Elman Neural Networks Combined with Extended Kalman Filters for Data-Driven Dynamic Data Reconciliation in Nonlinear Dynamic Process Systems

Accurate feedback signals play an important role in the control system. Sensors used for obtaining outputs are inevitably corrupted by the measurement noise in both devices themselves and outside the environment, which may lead to the deterioration of process monitoring and regulation. Inferring the true outputs of nonlinear dynamic systems from noisy measurements can be accomplished by the extended Kalman filter (EKF). However, the limitation of the EKF is that the dynamic mathematical models of processes under investigation are required. This makes the EKF often unsatisfied in some complex and unknown dynamic systems, where the current trends in system identification focus on only mapping the information from inputs and outputs, called data-driven modeling. In this paper, the Elman neural network (ENN) is efficiently combined with the EKF to form a data-driven dynamic data reconciliation scheme named the ENN-EKF. In this combinational method, the ENN is employed to predict system outputs and the EKF is used for dynamic data reconciliation of the measurements. The performance of the ENN-EKF is demonstrated on a classical nonlinear dynamic process and a complex chemical process, namely, free radical polymerization of styrene. The implementation results illustrate that the proposed approach can effectively suppress the impact of the measurement noise and improve the dynamic behavior of the system.