ABSTRACT
ABST R AC T An in-depth statistical analysis of a dynamic enzymatic cellulose hydrolysis model, the NREL model, is presented. The uncertainty of model parameters was analysed using condence intervals (CI) of parameter estimates from non-linear regression. The 95% condence of the estimated parameters showed that some of them had unacceptably large bands (e.g. 120 times the mean estimates). This simply means the true parameter value can be found anywhere between these large intervals, hence statistically unidentifiable. Such results mean that the model is over-parameterized w.r.t. experimental data. To better understand the underlying reasons, sensitivity and collinearity analysis of the model structure was performed. The sensitivity
CONTENTS
Introduction ........................................................................................................... 94 Methods .................................................................................................................. 95
Dynamic Cellulose Hydrolysis Model of NREL ..................................... 95 Parameter Uncertainty and Correlation ................................................... 96 Identiability Analysis ................................................................................ 97
Results ..................................................................................................................... 98 Model Fits, Parameter Uncertainty and Correlation .............................. 98 Identiability Analysis: Sensitivity Versus Collinearity Index .......... 100
Implications to Future Research in Modeling Cellulose Hydrolysis and Some Caveats ............................................................................................... 103 Conclusions .......................................................................................................... 104 Acknowledgments .............................................................................................. 105 References ............................................................................................................. 105
analysis showed that among 26 model parameters, only few (ca 10) were signicant while the rest had negligible impact on the model predictions. The collinearity analysis showed that signicant correlations existed between the parameters, hence explaining the source of the large condence intervals. To obtain unique estimates with acceptable condence bands, therefore, one has to use an identiable subset. In this case, many potentially identiable subsets were found, however only six parameters (out of 26) could be uniquely identied. Finally, it should be emphasized that other dynamic hydrolysis models are likely to have severe identiability issues, which need to be overcome before one can reliably use them for engineering purposes such as biofuel process design.
