Adaptive dynamic prediction of effluent quality in wastewater treatment processes using partial least squares embedded with relevance vector machine

Abstract Recycling of water resources through wastewater treatment process (WWTP) is widely considered for a viable option for different water demands and sustainable production due to water shortage and pollution. Thus, accurate and real-time prediction of effluent quality is of vital importance to maintain the stable process control of WWTP system. Taking into account the complex biochemical characteristics of WWTP, an adaptive dynamic nonlinear partial least squares (PLS) model has been proposed to improve the prediction performance and stability of effluent quality indexes. First, an adaptive matrix expansion scheme is introduced to exploit the specific dynamic features of different data sets. Then the linear PLS model is conducted and the inner function between each pair of latent variables is rebuilt by relevance vector machine (RVM) with sparse and probabilistic structure, which is robust for the nonlinearity and random noises among process variables. The performance of the proposed adaptive dynamic RVM-based PLS (D-RVM-PLS) model is evaluated through two case studies based on benchmark simulation model No.1 and a real industrial WWTP, respectively. Experimental results show the superiority of the proposed model in prediction accuracy, stability, and execution efficiency. For the modeling accuracy of effluent chemical oxygen demand in real industrial case, adaptive D-RVM-PLS provides the lowest root-mean-square error, which is decreased by approximately 5.01%–49.19% in comparison with linear PLS model, Gaussian process regression-based PLS model, and their dynamic models without adaptive selection procedure.