Reliability Based Design Optimization Modeling Future Redesign With Different Epistemic Uncertainty Treatments

Abstract

Design under uncertainty needs to account for aleatory uncertainty, such as variability in material properties, and epistemic uncertainty including errors due to imperfect analysis tools. While there is a consensus that aleatory uncertainty be described by probability distributions, for epistemic uncertainty there is a tendency to be more conservative by taking worst case scenarios or 95th percentiles. This conservativeness may result in substantial performance penalties. Epistemic uncertainty, however, is usually reduced by additional knowledge typically provided by tests. Then, redesign may take place if tests show that the design is not acceptable. This paper proposes a reliability based design optimization (RBDO) method that takes into account the effects of future tests possibly followed by redesign. We consider each realization of epistemic uncertainty to correspond to a different design outcome. Then, the future scenario, i.e., test and redesign, of each possible design outcome is simulated. For an integrated thermal protection system (ITPS) design, we show that the proposed method reduces the mass penalty associated with a 95th percentile of the epistemic uncertainty from 2.7% to 1.2% compared to standard RBDO, which does not account for the future. We also show that the proposed approach allows trading off mass against development costs as measured by probability of needing redesign. Finally, we demonstrate that the tradeoff can be achieved even with the traditional safety factor based design.

Simulating Future Test and Redesign Considering Epistemic Model Uncertainty

“…Previous work has illustrated this tradeoff when there is only a fixed constant model bias. [1][2][3] This study builds on previous work by considering spatial correlation in the epistemic model uncertainty. A Kriging surrogate is used to provide a flexible representation of the epistemic model uncertainty that allows the method to be applicable to a wide range of engineering problems.…”

“…18 In the context of constant model bias, Matsumura et al compared RBDO considering future redesign to traditional RBDO. 1 Villanueva et al also studied the tradeoff between future redesign and performance for an integrated thermal protection system. 2 Price et al compared starting with a more conservative design and possibly redesigning to improve performance to starting with a less conservative design and possibly redesigning to improve safety.…”

Deciding Degree of Conservativeness in Initial Design Considering Risk of Future Redesign

“…Villanueva et al simulated the effects of future tests and redesign on an integrated thermal protection system (ITPS) considering the effect of redesign on the uncertainty in the probability of failure [13]. Matsumura et al compared reliability-based design optimization (RBDO) considering future redesign to traditional RBDO [14]. Villanueva et al demonstrated the tradeoff between expected design performance and probability of redesign for the ITPS example [15].…”

Multi-disciplinary analysis and optimization under uncertainty

“…However, only a small number of studies have addressed the propagation of both aleatory uncertainty and epistemic uncertainty in single disciplinary analysis [34,35,36,37,38,39,40,41,42]. Studies on uncertainty propagation through feedback-coupled MDA are even fewer [9,10,11,26,19], and have only addressed aleatory uncertainty.…”

“…Or an input variable may have natural variability (aleatory), but due to lack of data, its distribution type and/or parameters may be uncertain. Epistemic uncertainty regarding the inputs has been addressed through evidence theory [35,36], possibility theory [43], fuzzy sets [23], imprecise probabilities [44], p-boxes [40], aleatory-like but conservative treatment [41], likelihood-based probabilistic approaches [42,45], etc., but has been mostly applied to feed-forward or monolithic problems.…”