Influence of experimental observations on n-propylbenzene kinetic parameter estimates

We calculate the derivatives of best estimates of kinetic parameters of an n-propylbenzene shock tube oxidation model, as determined by a weighted least-squares optimisation, with respect to experimental observations and compare these derivatives to some influence diagnostics based on omission of data points which are widely used in linear regression analysis. The considered data set comprises of 2378 measured concentrations of 37 stable species at various temperatures, pressures, and equivalence ratios. The methods studied are computationally affordable, as they require only a single optimisation and do not require the use of surrogate models. We find that the diagnostics offer many insights into how individual observations influence parameter estimates, such as which observations determine which parameters to what extent. Additionally, the significance of non-linearities in the model responses is investigated. While we observe that they can be of substantial importance to the derivatives of the best parameter estimates with respect to the experimental data, and improve the numerical conditioning of the involved matrix inversion, we find that results obtained from the linear omission-based diagnostics frequently agree, at least qualitatively, with those obtained from the derivatives.