Online nonlinear sequential Bayesian estimation of a biological wastewater treatment process

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.     

Microbial production of enzymes: Nonlinear state and kinetic reaction rates estimation

The nonlinearity of the biotechnological processes and the absence of cheap and reliable instrumentation require an enhanced modelling effort and estimation strategies for the state and the kinetic parameters. This work approaches nonlinear estimation strategies for microbial production of enzymes, exemplified by using a process of lipase production from olive oil by Candida rugosa. First, by using a dynamical mathematical model of this process, an asymptotic observer which reconstructs the unavailable state variables is proposed. The design of this kind of observers is based on mass and energy balances without the knowledge of kinetics being necessary; only minimal information concerning the measured concentrations is used. Second, a nonlinear high-gain observer is designed for the estimation of imprecisely known kinetics of the bioprocess. An important advantage of this high-gain estimator is that the tuning is reduced to the calibration of a single parameter. Numerical simulations in various scenarios are provided in order to test the behaviour and performances of the proposed nonlinear estimation strategies.     

Structured modeling and state estimation in a fermentation process: Lipase production by Candida rugosa

A simple structured mathematical model coupled with a methodology of state and parameter estimation is developed for lipase production by Candida rugosa in batch fermentation. The model describes the system according to the following qualitative observations and hypothesis: Lipase production is induced by extracellular oleic acid present in the medium. The acid is transported into the cell where it is consumed, transformed, and stored. Lipase is excreted to the medium where it is distributed between the available oil-water interphase and aqueous phase. Cell growth is modulated by the intracellular substrate concentration. Model parameters have been determined and the whole model validated against experiments not used in their determination. The estimation problem consists in the estimation of three state variables (biomass, intra- and extracellular substrate) and two kinetic parameters by using only the on-line measurement provided by exhaust gas analysis. The presented estimation strategy divides the complex problem into three subproblems that can be solved by stable algorithms. The estimation of biomass (X) and the specific growth rate (mu), is achieved by a recursive prediction error algorithm using the on-line measurement of the carbon dioxide evolution rate. mu is then used to perform an estimation of intracellular substrate and the other kinetic parameter related to substrate transport (A) by an adaptive observer. Extracellular substrate is then evaluated by means of the estimated values of intracellular substrate and biomass through the material balance of the reactor. Simulation and experimental tests showed good performance of the developed estimator, which appears suitable to be used for process control and monitoring. (c) 1995 John Wiley & Sons, Inc.     

Modeling and advanced control of recombinant Zymomonas mobilis fed-batch fermentation

This work presents the development of an unstructured kinetic model incorporating the differing degrees of product, substrate, and pH inhibition on the kinetic rates of ethanol fermentation by recombinant Zymomonas mobilis CP4:pZB5 for growth on two substrates. Product inhibition was observed to start affecting the specific growth rate at an ethanol concentration of 20 g/L and the specific productivity at about 35-40 g/L. Specific growth rate was also shown to be more sensitive to inhibition by lowered pH as well. A model for the inhibition of two competing substrates' cellular uptake via membrane transport is proposed. Inhibition functions and model parameters were determined by fitting experimental data to the model. The model was utilized in a nonlinear model predictive control (NMPC) algorithm to control the product concentration during fed-batch fermentation to offset the inhibitory effects of product inhibition. Using the optimal feeding policy determined online, the volumetric productivity of ethanol was improved 16.6% relative to the equivalent batch operation when the final ethanol concentration was reached.     

Development of a phenomenological modeling approach for prediction of growth and xanthan gum production using Xanthomonas campestris

An unstructured kinetic model for xanthan production is described and fitted to experimental data obtained in a stirred batch reactor. The culture medium was composed of several nitrogen sources (soybean hydrolysates, ammonium and nitrate salts) consumed sequentially. The model proposed is able to describe this sequential consumption of nitrogen sources, the consumption of inorganic phosphate and carbon, the evolution of biomass, and production of xanthan. The parameter estimation has been performed by fitting the kinetic model in differential form to experimental data. Runs of the model for simulating xanthan gum production as a function of the initial concentration of inorganic phosphate have shown the positive effect of phosphate limitation on xanthan yield, though diminishing rates of production. The model was used to predict the kinetic parameters for a medium containing a 2-fold lower initial phosphate concentration. When tested experimentally, the measured fermentation parameters were in close agreement with the predicted model values, demonstrating the validity of the model.     

