Obtaining the Best Model Predictions and Parameter Estimates Using Limited Data
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Engineers who develop fundamental models for chemical processes are often unable to estimate all of the model parameters due to problems with parameter identifiability and estimability. The literature concerning these two concepts is reviewed and techniques for assessing parameter identifiability and estimability in nonlinear dynamic models are summarized. Modellers often face estimability problems when the available data are limited or noisy. In this situation, modellers must decide whether to conduct new experiments, change the model structure, or to estimate only a subset of the parameters and leave others at fixed values. Estimating only a subset of important model parameters is a technique often used by modellers who face estimability problems and it may lead to better model predictions with lower mean squared error (MSE) than the full model with all parameters estimated. Different methods in the literature for parameter subset selection are discussed and compared. An orthogonalization algorithm combined with a recent MSE-based criterion has been used successfully to rank parameters from most to least estimable and to determine the parameter subset that should be estimated to obtain the best predictions. In this work, this strategy is applied to a batch reactor model using additional data and results are compared with computationally-expensive leave-one-out cross-validation. A new simultaneous ranking and selection technique based on this MSE criterion is also described. Unfortunately, results from these parameter selection techniques are sensitive to the initial parameter values and the uncertainty factors used to calculate sensitivity coefficients. A robustness test is proposed and applied to assess the sensitivity of the selected parameter subset to the initial parameter guesses. The selected parameter subsets are compared with those selected using another MSE-based method proposed by Chu et al. (2009). The computational efforts of these methods are compared and recommendations are provided to modellers.