights
Reliability-Based Design Optimization (RBDO) methods seek engineering designs that are both economically profitable and meet the desired safety and functionality requirements with high probability
The approach proposed in [1], which is applicable to RBDO problems having reliability functions depending arbitrarily on d, yields a probabilistic certificate of performance for the optimal design
This paper extends the developments therein by providing tighter bounds when the RBDO program can be assumed convex
Summary
Reliability-Based Design Optimization (RBDO) methods seek engineering designs that are both economically profitable and meet the desired safety and functionality requirements with high probability. Reliability Engineering and System Safety 216 (2021) 107900 less stable, i.e., an outlier can significantly change the value of the estimated CVaR In addition to these computational issues with RBDO and CVaRbased CCPs, the majority of the existing methods rely on a precise characterization of a probabilistic model, which is used to estimate failure probabilities and tail expectations. The proposed scenario program shares similar benefits when compared to a traditional work of Rockafellar et al [31] on buffered failure probabilities and CVaR-based reliability optimization. In contrast to the CVaR approach, a prospective reliability certificate for the optimized design can be obtained from the approach printed in this work This certificate bounds the probability of exceeding a predefined Value-atRisk (VaR) level.
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