Abstract
Online estimation of unknown state variables is a key component in the accurate modelling of biological wastewater treatment processes due to a lack of reliable online measurement systems. The extended Kalman filter (EKF) algorithm has been widely applied for wastewater treatment processes. However, the series approximations in the EKF algorithm are not valid, because biological wastewater treatment processes are highly nonlinear with a time-varying characteristic. This work proposes an alternative online estimation approach using the sequential Monte Carlo (SMC) methods for recursive online state estimation of a biological sequencing batch reactor for wastewater treatment. SMC is an algorithm that makes it possible to recursively construct the posterior probability density of the state variables, with respect to all available measurements, through a random exploration of the states by entities called ‘particle’. In this work, the simplified and modified Activated Sludge Model No. 3 with nonlinear biological kinetic models is used as a process model and formulated in a dynamic state-space model applied to the SMC method. The performance of the SMC method for online state estimation applied to a biological sequencing batch reactor with online and offline measured data is encouraging. The results indicate that the SMC method could emerge as a powerful tool for solving online state and parameter estimation problems without any model linearization or restrictive assumptions pertaining to the type of nonlinear models for biological wastewater treatment processes.
Similar content being viewed by others
References
Guclu D, Dursan S (2010) Artificial neural network modelling of a large-scale wastewater treatment plant operation. Bioprocess Biosyst Eng 33:1051–1058
Hong YS, Bhamidimarri R (2003) Evolutionary self-organising modelling of a municipal wastewater treatment plant. Water Res 37:1199–1212
Hong YST, Paik BC (2007) Evolutionary multivariate dynamic process model induction for a biological nutrient removal process. J Environ Eng 133:1126–1135
Farza M, Othman S, Hammouri H, Fick M (1997) Discrete-time nonlinear observer-based estimators for the on-line estimation of the kinetic rates in bioreactors. Bioprocess Eng 17:247–255
Shu Q, Kemblowski MW, Mckee M (2005) An application of ensemble Kalman filter in integral-balance subsurface modeling. Stoch Environ Res Risk Assess 19:361–374
van Delft G, El Serafy GY, Heemink AW (2009) The ensemble particle filter (EnPF) in rainfall-runoff models. Stoch Environ Res Risk Assess 23:1203–1211
Papaodysseus C, Alexiou C, Panagopoulos Th, Roussopoulos G, Kravaritis D (2003) A novel general methodology for studying and remedying finite precision error with application in Kalman filter. Stoch Environ Res Risk Assess 17:1–19
Vanek M, Hrncirik P, Vovsik J, Nahlik J (2004) On-line estimation of biomass concentration using a neural network and information about metabolic state. Bioprocess Biosyst Eng 27:9–15
Veloso ACA, Rocha I, Ferreira EC (2009) Monitoring of fed-batch E. coli fermentations with software sensors. Bioprocess Biosyst Eng 32:381–388
Marsili-Libelli S (1984) Optimal control of the activated sludge process. Trans Inst Meas Control 6:146–152
Beck MB (1986) Identification, estimation and control of biological wastewater treatment processes. IEE Proc D 133:254–266
Jeppsson U, Olsson G (1993) Reduced order models for on-line parameter identification of the activated sludge process. Water Sci Technol 28:173–183
Zhao H, Kummel M (1995) State and parameter estimation for phosphorus removal in an alternating activated sludge process. J Proc Control 5:341–351
Lukasse LJS, Keesman KJ, van Straten G (1999) A recursively identified model for short-term predictions of NH4/NO3—concentrations in alternating activated sludge processes. J Proc Control 9:87–100
Boaventura KM, Roqueiro N, Coelho MAZ, Araujo OQF (2001) State observers for a biological wastewater nitrogen removal process in a sequential batch reactor. Bioresource Technol 79:1–14
Dochain D (2003) State and parameter estimation in chemical and biochemical processes: a tutorial. J Proc Control 13:801–818
Anderson BD, Moore JB (1979) Optimal filtering. Prentice Hall, New Jersey
Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, New York
Gelb A, Kasper JF, Nash RA, Price CF, Sutherland AA (1974) Applied optimal estimation. The MIT Press, London
