Recursive Bayesian Filtering for States Estimation: An Application Case in Biotechnological Processes

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1 Recursive Bayesian ing for States Estimation: An Application Case in Biotechnological Processes Lucía Quintero, Adriana Amicarelli, Fernando di Sciascio Instituto de Automática (INAUT) Universidad Nacional de San Juan, Av. Lib. San Martín 9 54 San Juan Argentina. {olquinte,amicarelli,fernando}@inaut.unsj.edu.ar Abstract In this work a state estimator for a continuous bioprocess is presented. To reach this aim a nonlinear filtering technique, based on the recursive application of the Bayes rule and Monte Carlo techniques, is used. To the best of author s knowledge, not many applications in the biotechnological area applying such techniques have been reported. Generally, a bioprocess has strong nonlinear and non Gaussian characteristics and so this methodology becomes more attractive. Specifically, the recursive Bayesian s SIR (Sampling Importance Resampling) are used, including different kinds of resampling; also the uncertainties of states and measurements are modelled. The estimator behaviour and performance are illustrated for the continuous alcoholic fermentation process of Zymomonas mobilis. There is an industrial interest in the use of Zymomonas due to its capability to produce ethanol; and for the fuel ethanol industry to expand; Zymomonas mobilis has attracted the attention as a promising bacterium regarding the ethanol production improvement. Keywords Recursive Bayesian ing, State estimation, Biotechnological process, Monte Carlo techniques. I.INTRODUCTION Over the last few years, the progress reached on the technology used for the development of online sensors has been manifested. Despite this, in the bioprocess field, the lack of real information of chemical and biological variables such as: biomass concentration, specific bacterial activity, intermediate products concentration among others; is very common. Frequently, these variables constitute the states of the bioprocess and they are very important for its monitoring and control. The choice of an observer or a state estimator depends inherently on the particular problem specifications. In practice, this choice is mainly influenced by the availability of a sufficiently representative model of the process, and the reliability of experimental data. In general, looking for the state estimation from the input/output information, different approximation techniques can be used, when the a-priori knowledge about the process or the model is incomplete. To the best of author s knowledge, not many applications in the biotechnological area with nonlinear filtering tools have been reported. In particular, the continuous fermentation process of Zymomonas mobilis (Z. m), presents a difficult problem. These microorganisms exhibit a highly nonlinear and oscillatory kinetic behaviour; besides, some process states are difficult to measure, and they are: biomass concentration and the intermediate variables that represent the ethanol production rate and the inhibition effect. There is an industrial interest in the use of Z. m due to its capability to produce ethanol and sorbitol (Oliveira I. et al, 5). The micro organism can

2 represent one of the most important ones with respect to its features mentioned previously and also, because its feasibility in terms of product optimization and control (Echeverry et al, 4). The time evolution of the states is modelled through a dynamical system with uncertainties term added, perturbed by a stochastic process (diffussion term and state noise); it makes the equation that describes the system, a stochastic differential equation. In this work, a state estimator to the continuous alcoholic fermentation process of Z.m is developed. As a novel tool in biotechnological field, a non linear filtering technique was used. Specifically in this work, a variation of a Bayesian recursive filter SIR (Sampling Importance Resampling) is developed, and different resampling schemes were applied to reduce the effect of the sampling Impoverishment (Doucet A., 998; Doucet A. et al, ; Doucet A. et al, 6). The biotechnological process has non linear and non Gaussian characteristics and so quantification of the uncertainty, represented through Bayes theory, relies on complex statistical inference procedures. Other estimation techniques, applied to the mentioned process, have not provided satisfactory results. In this work, the states of the system are estimated (Biomass concentration and the intermediate variables) from input/output information and an available process model. The states (Biomass, Substrate, and Product) are a Markov process, satisfying the Langevin chemical equation (Joannides M. et al, 5). II.STUDY CASE AND ESTIMATION TOOLS A. Study case: Alcoholic Continuous Fermentation of Zymomonas Mobilis The continuous alcoholic fermentation process of Zymomonas mobilis presents a high ethanol performance, but it has oscillatory behaviour on the state process variables. Biomass concentration X, Sustrate concentration S, D is the total dilution rate, Ds is the substract dilution rate and Sin is the substract concentration on the input flow, Product concentration P, Weighted average of the ethanol concentration rate Z and I is the intermediate auxiliary variable for the inhibition effect determination. In this process, an accurate estimation of the non measurable system states is very important with the purpose of using them for monitoring and control. Figure. Continuous Fermentation Process scheme

