Chemical Process Systems (CPSs) is complicated nonlinear processes. In the cognitive process of a system, two kinds of knowledge can be gotten that is reaction mechanism and sampled data information, causing two different modeling methods. Based on the reaction mechanism, first-principle methods are developed to establish a rough description model via mass energy equations, the reaction kinetics equations and other mechanisms. With adding complexity of modern CPSs and the improving controlling accuracy, first-principle models are often difficult to describe systems precisely, sometimes fails because of the unknown reaction knowledge. Meanwhile, data-driven methods, based on the historical or operational sampled data and requiring no detailed information about systems, are rapidly developing and widely used in CPSs’ modeling and optimization process. Distinctly, neither modeling method makes full use of all information. Drawing on each other's strength, hybrid modeling becomes a hot topic in the modeling field.
Common structure of a hybrid model is parallel or serial structures. Parallel structures need clear reaction mechanism, which is very difficult for a complex CPS. Serial structures build each separate model and combine models by superposition or multiplication, i.e. the weighted method. Unfortunately, one serial sub-model may violate another, especially that the data-driven model with noise samples may violate the rough first-principle model. There is no verification between sampled data and reaction mechanism.
In order to fully utilize all information and verify two kinds of information mutually, a new hybrid modeling strategy to model a nonlinear industrial process is proposed. This approach is based on data-driven models combining with constraint from the reaction mechanism analysis. The main contribution is to construct a unified framework for modeling process by integrating data-driven model, knowledge detection, constraint handling method, and evolutionary algorithm. Initially, a data-driven model, e.g. artificial neural network model, is chosen to describe the input-output relationship. In the preparation stage, constraint conditions are extracted through the reaction mechanism analysis, for example, response restrictions, restricting response derivatives, the initial or extensional values, equal or unequal functions. Thus, the training process changes to a constraint optimization problem (COP) to solve optimal model parameters matching reaction mechanism constraints. Intelligent algorithm combining constraint handling method is applied to solve such a COP. Finally, the model parameters are solved and taken into the original data-driven model.
Moreover, both function simulation and the soft-sensor application to estimate average particle size of ZrO2-TiO2 composite colloidal sols indicate that the novel hybrid modeling approach can avoid the over-fitting problem to some extent. In addition, the Bayesian inference gives an explanation for the effectiveness of this method theoretically.
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