Modeling and observer design for recombinant Escherichia coli strain

A mathematical model for recombinant bacteria which includes foreign protein production is developed. The experimental system consists of an Escherichia Coli strain and plasmid pIT34 containing genes for bioluminescence and production of a protein, β-galactosidase. This recombinant strain is constructed to facilitate on-line estimation and control in a complex bioprocess. Several batch experiments are designed and performed to validate the developed model. The design of a model structure, the identification of the model parameters and the estimation problem are three parts of a joint design problem. A nonlinear observer is designed and an experimental evaluation is performed on a batch fermentation process to estimate the substrate consumption.     

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers' family achieves convergence to time-varying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.     

重组毕赤酵母产青霉素G酰化酶的分批发酵动力学研究

构建了重组毕赤酵母产青霉素G酰化酶的分批发酵动力学模型。实验考察了分批发酵过程中甘油消耗、甲醇浓度、菌体浓度、溶氧、补料时间对青霉素G酰化酶活力的影响。应用Matlab软件,对菌体生长、基质消耗和产物生成方程进行最优参数估算和非线性拟合,得到相应的动力学模型。模型的计算值与实验值能较好地拟合,表明所建模型能较好反映重组毕赤酵母产青霉素G酰化酶的分批发酵过程。     

A structured kinetic model for Zymomonas mobilis ATCC10988

The inhibitory effects of glucose and ethanol on Zymomonas mobilis ATCC10988 were isolated through kinetic analysis of transient batch fermentation data. Growth of Z. mobilis was inhibited above a glucose concentration of 80 g/L. Growth was mildly inhibited by ethanol to 50 g/L, and severely inhibited above this concentration. Specific rates of ethanol production and glucose uptake were essentially invariant during batch fermentation. A structured kinetic model was developed, by way of augmentation of the Extended Bottleneck model, to quantify the kinetics of the growth and product formation processes. The model successfully describes the transient batch fermentation of Z. mobilis over a wide range of initial glucose concentration in a semidefined medium.     

Study of kinetic parameters in a mechanistic model for enzymatic hydrolysis of sugarcane bagasse subjected to different pretreatments

The goal of this work is to evaluate the influence of different pretreatments in the kinetics of enzymatic hydrolysis of sugarcane bagasse and to propose a reliable methodology to easily perform sensitivity analysis and updating kinetic parameters whenever necessary. A kinetic model was modified to represent the experimental data of the batch enzymatic hydrolysis of sugarcane bagasse pretreated with alkaline hydrogen peroxide. The simultaneous estimation of kinetic parameters of the mathematical model was performed using the Pikaia genetic algorithm using batch hydrolysis experimental data obtained with different enzymatic loads. Subsequently, Plackett–Burman designs were used to identify the kinetic parameters with the higher influence on the dynamic behavior of the process variables, which were re-estimated to describe experimental data of the hydrolysis of bagasse pretreated with phosphoric acid + sodium hydroxide. The methodology was accurate and straightforward and can be used whenever there are changes in pretreatment conditions and/or fluctuations in biomass composition in different harvests.     

Control in bioreactors showing gradients

In large-scale bioreactors gradients often occur as a result of non-ideal mixing. This phenomenon complicates design and control of large-scale bioreactors. Gradients in the oxygen concentration can be modeled with a two-compartment model of the liquid phase. Application of this model had been suggested for the control of the dissolved oxygen concentration with a batch gluconic acid fermentation process as the model system. The control system consists of a controller, an observer and a parameter estimator. In this work, the controller design is reconsidered and, in simulation experiments, the performance of the control system has been investigated. When the parameter values are known, the controller in combination with the observer works adequately. The parameter estimator, however, yields incorrect parameters, which are caused by a coupling between two parameters. This causes a deviation of the estimated states from the process states. The simulation results suggest that a priori knowledge of the parameters is required for application of the model for control and state estimation.     

