A fast food-freezing temperature estimation framework using optimally located sensors

Abstract: This article presents and assesses a framework for estimating temperature fields in real time for food-freezing applications, significantly reducing computational load while ensuring accurate temperature monitoring, which represents a promising technological tool for optimizing and controlling food engineering processes. The strategy is based on (i) a mathematical model of a convection-dominated problem coupling thermal convection and turbulence, and (ii) a least-squares approach for solving the inverse data assimilation problem, regularized by projecting the governing dynamics onto a reduced-order model (ROM). The unsteady freezing process considers a salmon slice in a freezer cabinet, modeled with temperature-dependent thermophysical properties. The forward problem is approximated using a third-order WENO finite volume solver, including an optimized second-order backward scheme for time discretization. We employ our data assimilation framework to reconstruct the temperature field based on a limited number of sensors and to estimate temperature distributions within frozen food. Sensor placement is optimized using a novel greedy algorithm, which maximizes the observability of the reduced-order dynamics for a fixed set of sensors. The proposed approach allows efficient extrapolation from external sensor measurements to the internal temperature of the food under realistic turbulent flow conditions, which is crucial for maintaining food quality.

• The paper proposes a reduced-order framework for efficient temperature estimation in food freezing, significantly cutting computational costs.
• Using a greedy algorithm, sensors are optimally placed to enhance system observability for accurate temperature reconstruction from limited data.
• Numerical results confirm the framework accurately reconstructs internal temperature fields, essential for ensuring food quality and optimizing freezing processes.

A Reduced-Order Framework for Temperature Estimation in Food Freezing Applications

The paper "A reduced-order framework for temperature estimation in food freezing from optimally located sensors, including turbulent conjugate flow scenarios" introduces a method designed to estimate temperature fields within food freezing processes. This framework aims to improve temperature monitoring accuracy while significantly reducing computational demands, which is crucial for optimizing and controlling processes in food engineering. The authors propose a strategy utilizing a mathematical model to solve inverse data assimilation problems, addressing the convection-dominated issues by coupling thermal convection with turbulence.

Key Aspects of the Research

1. Mathematical Modeling: The study models the scenario of freezing an idealized salmon slice within a freezer cabinet. The scenario considers temperature-dependent thermophysical properties to capture the complex interaction between phases. The authors use a third-order weighted essentially non-oscillatory (WENO) finite volume solver for the forward problem, integrating a simple backward differentiation approach for time discretization.
2. Reduced Order Model (ROM): To regularize the inverse problem, the dynamical system is projected onto a reduced-order model using the Parametrized Background Data-Weak (PBDW) method. This reduces the problem's dimensionality, aiding efficient computation. The ROM fundamentally relies on the proper orthogonal decomposition (POD) of the system's snapshots, capturing the primary dynamics with a few modes. This method ensures the model retains its essential characteristics despite the dimensionality reduction.
3. Optimal Sensor Placement: The reconstruction of temperature fields employs a new greedy algorithm, which places sensors optimally by maximizing the observability of the reduced-order dynamics. This placement strategy enhances measurement extrapolation efficiency and the overall observability of the system, facilitating accurate temperature estimation even in less directly observed regions like the inside of food.

Numerical Results

In the numerical experiments, temperature fields were reconstructed from limited sensor data with impressive fidelity. The algorithm demonstrated strong performance in estimating temperature distributions within food, essential for ensuring quality in freezing applications. The results indicate that the proposed approach can accurately predict quantities of interest such as Nusselt numbers and freezing times, even when extrapolating from external measurements.

Implications and Future Directions

This research has significant practical implications for the food industry. Ensuring food quality during freezing is critical for consumer safety and product longevity, and the developed model supports these goals by allowing precise temperature monitoring. The theoretical implications suggest a robust interplay between reduced-order modeling and data assimilation, offering a powerful toolkit for handling high-dimensional systems in real-time applications.

Future work could extend this framework to diverse food items with varying thermophysical properties, enhancing its versatility. Moreover, incorporating real experimental conditions, including non-idealities in sensor data, could further validate and refine this methodology. The exploration of other reduced-order modeling techniques like dynamic mode decomposition (DMD) might offer alternative pathways to optimize computational efficiency and model accuracy in similar applications.

Overall, this paper contributes a substantive advancement in the nexus of computational modeling and food process engineering, presenting a methodical approach to enhancing the efficiency and accuracy of temperature monitoring in food freezing processes.