Selection of model parameters for off-line parameter estimation

Mechanistic dynamic models often contain unknown parameters whose values are difficult to determine even with highly specialized laboratory experiments. A practical approach is to estimate such parameters from available process data. Typically only a subset of the parameters can be estimated due to restrictions imposed by the model structure, lack of measurements, and limited data. We present a simple parameter selection method which accounts for the first two factors independent of the data available for parameter estimation. The magnitude of each parameter effect on the measured variables is quantified by applying principal-component analysis to the steady-state parameter-output sensitivity matrix. The uniqueness of each parameter effect is determined by computing the minimum distance between the sensitivity vector of the particular parameter and the vector spaces spanned by sensitivity vectors of the parameters already selected for estimation. A recursive algorithm that provides a tradeoff between the magnitude and linear independence of parameter effects yields a ranking of the parameters according to their inherent ease of estimation. The parameter-selection procedure is applied to the problem of kinetic parameter estimation for an industrial model of a polymerization reactor. For this specific example, the proposed method yields superior estimation results than those obtained with a parameter-selection technique based on the Fisher information matrix (FIM).