Mean-Squared-Error Methods for Selecting Optimal Parameter Subsets for Estimation

Engineers who develop fundamental models for chemical processes are often unable to estimate all of the parameters, especially when available data are limited or noisy. In these situations, modelers may decide to select only a subset of the parameters for estimation. An orthogonalization algorithm combined with a mean squared error (MSE) based selection criterion has been used to rank parameters from most to least estimable and to determine the parameter subset that should be estimated to obtain the best predictions. A robustness test is proposed and applied to a batch reactor model to assess the sensitivity of the selected parameter subset to initial parameter guesses. A new ranking and selection technique is also developed based on the MSE criterion and is compared with existing techniques in the literature. Results obtained using the proposed ranking and selection techniques agree with those from leave-one-out cross-validation but are more computationally attractive.