Sparse optimization assisted hybrid data driven modeling of process systems

Digitization, which involves the adoption of various domain-relevant technologies to create a digital equivalent of physical assets, is the main principle of Industry 4.0. As most process plants such as Waster water treatment process (WWTP) and Post-carbon combustion capture (PCC) process exhibit multi-scale dynamics, identification of models in differential equation form (continuous-time) is advantageous. Further, any underlying physical understanding of the system can be easily captured in this modeling strategy, through appropriate choice of functionality resulting the model Gray-box in nature. Since models in differential equation form are considered, the accuracy of modeling depends on the estimation of derivatives from the sampled data. Therefore, the main objective of this paper is to develop an identification methodology in continuous-time (CT) framework that can capture the physical behavior of the system. To address the issue with the derivative information, the data set is fitted using functions like B-splines subjected to a model-based penalty to ensure that the data fit also satisfies the model of the process. For estimation of a parsimonious model, a sparsity constraint in terms of zero norm on the parameter vector of the model is considered. The efficacy of the method is demonstrated on a Van der Pol oscillator and a Continuous stirred tank reactor (CSTR) system and the results are compared with the existing methods.