For any modeling problem an ensemble of models is initially developed, which may comprise phenomenological, semi-empirical and/or "black box" models, each category containing more than one candidates, developed for instance with different model parameters. Then, there are two approaches for deciding about the most proper model. On the one hand, the "winner model" approach assumes that a single model from this ensemble can capture all the necessary information about the modeling problem and therefore the other models are redundant. According to this approach the "winner model" is typically selected based on its generalization performance during a validation procedure. On the other hand, the hybrid modeling approaches combine some of the developed candidate models, assuming that they may contain different portions of the available information and therefore their combination should perform better compared to a single "winner model". To the best of our knowledge, the problem of detecting those members of a given ensemble of models that have indeed captured different parts of the modeling problem information has not been studied sufficiently in literature. Moreover, another open issue is the functional form of the subsequent models combination.

This study presents a framework consisting of three steps for dealing with the problem of models selection and combination. In the first step the models characteristics are inferred, based on quantitative and qualitative indicators for model accuracy and variables influence which are analyzed with statistical techniques (PCA), in the second step the models are grouped, based on the principal components of the first step and applying clustering algorithms, and in a third step diverse forms of combinations of the model groups are tested. Different types of neural networks are used as typical examples of "black box" models, while the form of the phenomenological or semi-empirical models is problem dependent. The proposed framework for hybrid modeling techniques is compared with the "winner model" approach in a variety of case studies regarding chemical engineering systems identification: the prediction of the overall weight conversion in an industrial fluid catalytic cracking unit, the correction of reaction mechanism and kinetic parameters fitting, the experimental determination of the specific heat capacity of solvents, and the prediction of the cumulative energy demand for the production of chemical substances, an indicator widely used for the evaluation of the life-cycle environmental impacts. The results demonstrate the advantages of the proposed methodology both in terms of systems identification accuracy and interpretation. Keywords

Model selection, hybrid modeling, "black box" modeling, neural networks, principal components analysis, clustering, systems identification, process identification, reaction kinetics, cumulative energy demand.