Robust Identification of Nonlinear Errors-in-Variables Systems With Parameter Uncertainties Using Variational Bayesian Approach

Major impediments in developing models based on the input-output data of an industrial process are the outliers in the output and uncertainties in the inputs. To address this problem, this article proposes a robust identification approach for nonlinear errors-in-variables systems. The t-distribution is employed to model the process data to account for the outliers through the adjustable degrees of freedom. Furthermore, we propose to approximate the nonlinear dynamics of the process using multiple local ARX models and combine them using a softmax function based weighting approach. To deal with parameter uncertainties, the identification problem is casted in the Bayesian framework and posterior distributions of the model parameters are estimated using the variational Bayesian approach, instead of point estimations. A numerical example of continuous fermenter as well as an experiment study on the multitank system is employed to demonstrate potential of the proposed method.