Diagnosing Parameter Estimability Problems in Polymerization Models

Abstract

To understand why some parameters are difficult to estimate in polymerization models, a new diagnostic methodology is proposed. This method is then used to investigate whether parameter estimability difficulties arise from the small influence of certain parameters on model predictions or from correlated effects with other parameters. The proposed method builds on a popular orthogonalization‐based parameter‐ranking algorithm that ranks parameters from the most estimable to the least estimable. A nylon 6/6,6 copolymerization model and a bio‐based polyether (PO3G) model are used to illustrate the effectiveness of the proposed methodology. Diagnosis of the nylon 6/6,6 model reveals that correlated behavior among six parameters related to nylon 6 cyclic dimer formation leads to parameter‐estimation difficulties. Diagnosis of the PO3G model reveals that difficulties in estimating low‐ranked parameters are mainly due to low‐sensitivities of some parameters and to lack of information about these parameters in the data. The proposed methodology will help future modelers make decisions about simplification of their model equations and about possible future experiments aimed at obtaining reliable parameter estimates and model predictions.

Orthogonalization-Based Gain Conditioning for Linear Model Predictive Control

“…Additional details about how the algorithm is implemented and used are provided elsewhere. [20][21][22]24,26,27…”

“…After the ranked parameter list is obtained, it is common to use a mean-squared error criterion to decide how many parameters should be estimated from the ranked list. − Lower-ranked parameters are held constant at their nominal values to prevent overfitting of the data and prevent numerical problems associated with estimating collinear parameters. Additional details about how the algorithm is implemented and used are provided elsewhere. − ,,, …”

Combining 13C‐NMR Triad Sequence Data with Joint Molecular Weight and Composition Data to Estimate Parameters in a Gas‐Phase Polyethylene Reactor Model

“…[4] It is difficult for mathematical modelers to select suitable values for the large number of kinetic parameters that are encountered when multi-site metallocene catalysts are used. [5] Each type of site has its own values for parameters associated with site activation, propagation with ethylene and comonomer, chain transfer to hydrogen, chain transfer to comonomer, 𝛽-hydride elimination, and catalyst deactivation. Estimating all kinetic parameters in a three-site polymerization model is often impossible with the available data.…”