A Hierarchical Soft-Sensor Using Spatiotemporal Information Transformation and ARMA With Application in Wastewater Treatment

A large amount of quality-related but difficult-to-measure variables usually make industrial processes unable to be operated safely and efficiently. Nonlinearity, time delay, and dynamics usually add further complexity and difficulties to this issue. To achieve accurate and reliable prediction of such quality-related but difficult-to-measure variables, a novel hierarchical soft sensor, termed spatiotemporal information transformation autoregressive moving average (SIT-ARMA), is proposed in this article to enable single-step and multistep-ahead prediction of these hard-to-measure variables. Inspired by hierarchical ensemble learning, this method applies the spatiotemporal information transformation (SIT) model to model the original dataset and the autoregressive moving average (ARMA) model to model the residuals from the SIT model. Furthermore, to increase the robustness of the SIT-ARMA model, this article uses the median and the median absolute deviation (MAD) to approach the Cauchy distribution, which can identify and smooth the outliers of the prediction derived by the SIT model. In addition, the moving window (MV) approach is applied to the SIT-ARMA model to update the parameters online and improve the adaptive performance of the model. The superiority of the proposed SIT-ARMA method has been verified through two studies of wastewater treatment plants (WWTPs) with different process characteristics.