Measurement and mathematical modelling of competition between fast- and slow-growing ordinary heterotrophic organisms in low and high substrate-loaded systems

Ordinary heterotrophic organisms (OHO) of an activated sludge wastewater treatment system showed an atypical growth behaviour when they are inoculated to batch aerobic growth tests with a high substrate-loaded condition. For example, the OHO maximum specific growth rates on readily biodegradable substrates (μ _H) increased with a high ratio of substrate concentration to OHO active biomass concentration (So/Xo), although they were assumed to be constant in a conventional microbial growth kinetic model with a single OHO population group. We, therefore, set a hypothesis in that the change of OHO maximum specific growth rates in the batch test condition is caused by turnover of fast-growing OHO population against slow-growing OHO population. And, a competitive microbial growth kinetic model of the fast- and slow-growing OHO population groups was developed and validated with model-data fitting analysis for the batch test results. The competitive microbial growth kinetic model of process selection, rather than that of kinetic selection, was capable of simulating microbial growth kinetics in high substrate-loaded dynamic systems (i.e., batch tests) and low substrate-loaded steady-state systems (i.e., continuously operated wastewater treatment systems), better than the conventional non-competitive growth kinetic model.     

Modelling the growth and ethanol production of Brettanomyces bruxellensis at different glucose concentrations

Aim: To study the effect of glucose concentrations on the growth by Brettanomyces bruxellensis yeast strain in batch experiments and develop a mathematical model for kinetic behaviour analysis of yeast growing in batch culture. Methods and Results: A Matlab algorithm was developed for the estimation of model parameters. Glucose fermentation by B. bruxellensis was studied by varying its concentration (5, 9·3, 13·8, 16·5, 17·6 and 21·4%). The increase in substrate concentration up to a certain limit was accompanied by an increase in ethanol and biomass production; at a substrate concentration of 50–138 g l^?1, the ethanol and biomass production were 24, 59 and 6·3, 11·4 g l^?1, respectively. However, an increase in glucose concentration to 165 g l^?1 led to a drastic decrease in product formation and substrate utilization. Conclusions: The model successfully simulated the batch kinetic observed in all cases. The confidence intervals were also estimated at each phase at a 0·95 probability level in a t‐Student distribution for f degrees of freedom. The maximum ethanol and biomass yields were obtained with an initial glucose concentration of 138 g l^?1. Significance and Impact of the Study: These experiments illustrate the importance of using a mathematical model applied to kinetic behaviour on glucose concentration by B. bruxellensis.     

Modeling of yeast <Emphasis Type="Italic">Brettanomyces bruxellensis</Emphasis> growth at different acetic acid concentrations under aerobic and anaerobic conditions

Glucose utilization by Brettanomyces bruxellensis at different acetic acid concentrations under aerobic and anaerobic conditions was investigated. The presence of the organic acid disturbs the growth and fermentative activity of the yeast when its concentration exceeds 2 g l⁻¹. A mathematical model is proposed for the kinetic behavior analysis of yeast growing in batch culture. A Matlab algorithm was used for estimation of model parameters, whose confidence intervals were also calculated at a 0.95 probability level using a t-Student distribution for f degrees of freedom. The model successfully simulated the batch kinetics observed at different concentrations of acetic acid under both oxygen conditions.     

Kinetics of growth and elemental sulfur oxidation in batch culture of thiobacillus ferrooxidans

The kinetics of oxidation of elemental sulfur by Thiobacillus ferrooxidans in a batch reactor was followed by measuring the concentration of adsorbed cells on the sulfur surface, the concentration of free cells in liquid medium, and the amount of sulfur oxidized. As the elemental sulfur was oxidized to sulfate, the liquid-phase concentration of free cells continued to increase with time, whereas the surface concentration of adsorbed cells per unit weight of sulfur approached a limiting value, i.e., the maximum adsorption capacity. During sulfur oxidation, there was a close correlation between the concentrations of adsorbed and free cells, and these data were well correlated with the Langmuir isotherm. The observed rates of batch growth and sulfur oxidation were consistent with a kinetic model, assuming that the growth rate of batch growth and sulfur oxidation were consistent with a kinetic model. Assuming that the growth rate of adsorbed bacteria is proportional to the product of the concentration of adsorbed cells and the fraction of adsorption sites unoccupied by cells. The kinetic and stoichiometric parameters appearing in the model were evaluated using the experimental data and were compared with parameters determined previously for a few metal sulfides. (c) 1994 John Wiley & Sons, Inc.     

