Sequential parameter estimation for large-scale systems with multiple data sets. 1. Computational framework

A sequential approach to solving large-scale parameter estimation problems with multiple data sets is presented. A nested three-stage computation framework is proposed to decompose the problem. The upper stage is an NLP with only the parameters to be estimated as optimization variables. The middle stage consists of multiple sub-NLPs in which the independent variables of each data set are treated as optimization variables. In the lower stage the dependent variables and their sensitivities are computed through a simulation step. The sensitivities for the upper stage NLP and for the middle stage sub-NLP's can be easily computed by employing the Jacobians of the model equations at the lower stage. This approach is an extension of the work by Dovi and Paladino (Comput. Chem. Eng. 1989,6, 731-735) and Kim et al. (AIChE J. 1990,36,985-993). The advantage of this approach lies in the fact that it needs very few mathematical manipulations and can be easily implemented with standard NLP software. And the existing simulator can be connected for the function evaluation and sensitivity computation. Three practical examples are used to demonstrate the performance of this approach.