Development of RVM-based multiple-output soft sensors with serial and parallel stacking strategies

Soft sensors are the most commonly used tools to predict hard-to-measure variables in industrial processes. However, the presence of a large number of hard-to-measure variables always renders a generic single-output soft-sensor inadequate. This brief proposed two multiple-output soft sensors, the former based on a novel serial stacking relevant vector machine (RVM) models, called RVMS, by transforming multiple-output into single-output problems inspired by stacking generation and the latter based on ensemble multivariable RVM (EMRVM) models that are improved by ensemble learning. To further strengthen the predicted ability, least absolute shrinkage and selection operator and canonical correlation analysis are used to remove irrelevant and redundant information from raw features under the supervision of multivariate targets for RVMS and EMRVM, respectively. The proposed methodologies were first accessed by a well-established wastewater plant (WWTP) validation platform, Benchmark Simulation Model No.1 then evaluated by a real WWTP with data being collected from the field. The results demonstrated that the proposed strategies were able to significantly improve the prediction performance.