Mixed culture biooxidation of phenol. I. Determination of kinetic parameters

A mixed culture derived from soil and activated sludge organisms was used to degrade phenol which was inhibitory to microorganisms at higher concentrations. The purpose of the experiments was to determine the kinetic parameters governing growth of the organisms by measuring growth rates in batch culture. To maintain a constant inoculum for the experiments inoculum was taken from a continuously operating continuous culture. Two populations were studied corresponding to two separate residence times in the continuous culture apparatus. One contained predominantly filamentous organisms, the other nonfilamentous. Five kinetic models were applied to the data and the best kinetic parameters for each model were determined by nonlinear least squares techniques. The models were then evaluated for best relative fit to the data. No significant differences were found between the models on the basis of fit and so a choice was made on the grounds of simplicity. A model proposed by Haldane was chosen as the best. No function however gave a satisfactory fit at the highest growth rates obtained. This experimental maximum in the plot of growth rate against substrate concentration was very sharp.     

Least-squares estimation of batch culture kinetic parameters

This article concerns the development of a simple and effective least-squares procedure for estimating the kinetic parameters in Monod expressions from batch culture data. The basic approach employed in this work was to translate the problem of parameter estimation to a mathematical model containing a single decision variable. The resulting model was then solved by an efficient one-dimensional search algorithm which can be adapted to any microcomputer or advanced programmable calculator. The procedure was tested on synthetic data (substrate concentrations) with different types and levels of error. The effect of endogeneous respiration on the estimated values of the kinetic parameters was also assessed. From the results of these analyses the least-squares procedure developed was concluded to be very effective.     

A nonlinear approach for the on-line estimation of the kinetic rates in bioreactors

The objective of this paper is to propose simple nonlinear observer-based estimators which allow the on-line estimation of kinetic rates inside a bioreactor from the measurements of components' concentrations. The design of these estimators does not require any model for the kinetic rates and the corresponding gains do not necessitate the resolution of any dynamical system. One of the main characteristics of these estimators lies in the easiness of their implementation and in particular their calibration. Their performances are firstly illustrated in simulation through a typical example. Then, estimation results corresponding to a real-life experiment are given in order to confirm the theoretical results and to demonstrate the usefulness of the proposed estimators in practical situations.     

Uniform step-by-step observer for aerobic bioreactor based on super-twisting algorithm

This paper describes a fixed-time convergent step-by-step high order sliding mode observer for a certain type of aerobic bioreactor system. The observer was developed using a hierarchical structure based on a modified super-twisting algorithm. The modification included nonlinear gains of the output error that were used to prove uniform convergence of the estimation error. An energetic function similar to a Lyapunov one was used for proving the convergence between the observer and the bioreactor variables. A nonsmooth analysis was proposed to prove the fixed-time convergence of the observer states to the bioreactor variables. The observer was tested to solve the state estimation problem of an aerobic bioreactor described by the time evolution of biomass, substrate and dissolved oxygen. This last variable was used as the output information because it is feasible to measure it online by regular sensors. Numerical simulations showed the superior behavior of this observer compared to the one having linear output error injection terms (high-gain type) and one having an output injection obtaining first-order sliding mode structure. A set of numerical simulations was developed to demonstrate how the proposed observer served to estimate real information obtained from a real aerobic process with substrate inhibition.     

Extended Kalman Filtering technique for the on-line control of OKT3 hybridoma cultures

Summary Extended Kalman Filter (EKF) is used for the on-line estimation of viable cell and monoclonal antibody (MAb) concentrations during batch and fed batch cultures of the OKT3 hybridoma cell line. A kinetic model and an experimental system are presented. The practicability of EKF is demonstrated under both cultivation modes using glucose and ammonia as observation variables. For the same process duration, the concentration of viable cells and antibodies are twice as high in the fed batch as in the batch culture.