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Uncertainty quantification of reduced models

  • Author(s): Liu, Zhenyuan
  • Advisor(s): Frenklach, Michael
  • et al.
Abstract

Detailed reaction models such as detailed soot models, describing complex phenomena in combustion are typically computationally intensive. Reduced reaction models derived from a detailed, full-size reaction model are, thus, necessary in combustion simulations. The validation of a reduced model typically requires its predictions for selected quantities of interest (QOIs) to be close to those of the detailed model. Moreover, an accurate reduced model should be capable of reproducing faithfully the propagation of uncertainty by the detailed model.

Several reduced models for syngas combustion were developed by the "detailed reduction" method. This method was also adapted to develop several reduced models for a stochastic soot oxidation model, which are typically difficult to develop with other reduction methods. Different measures were developed to assess how uncertainties in the model parameters and in the model predictions behave for reduced models as compared to those for the detailed model. The uncertainty quantification (UQ) analysis was carried out through a numerically efficient, deterministic, and optimization-based framework of Bound-to-Bound Data Collaboration (B2BDC) and a Gibbs sampling algorithm adopted for B2BDC. The measures developed can be categorized into the sampling- and optimization-based measures.

The measures were applied to several reduced models of syngas combustion and several reduced models of soot oxidation in three different examples. The developed measures successfully quantified the propagation of uncertainty by the detailed and reduced models, and numerically demarcated the performance of different reduced models. The results demonstrated that assessment of the quality of a reduced model without considering parameter uncertainty may be misleading in that the deviation can be much larger when the uncertainties in the model parameters are taken into account, highlighting the significance of UQ analysis in the validation of reduced models. The performed analysis demonstrated that when the experimental data are of bad quality, the posterior region of the model parameters (the feasible set) could have a very complex shape, posing a substantial challenge to the sampling-based measures. If no verifiably accurate experimental data exist, computer-generated data from the solution of the detailed model offer a reliable alternative, in which the desired level of reduced-model accuracy can be prescribed by specifying the accepted ranges of variations in prediction of training targets. If a feasible set has a very complex shape, uniform sampling of the feasible set could be very expensive. In such situations, the B2BDC framework offers a more practical alternative by quantifying the propagated uncertainty through numerically efficient computations of uncertainty intervals and their overlap, all with the added benefit of obtaining the uncertainty sensitivities.

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