Time-variant parameter estimation using a SVM Gray-Box model: Application to a CSTR Process

Gray-Box models (GBM) which combine a priori knowledge of a process -e.g. first principle equations- with a black-box modeling technique are useful when some parameters of the first-principle model -normally time-variant parameters cannot be easily determined. In this case the black-box part of the GBM can be used to model the influence of input and state variables on the evolution of those parameters. The most commonly used black-box technique for GBM is Artificial Neural Networks (ANN). However Support Vector Machine (SVM) has shown its usefulness by improving over the performance of different supervised learning methods, either as classification models or as regression models. In this paper, a kind of SVM -the Least-Square Support Vector Machine (LS-SVM)- is used to develop a GBM for a Continuous Stirred Tank Reactor (CSTR) process. The aim of the present work is then to build a GBM to estimate a time-varying parameter, ρ, of the CSTR process. Good results confirm that SVM can be effectively used for developing GBM to estimate time-varying parameters of non-linear processes like CSTR.