Recursive nonlinear/non-Gaussian Bayesian estimation for a biological wastewater treatment process in a dynamic state-space model

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Hong, Y.S.; Suh, C.-W.; Lee, J.-W.; Shin, H.-S. 2009 Recursive nonlinear/non-Gaussian Bayesian estimation for a biological wastewater treatment process in a dynamic state-space model. Lower Hutt, N.Z.: GNS Science. GNS Science report 2009/07 20 p.

Abstract: Online estimation of unknown states/parameters is a key component in the accurate modelling of biological wastewater treatment processes due to a lack of reliable online measurement systems. The Kalman filtering algorithm has been widely applied for wastewater treatment processes. The assumption of linearity in Kalman filtering algorithm is not valid because wastewater treatment processes are highly nonlinear with a time-varying characteristic. This paper proposes the use of sequential Monte Carlo (SMC) method for the recursive online state estimation of a biological sequencing batch reactor for wastewater treatment. The simplified Activated Sludge Model No.1 with nonlinear biological kinetic models is used as a process model and formulated in a dynamic Bayesian state-space model applied to SMC method. SMC method based on a recursive Bayesian estimation theory implemented in this study offers that: (1) it provides a general, flexible and robust modelling framework for nonlinear state/parameter estimations so the nonlinear mechanistic wastewater treatment process models can be directly applicable without any model linearization procedure or restrictive assumptions about the type of models or prior distributions; (2) it allows incorporating a wide range of uncertainties into the model; and (3) it provides a quantitative basis for probabilistic representation of a posteriori estimates, particularly slowly time-varying dynamics of microbial process. It is demonstrated that the SMC method can emerge as a powerful tool for solving online state/parameter estimation problems for wastewater treatment processes without restrictive assumptions about the process dynamics. Our study shows that the SMC method is very attractive for applications requiring online estimation of mechanistic wastewater treatment models, such as model-based monitoring, predictive control and data rectification. Further work is being undertaken to implement SMC to apply to a full cycle operation of a sequencing batch reactor. (auth)