A Comprehensive Methodology for Development, Parameter Estimation, and Uncertainty Analysis of Group Contribution Based Property ModelsAn Application to the Heat of Combustion

A rigorous methodology is developed
that addresses numerical and
statistical issues when developing group contribution (GC) based property
models such as regression methods, optimization algorithms, performance
statistics, outlier treatment, parameter identifiability, and uncertainty
of the prediction. The methodology is evaluated through development
of a GC method for the prediction of the heat of combustion (ΔHco) for pure components. The results showed that robust regression
lead to best performance statistics for parameter estimation. The
bootstrap method is found to be a valid alternative to calculate parameter
estimation errors when underlying distribution of residuals is unknown.
Many parameters (first, second, third order group contributions) are
found unidentifiable from the typically available data, with large
estimation error bounds and significant correlation. Due to this poor
parameter identifiability issues, reporting of the 95% confidence
intervals of the predicted property values should be mandatory as
opposed to reporting only single value prediction, currently the norm
in literature. Moreover, inclusion of higher order groups (additional
parameters) does not always lead to improved prediction accuracy for
the GC-models; in some cases, it may even increase the prediction
error (hence worse prediction accuracy). However, additional parameters
do not affect calculated 95% confidence interval. Last but not least,
the newly developed GC model of the heat of combustion (ΔHco) shows predictions of great accuracy and quality (the most data
falling within the 95% confidence intervals) and provides additional
information on the uncertainty of each prediction compared to other
ΔHco models reported in literature.