From Data to Insights: Enhancing Bioprocess Efficiency with Bayesian State Estimators

Motivation

The increasing need for process control in the chemical industry implies the development of expensive and sophisticated monitoring sensors, bringing up challenges regarding the construction of cost-effective automated industrial plants. However, to reduce the use of expensive sensors, estimation tools have been developed, also known as softsensors. Of the various existing state estimators, there is a class of methods called Bayesians. Among them, there are three that stand out for their applicability and effectiveness: Extended Kalman Filter (EKF), Kalman Unscented Filter (UKF), and Moving Horizon Estimator (MHE). 

This blog post explores the application of Bayesian state estimators in the context of extractive alcoholic fermentation—a complex process enhanced by ethanol removal through CO2 stripping. By simulating this bioprocess in MATLAB™ and incorporating noise, disturbances, and model uncertainties, we investigate how these estimators enhance efficiency and production outcomes.

Methodology

The extractive alcoholic fermentation process to be used as a case study in this work is characterized by the removal of ethanol from the reaction medium through stripping with CO2, where the decrease in the ethanol concentration of the broth causes the effects of inhibition by product to be minimized, increasing ethanol production by 65.4% compared to conventional fermentation without stripping (RODRIGUES, 2019; SONEGO et al., 2018).

The fermentation process employed by Sonego et al. (2018) is carried out in two stages of operation (fed batch and batch). The dynamics of the of the process is described by Equation below.

The study involves simulating the extractive alcoholic fermentation process and integrating Bayesian state estimators to manage uncertainties inherent in real-world applications. Using MATLAB™, we used the bioprocess dynamics' model and evaluate estimator performance through rigorous metrics such as Average Time per Iteration (ATI) and Average Error Quadratic (AEQ). This approach not only validates the efficacy of Bayesian methods but also provides actionable insights for optimizing industrial processes.

Through this exploration, we aim to demonstrate the transformative potential of advanced data analysis techniques in driving operational efficiency and achieving sustainable production gains in biochemical industries.

Results: Evaluating Bayesian State Estimators in Bioprocess Control

After simulating the extractive alcoholic fermentation process using MATLAB™ and applying Bayesian state estimators—Extended Kalman Filter (EKF), Kalman Unscented Filter (UKF), and Moving Horizon Estimator (MHE)—we observed distinct performance outcomes.

The procedure revealed significant insights, particularly highlighted in Figure 1, which depicts the behavior of each state variable and the relative errors between estimated and actual values throughout the simulation. Here’s a breakdown of the findings:

Figure 1 - Estimates from (a) EKF, (b) UKF, and (c) MHE applied to extractive alcoholic fermentation and relative errors throughout the process.

• Performance Comparison: EKF (Figure 1a)  and MHE  (Figure 1c) consistently underestimated CX, CS, and CE throughout the simulation, showing oscillations and lack of convergence to actual states. In contrast, UKF demonstrated superior performance by quickly converging estimates with high accuracy.

• Quantitative Assessment: The Average Error Quadratic (AEQ) criterion quantified the performance, with MHE showing an AEQ of 0.556 ± 0.005, approximately thirty times higher than UKF (0.018 ± 0.002) and statistically similar to EKF (0.549 ± 0.002). This unexpected outcome challenges theoretical expectations of MHE's robustness, possibly due to challenges in its design and tuning.

• Sampling Time: Assessing the Average Time per Iteration (ATI), MHE exhibited the highest ATI of 0.110 ± 0.005 s, suggesting a sampling time suitable for bioprocess dynamics in the order of seconds.

These results underscore the efficacy of UKF in optimizing bioprocess control compared to EKF and MHE, despite theoretical assumptions favoring MHE. Such findings not only contribute to understanding Bayesian estimator performance but also provide actionable insights for enhancing industrial process efficiency.