A Mean-Squared-Error-Based Methodology for Parameter Ranking and Selection to Obtain Accurate Model Predictions at Key Operating Conditions
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In this thesis, a new mean-squared-error (MSE)-based criterion, rCCW, is proposed to select the optimal number of parameters to estimate from the ranked list of parameters considering the operating region where accurate model predictions are desired. This new approach accounts for the trade-off between bias and variance as additional parameters from this ranked list are estimated. Next, a new forward-selection methodology based on rCCW MSE-based criterion is devised to simultaneously rank and select the parameters while considering the conditions in the desired operating region. The information about the desired operating conditions is considered during both ranking and selection step in this parameter subset selection technique. This approach is valuable to modelers who want to make predictions about new products or grades or at new operating conditions, using models that are fitted only by utilizing data which were obtained at prior operating conditions. The forward selection MSE-based rCCW criterion is then extended to the cases in which the Fisher information matrix (FIM) is not invertible. A singular FIM has been reported in many industrial chemical engineering models, many high-dimensional parameter estimation problems, and over-parameterized models. A singular FIM leads to a significant complication in the analysis of parameter estimation problems. In this thesis, two different approaches for parameter ranking and selection are undertaken and compared when the FIM is not invertible. The method that uses a reduced invertible FIM is shown to be superior to the alternative method that uses a pseudo inverse, using a linear regression case study. The methodology is extended for use in fundamental nonlinear dynamic models and illustrated using a film casting example.