A Proof of Concept for a Digital Twin of an Ultrasonic Fermentation System

TL;DR

This paper introduces a conceptually complete digital twin for an ultrasound-enhanced beer fermentation system, linking real-time sensing with a Bayesian Gompertz growth predictor and actuation. The core idea maps environmental inputs—temperature, ultrasound frequency, and duty cycle—to Gompertz parameters via a single-hidden-layer neural network, regularized by informative priors to cope with a small dataset. Evaluation shows a promising 6.59% mean absolute percentage error and qualitative agreement with observed growth, though the mean-squared error is higher than a reference study due to dataset size and the nonlinear, frequency-dependent effects of ultrasound. The work lays a foundation for autonomous experimentation and real-time optimization, with future plans for thermal control and automated optical-density sensing to fully close the feedback loop.

Abstract

This paper presents the design and implementation of a proof of concept digital twin for an innovative ultrasonic-enhanced beer-fermentation system, developed to enable intelligent monitoring, prediction, and actuation in yeast-growth environments. A traditional fermentation tank is equipped with a piezoelectric transducer able to irradiate the tank with ultrasonic waves, providing an external abiotic stimulus to enhance the growth of yeast and accelerate the fermentation process. At its core, the digital twin incorporates a predictive model that estimates yeast's culture density over time based on the surrounding environmental conditions. To this end, we implement, tailor and extend the model proposed in Palacios et al., allowing us to effectively handle the limited number of available training samples by using temperature, ultrasonic frequency, and duty cycle as inputs. The results obtained along with the assessment of model performance demonstrate the feasibility of the proposed approach.

Figures (5)

• Figure 1: A schematic overview of the proposed solution. On the left there is the physical fermentation tank, connected via the sensors to the Digital Twin, whose scheme is reported on the right. Inverse communication is established via the Act flow and implemented by actuators. The environmental parameters, temperature, ultrasonic frequency, and duty cycle, serve as inputs to a neural network that infers the parameters $D, \lambda, \mu$ of the Gompertz model used to estimate the growth of the yield. To address the limited size of the available dataset, prior knowledge is incorporated into the neural network through Bayesian Inference, allowing the model to remain robust despite sparse observations.
• Figure 2: Distribution of performance metrics across folds. In the left panel Mean Absolute Percentage Error is displayed, in the central one the Mean Absolute Percentage Error, and on the right the Mean Squared Error.
• Figure 3: Predicted vs observed optical density at 600 nm values across all test points in the 5-fold cross-validation.
• Figure 4: Distribution of absolute percentage errors across all test points in the 5-fold cross-validation
• Figure 5: Real growth curve (in blue) expressed as absorbance at 600 nm of the yeast culture compared with the model prediction (in bright orange) and associated confidence interval (orange shaded area). The specific environmental conditions are omitted for confidentiality reasons.