Soft Sensing of Surface Temperature in Electrical Flow Heaters

Abstract

Electrical flow heaters are becoming increasingly popular as heat sources in thermal oil systems, in the wake of the ongoing energy transition. At the surface of these heaters, the heat-transfer fluid typically experiences the highest thermal power densities and thus the highest thermal stress within the system. The resulting surface temperature of the heater therefore represents the critical upper operating limit for heat-transfer fluids, that governs their thermal stability, service life, and fouling formation. However, accurate and reproducible measurement during heater operation is not feasible due to practical sensor limitations. As an alternative to direct measurement, this thesis investigates the possibility of using state-of-the-art machine learning approaches for the development of a data-driven soft sensor that estimates the surface temperature based on standard measurable process variables. A high-fidelity numerical model is constructed to generate dynamic simulation data, serving as a virtual test bed for systematic soft sensor development an evaluation. Two data-driven modeling approaches are investigated: an autoregressive end-to-end formulation including a linear baseline model and a nonlinear neural network model, and a structured neural state-space formulation combined with recursive state estimation. The models are trained and validated using systematically designed dynamic operating scenarios, and their predictive performance is evaluated with respect to accuracy, robustness, and dynamic consistency. The results demonstrate that while both approaches achieve high predictive accuracy, the structured state-space formulation provides enhanced robustness and improved stability across diverse operating scenarios. These findings highlight the potential of structured machine learning models for reliable soft-sensor development in complex heat-transfer applications.