Model building is an iterative process which starts from the definition of the purpose of the model and the use of the existing knowledge to choose an appropriate framework to propose a first model structure. Given such structure and a set of experimental data, the objective of parameter identification is to estimate the non measurable parameters and, possibly some initial conditions, so as to reproduce the experimental results in the best possible way.
The parameter identification problem is formulated as a nonlinear optimization problem, where the objective is to find the set of parameters to minimize the function quantifying the goodness of the fit subject to the system dynamics.
This apparently simple formulation hides several difficulties that will definitely condition the predictive capabilities of a given model. Particularly relevant are: the multimodal nature of the optimization problem, that is, the presence of several suboptimal solutions; and the lack of (structural or practical) identifiability, that is, the impossibility of giving an unique solution for the parameters.
This talk addresses such difficulties and presents and overview of the methodologies being developed at the Process Engineering Group-CSIC to deal with them. Particular emphasis will be paid to:
The applicability and advantages of the proposed techniques will be illustrated with several examples related to the modelling of biological systems.