An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties

Epistemic uncertainty analysis is an essential feature of any model application subject to ‘state of knowledge’ uncertainties. Such analysis is usually carried out on the basis of a Monte Carlo simulation sampling the epistemic variables and performing the corresponding model runs.In situations, however, where aleatory uncertainties are also present in the model, an adequate treatment of both types of uncertainties would require a two-stage nested Monte Carlo simulation, i.e. sampling the epistemic variables (‘outer loop’) and nested sampling of the aleatory variables (‘inner loop’). It is clear that for complex and long running codes the computational effort to perform all the resulting model runs may be prohibitive.Therefore, an approach of an approximate epistemic uncertainty analysis is suggested which is based solely on two simple Monte Carlo samples: (a) joint sampling of both, epistemic and aleatory variables simultaneously, (b) sampling of aleatory variables alone with the epistemic variables held fixed at their reference values.The applications of this approach to dynamic reliability analyses presented in this paper look quite promising and suggest that performing such an approximate epistemic uncertainty analysis is preferable to the alternative of not performing any.     

Decision making with epistemic uncertainty under safety constraints: An application to seismic design

The problem of accounting for epistemic uncertainty in risk management decisions is conceptually straightforward, but is riddled with practical difficulties. Simple approximations are often used whereby future variations in epistemic uncertainty are ignored or worst-case scenarios are postulated. These strategies tend to produce sub-optimal decisions. We develop a general framework based on Bayesian decision theory and exemplify it for the case of seismic design of buildings. When temporal fluctuations of the epistemic uncertainties and regulatory safety constraints are included, the optimal level of seismic protection exceeds the normative level at the time of construction. Optimal Bayesian decisions do not depend on the aleatory or epistemic nature of the uncertainties, but only on the total (epistemic plus aleatory) uncertainty and how that total uncertainty varies randomly during the lifetime of the project.     

Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty

In 2001, the National Nuclear Security Administration (NNSA) of the U.S. Department of Energy (DOE) in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories) initiated development of a process designated quantification of margins and uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. A previous presentation, “Quantification of Margins and Uncertainties: Conceptual and Computational Basis,” describes the basic ideas that underlie QMU and illustrates these ideas with two notional examples. The basic ideas and challenges that underlie NNSA's mandate for QMU are present, and have been successfully addressed, in a number of past analyses for complex systems. To provide perspective on the implementation of a requirement for QMU in the analysis of a complex system, three past analyses are presented as examples: (i) the probabilistic risk assessment carried out for the Surry Nuclear Power Station as part of the U.S. Nuclear Regulatory Commission's (NRC's) reassessment of the risk from commercial nuclear power in the United States (i.e., the NUREG-1150 study), (ii) the performance assessment for the Waste Isolation Pilot Plant carried out by the DOE in support of a successful compliance certification application to the U.S. Environmental Agency, and (iii) the performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, carried out by the DOE in support of a license application to the NRC. Each of the preceding analyses involved a detailed treatment of uncertainty and produced results used to establish compliance with specific numerical requirements on the performance of the system under study. As a result, these studies illustrate the determination of both margins and the uncertainty in margins in real analyses.