Proper monitoring of quality-related but hard-to-measure effluent variables in wastewater plants is imperative. Soft sensors, such as dynamic neural network, are widely used to predict and monitor these variables and then to optimize plant operations. However, the traditional training methods of dynamic neural network may lead to poor local optima and low learning rates, resulting in inaccurate estimations of parameters and deviation of predictions. This study introduces a general Kalman-Elman method to monitor the effluent qualities, such as biochemical oxygen demand (BOD), chemical oxygen demand (COD), and total nitrogen (TN). The method couples an Elman neural network with the square-root unscented Kalman filter (SR-UKF) to build a soft-sensor model. In the proposed methodology, adaptive noise estimation and weight constraining are introduced to estimate the unknown noise and constrain the parameter values. The main merits of the proposed approach include the following: First, improving the mapping accuracy of the model and overcoming the underprediction phenomena in data-driven process monitoring; second, implementing the parameter constraint and avoid large weight values; and finally, providing a new way to update the parameters online. The proposed method is verified from a dataset of the University of California database (UCI database). The obtained results show that the proposed soft-sensor model achieved better prediction performance with root mean square error (RMSE) being at least 50% better than the Elman network based on back propagation through the time algorithm (Elman-BPTT), Elman network based on momentum gradient descent algorithm (Elman-GDM), and Elman network based on Levenberg-Marquardt algorithm (Elman-LM). This method can give satisfying prediction of quality-related effluent variables with the largest correlation coefficient (R) for approximately 0.85 in output suspended solids (SS-S) and 0.95 in BOD and COD.
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