Evaluation of Quantification of Margins and Uncertainties Methodology for Assessing and Certifying the Reliability of the Nuclear Stockpile (2009) / Chapter Skim
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2 Use of the QMU Methodology
2 Use of the QMU Methodology
Pages 18-33
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From page 18... ...
• QMU aids the national security laboratories in allocating impor tant stockpile stewardship resources. The first number of the findings and recommendations numbering system refers to the task number with which the finding or recommendation is associated.
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QMU extends the concept of classic engineering factors that compute the ratio of design load to maximum expected load. Its use brings a systematic, quantitative approach to thinking about margins, M, and uncertainties, U
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The national security laboratories have focused much of their effort for uncertainty quantification on computing the sensitivity of code output to uncertainties in input parameters. A broader effort is necessary.
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The state of the art at the design labs is approximately as follows: • Given sufficient computational resources, the labs can sample from input-parameter distributions to create output-quantity distributions that quantify code sensitivity to input variations. However, -- Resources are not sufficient to do this with high fidelity; -- ampling from the actual high-dimensional input space is not S a solved problem and is not done in the nuclear weapons c ontext; -- ften the unstated premise is that imperfect code is somehow O good at calculating sensitivities to input variations.
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The national security laboratories should continue to focus attention on quantifying uncertainties that arise from epistemic uncertainties such as poorly modeled phenom ena, numerical errors, coding errors, systematic uncertainties in experiment. Because discretization errors, code errors, and subgrid-model errors (poorly modeled physical phenomena)
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Nuclear Regulatory Commission (1994)
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example to illustrate a potentially useful concept for communicating assessment results. This concept is taken from the probabilistic risk assessment community (see Appendix A)
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If a particular experiment were perfectly characterized, measured data were free from error, and the mathematical model equations were solved perfectly, the difference between the mathematical solution and the experimental measurement would be the model error for the measured quantity. In practice the picture is muddied by imperfect characterization of experiments, imperfect measurements, numerical approximations of the mathematical model equations, and coding errors.
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Here M is the difference between the best-estimate value of the lower bound of the design range of metric VBE (in the figure, the primary yield) and the best-estimate value of the upper bound of the threshold, T BE (in the figure the minimum primary yield)
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This calls into question the interpretations of "maximum credible value" and "minimum credible value." In order for these uncertainties to be meaningful, they should be prescribed unambiguously. A commonly used measure is the number s of standard deviations -- such as 1s, 2s, or 3σ -- of the uncertainty probability distribution.
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DIRECT COMPUTATION OF DISTRIBUTION OVERLAP A similar approach that has been suggested is to compute distributions and use them directly -- that is, without necessarily trying to identify values for M or U -- to assess confidence that a performance gate is passed. This general idea appears to avoid some of the issues discussed above, such as how to rigorously define numbers such as M and U
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. In the first stage, for example, uncertainties in pit mass and surface finish propagate to variations in cavity compactness; the latter then lead to variations in boost yield and, ultimately, variations in primary yield.
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The successful application of QMU requires a great deal of expert judgment from scientists and engineers with relevant weapons expertise -- especially weapons designers -- particularly in quantifying uncertainties.10 This expertise is supported by advanced computer facilities. Several designers noted that expert judgment is based on experience; the number of experts with these capabilities will decline unless ongoing efforts to support necessary projects and experiments and to attract and retain quality staff continue to succeed.
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Each knob is a parameter in the simulation codes that can be adjusted to match important features of underground nuclear test data and of experiments on devices of similar design. Collectively, these four knobs represent the largest gap in scientific understanding of the nuclear explosive process.
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PRA concepts have demonstrated their value in assessing performance measures or gates such as safety and security and could contribute to making the assessment of weapons risk issues more transparent. The committee observed that the national security laboratories have considerable expertise in probabilistic risk assessment, a discipline developed over the past several decades to facilitate the assessment of rare events for which there are limited data and testing results.
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The national security laboratories should investigate the utility of a probability of frequency approach in presenting uncertainties in the stockpile.12 As noted in the simplified example illustrated in Figure 2-1 and further discussed in Appendix A, representing failure modes in terms of probability of frequency could provide decision makers with a richer understanding of the uncertainties -- and a clearer notion of how to address them -- than could estimating the reliability or M/U. 12 See,for example, J.C.
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