3 III. APPLICATION FEATURES For the simulation approach, disturbance and uncertainty models were added to the basis model, under considerations of modelling and measurement uncertainties of diverse nature. For simulation and real data procedure the estimation scheme was the classical used in estimation. The input signals u(t) (input substrate concentration Sin, dilution rate D and micro-organisms recycle term R ) and the output signals y(t) (outflow Substrate S and product P ) corresponding to the (simulated) real data pre processed, feed the filter block that makes the state estimation. The estimations are compared with the results obtained by Câmelo et al, 5, which are taken to be accurate. IV. RESULTS ANALYSIS AND DICUSSION It can be see from simulation results, that Particle filter performance is good enough to simulated data. These results are remarkable from the perspective level of accuracy model used (Daugulis A.J et al, 997, 999),(Câmelo A. et al, 5), and its closeness to the data reported in the literature. The relevance of Fig., relies on the fact that, for biotechnological variables, the measurements cannot be easily sampled and this approach provides an approximated estimation value, that can replace the real measurement over a time interval. In the same way, the filter performance allows us to assume the uncertainties on measures and disturbances in the measurement methods. The values of Inhibition variables are shown in Fig 3. that presents the inhibition variables I and Z, present in the dynamic behaviour of the Z.m bacteria..6 Z. M cells Estimation.4. Biomass Concentration [g/l] Figure. The dotted line describes the estimated biomass concentration by the SIR filter and the solid line describes the real data interpolation value. The second test was performed with deviation of the mean in diffusions terms.

4 .7.6 Inhibition Term Z Filtro SIR Modelled.5 Inhibition Term I Filtro SIR Modelled.5 Inhibition degree Inhibition degree Figure 3 The dotted lines represent the dynamics of Inhibition Z and I estimated by the SIR filter while the solid lines are the modelled dynamics of the system, considered as real. Biomass Concentration [g/l] Z. M cells Estimation Figure 4. The dotted line describes the biomass estimation obtained by the SIR while the solid line describes the biomass considered real. Disturbance model has mean zero in diffusion term and high noise power. Test 3 An important remark is that the filter properly follows the model, and as approach to the real problem, the performance to online implementation was tested. To apply the SMC Particle ing methodology the assumption of a sampled data model for the SDE s was necessary; thus, the set of equations are posed as a new and improved model that includes uncertainties and disturbances. SIR s are satisfactory but even if this is a novel application of the SMC, it may require a more advanced SMC method to the real data problem solution (Briers, 4,5,6)(Klaas et al, 6). Note: A big challenge and a good goal for control engineers is to reach an appropiate level of accuracy in the estimator results and close effectively the control loop for the control of Biomass, Sustrate and Product optimum paths. That idea has been studied and tested in simulation (Quintero et al, 7); authors will develop the closed loop of a numerical methods based controller with the real data estimator.

5 Inputs estimation Test: This was performed by using less information than real data interpolation. This procedure was performed looking for a better estimator, with the capacity to remain accurate even if the input data are missed by long sample times, by simulating some loss of information when a sensor is disconnected or out of service; or just in cases where the measurement available is only the substrate or product one. Fig 5 shows the good performance of the particle filter in cases of lost of information. This feature can be explored and used for optimization, control and information process. Substrate Estimation Product Estimation Glucose Concentration [g/l] Ethanol Concentration [g/l] Figure 5. Input estimation. a) Substrate estimation, real data interpolation and real data. b) Product concentration estimation, real data interpolation and real data. V. CONCLUSIONS In this work, a state estimator based on Nonlinear filtering techniques was presented. The technique and methodology was illustrated for the case of a bioreactor for the alcoholic fermentation continuous process of Zymomonas Mobilis, one of the most promising microorganisms for genetic engineering envisaging the development of strains for lignocellulose fermentation. An approach to a SDE s model containing uncertainties and disturbances, for a Zymomonas mobilis continuous fermentation was presented, looking for the correct modelling and the right implementation of the SMC methodology for state estimation. The results obtained showed the filter performance by the use of real data as observable measurements to the non measurable states value estimation. The application of the particle filtering as state estimator is acceptable and feasible for its implementation, to solve the problem of on line biomass estimation in a continuous process; due to its reliability and admissible computational cost to the real problem sampling time. showed a good performance with the inhibition variables, of relevant importance for the dynamic behaviour of bacteria in open and closed loop. These results will be used in a closed loop to control the biotechnological variables such as Biomass, Substrate and Product. ACKNOWLEDGEMENTS To Mark Briers, my example in knowledge, SMC-MCMC partner and friend. Thanks for your comments and your help. This work was partially funded by the German Service for Academic Exchange (DAAD Deutscher Akademischer Austausch Dients)