Epistemic uncertainty in reliability-based design optimization

2012 ◽  
Author(s):  
Xiaotian Zhuang ◽  
Rong Pan
Keyword(s):  
Design Optimization ◽  
Epistemic Uncertainty ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

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

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Taiki Matsumura ◽  
Raphael T. Haftka
Keyword(s):  
Design Optimization ◽  
Thermal Protection ◽  
Epistemic Uncertainty ◽  
Probability Distributions ◽  
Aleatory Uncertainty ◽  
Reliability Based Design Optimization ◽  
Worst Case ◽  
Reliability Based Design ◽  
The Future ◽  
Integrated Thermal Protection System

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.

Model Uncertainty Approximation Using a Copula-Based Approach for Reliability Based Design Optimization

2016 ◽  
Author(s):  
Hao Pan ◽  
Zhimin Xi ◽  
Ren-Jye Yang
Keyword(s):  
Design Optimization ◽  
Model Uncertainty ◽  
Design Space ◽  
Epistemic Uncertainty ◽  
Minimum Cost ◽  
Vehicle Design ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Model Inadequacy

Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting defined reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias which indicates the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty characterization in a defined product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias correction approach is proposed and results are demonstrated by two vehicle design case studies.

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

2012 ◽  
Author(s):  
Taiki Matsumura ◽  
Raphael T. Haftka ◽  
Bhavani V. Sankar
Keyword(s):  
Design Optimization ◽  
Epistemic Uncertainty ◽  
Single Point ◽  
Probabilistic Approach ◽  
Probability Of Failure ◽  
Aleatory Uncertainty ◽  
Engineering Systems ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Analysis Models

The design of engineering systems is often based on analysis models with substantial errors in predicting failures, that is epistemic uncertainty. The epistemic uncertainty is reduced by post design tests, and the safety of unsafe designs restored by redesign. When this process of design, test and redesign is to be based on probabilistic analysis, there is some controversy on whether uncertainty associated with variability (aleatory uncertainty) should be treated differently than the epistemic uncertainty. In this paper we compare several approaches to design and redesign and treatments of the epistemic uncertainties. These include safety factors, probabilistic approach disregarding redesign and regarding redesign, treating epistemic uncertainty and aleatory uncertainty the same, and more conservative treatment of the epistemic uncertainty. We demonstrate that the proposed approach can allow tradeoff of system performance against development cost (probability of redesign), while a standard reliability based design optimization, which does not take into account future redesign, provides only a single point on the tradeoff curve. We also show that the tradeoff can be achieved even with the traditional safety factor approach, without any probabilistic optimization. Furthermore, we investigate different treatments of epistemic error for probability of failure calculation. We find that it is possible to design to the 95th percentile of the probability of failure with modest mass penalty compared to treating epistemic and aleatory uncertainty alike.

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