(546b) Application of Sequential Monte Carlo Methods for Robust Monitoring of Lactic Acid Bacteria Fermentation

Lactic acid bacteria (LAB) are commonly used in the food industry, and in the dairy industry in particular (LAB are typically used as starter cultures) [1]. Like any other microorganisms, the LAB production is affected by the environmental conditions. The main conditions affecting the production of LAB are temperature, pH, substrate and lactic acid concentration. The production is carried on in batch or-fed –batch conditions and monitoring the environmental condition becomes a critical aspect of the production process [2]. However, the lack of some on-line measurements and rely on limited sensor placed in the fermenter (e.g., pH) makes the monitoring of the process difficult hence the usage of mechanistic models can give additional relevant information about the system.

In this study, monitoring of Streptococcus thermophilus production is investigated. The fermentation model has been proposed by Spann et al. [3]. The reaction occurring in the system can be defined as follows and the general material balance is shown in Equation (1) and Equation (2) respectively. The pH is also calculated by include the kinetics of mixed weak acid base [4].

Lactose + Ammonia + Phosphoric Acid --> Biomass + Lactic Acid + Galactose

dC_x/dt = μ_max f_lag f_s f_p f_pH C_x (1)

Where C_x is the concentration of a generic component x, while on the right-hand side of the equation there are terms that take into account the lag-time (f_lag), lactose and lactate inhibition (f_s and f_p respectively) and the pH (f_pH).

Spann et al. [3] have applied traditional Monte Carlo method to perform parameter estimation off-line which provided estimation of parameters of the model and its covariance matrix of the estimated parameters. Using Monte Carlo simulations the uncertainty of estimated parameters were propagated to model outputs (states) thereby providing a model-based method to monitor LAB fermentation. In this contribution, our aim to is to update information (its quality) on estimating parameters and state of the model simultenously in a online application context. To this end, other approaches can be followed for the on-line monitoring of LAB production. For this purpose the possibility to use sequential Monte Carlo methods can be considered [5], [6]. In this case, a particle filter is applied to the state space representation of the system (hence focusing on the state estimation ) recursively as each data is collected online during batch production. In this way, measurement errors and process disturbances are filtered which provides better estimation of the states and its uncertainty (probability density distribution) as new data is collected.

While many particle filters (SMC) methods focused on state estimation, the key challenge is to address both parameter and state estimation uncertainty. Several approaches can be followed when applying sequential Monte Carlo for on-line monitoring, such as defining an extended state that includes state and parameters, and then apply standard particle methods [5]. Further investigation can include artificial dynamics [7] and Markov Chain Monte Carlo within Sequential Monte Carlo algorithms [5], [8].

The aim of this study is develop a reliable process monitoring by using sequential monte carlo sampling techniques . The results will then be used to analyze and compare different SMC sampling methods and their ability to use few measured online data and predict unmeasured key process variables/states for monitoring production yield and impurities in a fermentation process. While the methods will be compared for LAB fermentation that contains typically few online data, future outlook and perspectives for extending the methods to reconcile noisy data from online aerobic fermentation systems (that features rich online data including offgas CO2 and oxygen measurements, online pH, DO and weight among others) will be presented and discussed.

References

[1] F. Leroy and L. De Vuyst, “Lactic acid bacteria as functional starter cultures for the food fermentation industry,” Trends Food Sci. Technol., vol. 15, no. 2, pp. 67–78, Feb. 2004.

[2] S. Ding and T. Tan, “l-lactic acid production by Lactobacillus casei fermentation using different fed-batch feeding strategies,” Process Biochem., vol. 41, no. 6, pp. 1451–1454, Jun. 2006.

[3] R. Spann, C. Roca, D. Kold, A. Eliasson Lantz, K. V. Gernaey, and G. Sin, “A probabilistic model-based soft sensor to monitor lactic acid bacteria fermentations,” Biochem. Eng. J., vol. 135, pp. 49–60, Jul. 2018.

[4] E. V. Musvoto, M. C. Wentzel, R. E. Loewenthal, and G. A. Ekama, “Integrated chemical–physical processes modelling—I. Development of a kinetic-based model for mixed weak acid/base systems,” Water Res., vol. 34, no. 6, pp. 1857–1867, Apr. 2000.

[5] N. Kantas, A. Doucet, S. S. Singh, J. Maciejowski, and N. Chopin, “On Particle Methods for Parameter Estimation in State-Space Models,” Stat. Sci., vol. 30, no. 3, pp. 328–351, Aug. 2015.

[6] N. Kantas, A. Doucet, S. S. Singh, and J. M. Maciejowski, “An Overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models,” IFAC Proc. Vol., vol. 42, no. 10, pp. 774–785, Jan. 2009.

[7] T. Higuchi, “Self-Organizing Time Series Model,” in Sequential Monte Carlo Methods in Practice, New York, NY: Springer New York, 2001, pp. 429–444.

[8] W. R. Gilks and C. Berzuini, “Following a moving target-Monte Carlo inference for dynamic Bayesian models,” J. R. Stat. Soc. Ser. B (Statistical Methodol., vol. 63, no. 1, pp. 127–146, Feb. 2001.