Gray-box nonlinear system identification using polynomial NARMAX models

Abstract

The usage of a collection of linear models to describe a nonlinear system has many disadvantages. In order to overcome these disadvantages, nonlinear models have been improved. The nonlinear model used in this work is the Nonlinear AutoRegressive Moving Average models with eXogenous inputs (NARMAX) of polynomial type. This type of model is linear on the parameters and accounts, in the model, for the existent noise, that is inherent of a measurement on a industrial plant. Broadly, there are two types of identification: the black-box identification, which is a typical input-output method, i.e., only requires data in order to identify the process; and the gray-box identification, which requires some system information, besides data. In the present work, a gray-box identification is compared with the black-box one for optimization and control purposes. The identification is performed using the Orthogonal Least Square algorithm and validation is made using k-stepahead cross-validation method. Dynamic real-time optimization was set based on both first principle models and estimated models, and compared, in order to evaluate improvement on the application of identified nonlinear models. The gray-box identification was more representative in relation to the nonlinearity of the system. The application in optimization and control generated instability of the algorithm. It can be due to the fact that the optimization algorithm used in dynamic real-time optimization had the same value for control horizon and prediction horizon. Despite the oscillations of one case study, the gray-box identification algorithm showed its capacity to improve the model.