An empirical approach to reliability-based design using scenario optimization

Scenario-based approaches to Reliability-Based Design-Optimization were recently proposed by the authors, Rocchetta et al. (2019). Scenario theory makes direct use of the available data thereby eliminating the need for creating a probabilistic model of the uncertainty in the parameters. This feature makes the resulting design exempt from the subjectivity caused by prescribing an uncertainty model from insufficient data. Most importantly, scenario theory renders a formally verifiable bound to the probability of failure. This bound is non-asymptotic and holds for any probabilistic model consistent with the available data. In this article we seek designs that minimize a combination of cost and penalty terms caused by violating reliability constraints. Similar to Conditional-Value-at-Risk programs, the proposed optimization approach is convex, thereby easing its numerical implementation. As opposite to a Conditional-Value-at-Risk method, a model for the uncertainty is not required and the method provides bounds on the reliability, which is valuable information to assess the robustness of the prescribed design. Furthermore, the proposed approach enables the analyst to shape the distribution of the design's performance according to a given value-at-risk. This is done by minimizing the empirical approximation of the integral of the design's performance in the loss/failure region. The effectiveness of the approach is tested on an easily reproducible numerical example with its strengths discussed in comparison to traditional methods.