A Holistic Approach to Uncertainty Quantification with Application to Supersonic Nozzle Thrust

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 numerically 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 which incorporates and quantifies all three sources of uncertainty.