Applications of Response Surface Techniques to Uncertainty Analysis in Gas Kinetic Models

5 Applications of Response Surface Techniques to Uncertainty Analysis in Gas Kinetic Models 

In the study, the reactions were treated as reversible, with reverse rates calculated from the appropriate equilibrium constants based on enthalpies of formatiOTi calculated using NASA polynomials (see Sect. 2.2.3). Because so many of the input parameters were estimated, derived from a low number of measurements or from single theoretical studies, the input distributions were cmisidered to be uniform between predefined minimum and maximum values (Tomlin 2006). Uncertainties in the rate coefficients were expressed using A-factors only, since for most reactions, there was insufficient information to determine the joint of the Arrhenius parameters. 

For 176 input parameters, the full second-order HDMR expansion consists of 15,577 component functions (1 zeroth-order term-1-176 first-order terms-1-15,400 second-order terms). However, using a threshold of 1 % for the first- and second-order component functions, only five of the 176 first-order component functions and none of the 15,400 second-order component functions were approximated by optimal-order polynomials. The resulting first-order HDMR metamodel gave 99.05 % of the tested samples within the 5 % RE (relative error) range (see Eq. (5.49)) compared to a sample of 2,000 full model runs. This suggests that despite the high-dimensionality of the input space of the model, the predicted NO 

Esposito and CheUiah (2012) investigated the effect of the uncertainty of binary diffusion coefficients and chemical kinetic parameters on the simulation results of 

An example of the propagated uncertainties for the non-optimised (prior) model, represented by la bands, is shown in the left panel of Fig. 5.26 for predicted laminar flame speeds, with the shaded regions showing the predicted pdf. The scatter in the 

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