Soft-Sensor Modeling Method Based on Ensemble Kalman Filter-Elman Neural Network

Wastewater treatment system is a dynamic system with complex nonlinearity and large time delay. Due to the complexity of the process, the incompleteness of the testing equipment and the constraint of economic cost, some important effluent indicators cannot be detected accurately. To solve this problem, this paper proposes a soft-sensor method based on an ensemble Kalman filter-Elman neural network. The traditional dynamic neural network has the dynamic memory ability to process time-delay data, so it can be used in data-driven soft sensing modeling. However, the conventional training method is easy to trap in a local minimum, resulting in poor prediction performance. This paper introduces the ensemble Kalman filter and the dual finite-size ensemble Kalman filter, and, together with the Elman neural network for gradient-free training, to construct two soft sensor models, which not only improve the prediction performance of Elman neural network but also provide a simple and gradient-free training method for neural network. The two models are then applied to a dataset of the University of California, Irvine (UCI data). The results show that the proposed method based on ensemble Kalman filter-Elman neural network possesses good prediction performance, and that the ensemble Kalman filter can be used as an alternative gradient-free method to train neural networks.