Virtual Sensing to Enable Real-Time Monitoring of Inaccessible Locations \& Unmeasurable Parameters

TL;DR

The paper addresses real-time monitoring of thermal-hydraulic conditions in inaccessible reactor subchannels by introducing Multi-Input Operator Network (MIONet) virtual sensors that fuse multiple input functions (e.g., power profile, inlet temperature, inlet velocity) to predict center-plane quantities $T_{center}$, $v_{center}$, and $k_{center}$. It demonstrates a data-generation pipeline using CFD with RNG $k$-$ extepsilon$ modeling and trains MIONet to learn mappings across multiple input functions, leveraging low-rank tensor fusion for efficiency. The approach achieves relative $L_2$ errors of approximately $0.2 extpercent$, $0.8 extpercent$, and $1.4 extpercent$ for $T_{center}$, $v_{center}$, and $k_{center}$, respectively, with inference times around $5.24 imes 10^{-3}$ s—over 100,000× faster than full CFD—while generalizing without continual retraining. This enables accurate, real-time virtual sensing in harsh environments and has potential implications across aerospace, manufacturing, and energy systems, with future work focusing on physics-informed constraints and time-series extensions.

Abstract

Real-time monitoring of critical parameters is essential for energy systems' safe and efficient operation. However, traditional sensors often fail and degrade in harsh environments where physical sensors cannot be placed (inaccessible locations). In addition, there are important parameters that cannot be directly measured by sensors. We need machine learning (ML)-based real-time monitoring in those remote locations to ensure system operations. However, traditional ML models struggle to process continuous sensor profile data to fit model requirements, leading to the loss of spatial relationships. Another challenge for real-time monitoring is ``dataset shift" and the need for frequent retraining under varying conditions, where extensive retraining prohibits real-time inference. To resolve these challenges, this study addressed the limitations of real-time monitoring methods by enabling monitoring in locations where physical sensors are impractical to deploy. Our proposed approach, utilizing Multi-Input Operator Network virtual sensors, leverages deep learning to seamlessly integrate diverse data sources and accurately predict key parameters in real-time without the need for additional physical sensors. The approach's effectiveness is demonstrated through thermal-hydraulic monitoring in a nuclear reactor subchannel, achieving remarkable accuracy.

Figures (7)

• Figure 1: (a): Perspective view of a nuclear fuel assembly illustrating the arrangement of fuel rods (green cylinders) and their vertical alignment. (b): Cross-sectional view at the fuel assembly's center plane, detailing the fuel rods' geometric layout and the subchannel (blue region) where coolant flows. (c) Typical temperature distribution inside the PWR subchannel. Direct measurement within these subchannels is challenging due to geometric constraints and the potential disruption caused by installing traditional sensors such as flowmeters or thermocouples, which could affect the reactor core's design and operation.
• Figure 2: Grid Generation over the Computational Domain, which illustrates the careful resolution of the boundary layer near the fuel rod walls
• Figure 3: (a) Description of branch inputs; $P_{rod}$ represents a functionally discretized input at fixed sensor locations, while $T_{in}$ and $v_{in}$ are treated as constant variables. (b) Representation of the output domain: it illustrates the node positions at the center of a subchannel, as specified in a computational mesh.(c) Architecture of the Multi-input Operator Network. Branch networks are utilized to encode $P_{rod}$ along the nuclear fuel rod, $T_{in}$, and $v_{in}$. The trunk network encodes the spatial domain of the outputs. The output quantities are distributions of $T_{center}$, $v_{center}$ and $k_{center}$.
• Figure 4: Distribution of model performance metrics for MIONet on the test dataset. Panels (a), (c), and (e) show histograms of the MSE for velocity, temperature, and turbulent kinetic energy predictions, respectively. Panels (b), (d), and (f) represent the histograms of the relative $L_2$ error percentage for the same respective quantities. Statistical summaries, including mean, standard deviation, and quantiles, are displayed in the insets for relative $L_2$ errors.
• Figure 5: MIONet velocity predictions compared to ground truth data. Panels (a) and (d) show the predicted velocity distributions for the best and worst test cases, respectively. Panels (b) and (e) display the corresponding ground truth data. Panels (c) and (f) depict the absolute difference between the predictions and ground truth.