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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003562
pages 363-381


Christopher J. Roy
Aerospace and Ocean Engineering Department, Virginia Tech, Blacksburg, Virginia 24061, USA
Michael S. Balch
Applied Biomathematics, Setauket, New York 11733, USA


In modeling and simulation (M&S), we seek to predict the state of a system using a computer-based simulation of a differential equation-based model. In general, the inputs to the model may contain uncertainty due to inherent randomness (aleatory uncertainty), a lack of knowledge (epistemic uncertainty), or a combination of the two. In many practical cases, there is so little knowledge of a model input that it should be characterized as an interval, the weakest statement of knowledge. When some model inputs are probabilistic and others are intervals, segregated uncertainty propagation should be used. The resulting uncertainty structure on the M&S output can take the form of a cumulative distribution function with a finite width; i.e., a p-box. Implications of sampling over interval versus probabilistic uncertainties in the outer loop are discussed and examples are given showing the effects of the choice of uncertainty propagation and characterization methods. In addition to the uncertainties in model inputs, uncertainties also arise due to modeling deficiencies and numerical approximations. Modeling uncertainties can be reduced by performing additional experiments and numerical uncertainties can be reduced by using additional computational resources; thus, both sources of uncertainty can be modeled as epistemic and can be characterized as intervals and included in the total predictive uncertainty by appropriately broadening the prediction p-box. A simple example is given for the M&S predictions of supersonic nozzle thrust that incorporates and quantifies all three sources of uncertainty.