Reliability-Based Design Optimization Incorporating Extended Optimal Uncertainty Quantification
Niklas Miska, Daniel Balzani
TL;DR
The paper addresses designing engineered systems under polymorphic uncertainty by integrating the extended OUQ framework into a reliability-based design optimization (RBDO) workflow using a double-loop strategy. It formalizes how to compute mathematically sharp bounds on both the PoF and the cost under both aleatory and epistemic uncertainties without prescribing PDFs, leveraging convex combinations of Dirac masses and moment constraints. Through two numerical demonstrations—a polymorphic-uncertainty buckling benchmark and a car bumper optimization with laser-hardened traces—it shows that OUQ-based bounds yield robust, information-consistent designs and quantify the impact of data availability on optimal sizing and material placement. While the approach demonstrates clear benefits in risk-informed design, it also highlights substantial computational costs and points to efficiency improvements as a key area for future work. Overall, the framework offers a principled, bound-tight methodology for engineering design under uncertainty with practical applicability to complex, data-limited problems.
Abstract
Reliability-based design optimization (RBDO) approaches aim to identify the best design of an engineering problem, whilst the probability of failure (PoF) remains below an acceptable value. Thus, the incorporation of the sharpest bounds on the PoF under given constraints on the uncertain input quantities strongly strenghtens the significance of RBDO results, since unjustified assumptions on the input quantities are avoided. In this contribution, the extended Optimal Uncertainty Quantification framework is embedded within an RBDO context in terms of a double loop approach. By that, the mathematically sharpest bounds on the PoF as well as on the cost function can be computed for all design candidates and compared with acceptable values. The extended OUQ allows the incorporation of aleatory as well as epistemic uncertainties, where the definition of probability density functions is not necessarily required and just given data on the input can be included. Specifically, not only bounds on the values themselves, but also bounds on moment constraints can be taken into account. Thus, inadmissible assumptions on the data can be avoided, while the optimal design of a problem can be identified. The capability of the resulting framework is firstly shown by means of a benchmark problem under the influence of polymorphic uncertainties. Afterwards, a realistic engineering problem is analyzed, where the positioning of laser-hardened lines within a steel sheet for a car crash structure are optimized.