Bernard O, Chachuat B, Steyer JP (2007) State estimation for wastewater treatment processes in wastewater quality monitoring and treatment. Wiley, New York
Jones RM (1989) State estimation in wastewater engineering: application to an anaerobic process. Environ Monit Assess 12:271–282
Chai Q, Furenes B, Lie B (2007) Comparison of state estimation techniques, applied to a biological wastewater treatment process. In: 10th International IFAC symposium on computer applications in biotechnology, Mexico
Benazzi F, Gernaey KV, Jeppsson U, Katebi R (2007) On-line estimation and detection of abnormal substrate concentrations in WWTPs using a software sensor: a benchmark study. Environ Technol 28:871–882
Busch J, Kuhl P, Schloder JP, Bock HG, Marquardt W (2009) State estimation for large-scale wastewater treatment plants. In: ADCHEM09-international symposium on advanced control of chemical processes, Istanbul
van der Merwe R, Doucet A, de Freitas N, Wan E (2000) The unscented particle filter. Technical Report CUED/F-INFENG/TR 380. Engineering Department, Cambridge University
van der Heijden F, Duin RPW, de Ridder D, Tax DMJ (2004) Classification parameter estimation and state estimation. Wiley, New York
Farza M, Othman S, Hammouri H, Biston J (1997) A nonlinear approach for the on-line estimation of the kinetic rates in bioreactors. Bioprocess Eng 17:143–150
Estler MU (1995) Recursive on-line estimation of the specific growth rate from off-gas analysis for the adaptive control of fed-batch processes. Bioprocess Eng 12:205–207
Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc F 140:107–113
Doucet A, Godsill S, Andrieu C (2000) On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput 10:197–208
Doucet A, de Freitas N, Gordon N (2001) Sequential Monte Carlo methods in practice. Springer, Berlin
Handschin JE, Mayne DQ (1969) Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering. Int J Control 9:547–559
Kitagawa G (1996) Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J Comput Graph Stat 5:1–25
Liu JS (2001) Monte Carlo strategies in scientific computing. Springer Series in Statistics
Pitt MK, Shephard N (1999) Filtering via simulation: auxiliary particle filters. J Am Stat Assoc 94:590–599
West M (1993) Approximating posterior distributions by mixtures. J R Stat Soc 55:409–422
Chen T, Morris J, Martin E (2005) Particle filters for state and parameter estimation in batch processes. J Proc Control 15:665–673
Chen T, Morris J, Martin E (2008) Dynamic data rectification using particle filters. Comput Chem Eng 32:451–462
Rawlings JB, Bakshi BR (2006) Particle filtering and moving horizon estimation. Comput Chem Eng 30:1529–1541
Hue C, Cadre JPL, Perez P (2002) Tracking multiple objects with particle filtering. IEEE Trans Aerosp Electron Syst 38:791–812
Cui N, Hong L, Layne JR (2005) A comparison of nonlinear filtering approaches with an application to ground target tracking. Signal Process 85:1469–1492
Moradkhani H, Hsu K-L, Cupta H, Sorroshian S (2005) Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter. Water Resour Res 41:W05012. doi:10.1029/2004WR003604
Weerts AH, El Serafy GYH (2006) Particle filtering and ensemble Kalman filtering for state updating with hydrological conceptual rainfall-runoff models. Water Resour Res 42:W09403. doi:10.1029/2005WR004093
Gujer W, Henze M, van Loosdrecht MCM (1999) Activated sludge model No. 3. Water Sci Technol 39:183–193
Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian Tracking. IEEE Trans Signal Process 50:174–188
Robert C, Casella G (1999) Monte Carlo statistical methods. Springer, Berlin
Smith AFM, Gelfand AE (1992) Bayesian statistics without tears: a sampling-resampling perspective. Am Stat 46:84–88
Liu JS, Chen R (1998) Sequential Monte Carlo methods for dynamical systems. J Am Stat Assoc 93:1032–1044
Bastin G, Dochain D (1990) On-line estimation and adaptive control of bioreactors. Elsevier, Amsterdam
Acknowledgments
This work was supported financially through the Eco-Technopia 21 project (contract number 071-071-118) of the Korea Ministry of Environment, Republic of Korea. The authors thank the reviewers, whose comments greatly improved the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, JW., Hong, YS.T., Suh, C. et al. Online nonlinear sequential Bayesian estimation of a biological wastewater treatment process. Bioprocess Biosyst Eng 35, 359–369 (2012). https://doi.org/10.1007/s00449-011-0574-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00449-011-0574-3