Identification of semi-parametric hybrid process models

Hybrid models are mathematical models that comprise both mechanistic and black-box or datadriven components. Typically, the parameters in the mechanistic part of a hybrid model (if any) are assumed to be known. However in this research, a two-level approach is proposed for the identification of hybrid models where some parameters in the mechanistic part of the model are unknown. At the first level, the black-box component is identified using a regularization method with given values for the regularization and mechanistic parameters. At the second level, the regularization and mechanistic parameters are determined simultaneously and optimized according to a specific criterion placed on the predictive performance of the hybrid model. This approach is tested through the modelling of a toluene nitration process, where a support vector machine (SVM) model is used to represent the chemical kinetics, with the mass transfer-related mechanistic parameters being estimated simultaneously. The case study shows that good results can be obtained in terms of both the prediction of the process variables of interest and the estimates of the mechanistic parameters, when the measurement error in the training data is small whilst when the magnitude of the measurement error increases, the accuracy of the estimates of the mechanistic parameters decreases. However, the predictive performance of the resulting hybrid model in the latter case is still acceptable, and can be much better than that attained from the application of a pure black-box model under certain extrapolation conditions.