Certifiable Risk-Based Engineering Design Optimization

TL;DR

This paper introduces certifiable risk-based design optimization (CRiBDO), a novel framework that ensures data-informed conservativeness and optimization convergence guarantees for reliable engineering system design under uncertainty.

Contribution

The paper proposes the concept of certifiability in risk-based optimization, analyzing risk measures like superquantile and buffered probability, and reformulates problems to ensure convexity and better conservativeness.

Findings

CRiBDO captures more information for appropriate conservativeness.

CRiBDO exhibits superior convergence by preserving convexity.

Reformulation leads to convex optimization problems in structural design.

Abstract

Reliable, risk-averse design of complex engineering systems with optimized performance requires dealing with uncertainties. A conventional approach is to add safety margins to a design that was obtained from deterministic optimization. Safer engineering designs require appropriate cost and constraint function definitions that capture the \textit{risk} associated with unwanted system behavior in the presence of uncertainties. The paper proposes two notions of certifiability. The first is based on accounting for the magnitude of failure to ensure data-informed conservativeness. The second is the ability to provide optimization convergence guarantees by preserving convexity. Satisfying these notions leads to \textit{certifiable} risk-based design optimization (CRiBDO). In the context of CRiBDO, risk measures based on superquantile (a.k.a.\ conditional value-at-risk) and buffered probability of failure are analyzed. CRiBDO is contrasted with reliability-based design optimization (RBDO), where uncertainties are accounted for via the probability of failure, through a structural and a thermal design problem. A reformulation of the short column structural design problem leading to a convex CRiBDO problem is presented. The CRiBDO formulations capture more information about the problem to assign the appropriate conservativeness, exhibit superior optimization convergence by preserving properties of underlying functions, and alleviate the adverse effects of choosing hard failure thresholds required in RBDO.