Sparse-sensor reconstruction of three-dimensional temperature fields in immersion-cooled battery modules under dynamic cooling

Full-field thermal-state estimation is challenging in immersion-cooled battery modules because direct optical access to battery surfaces is limited, deployable sensors are sparse, and high-fidelity computational fluid dynamics (CFD) is unsuitable for online estimation. This study evaluates a proper orthogonal decomposition (POD)-based sparse reconstruction framework for three-dimensional transient temperature fields in a two-phase immersion-cooled battery module under temperature-triggered dynamic cooling. Thirty operating conditions are generated using Latin hypercube sampling, and CFD snapshots are used to construct and validate the reduced-order model. Modal-energy and internal-validation analyses support a six-mode POD representation retaining 99.7720% of the cumulative energy. QR-pivoting is used to select six sensor locations and is compared with classical discrete empirical interpolation method (DEIM), Pearson correlation, and random placement under a common reconstruction framework. On five independent test conditions, the six-sensor QR-pivoting configuration achieves a mean case-wise time-averaged RMSE of 0.2166 K and a mean NRMSE of 2.56%, with a maximum time-averaged RMSE of 0.3159 K. Safety-oriented evaluation shows that localized and short-duration errors can be substantially larger than the domain-averaged RMSE. Robustness tests further indicate that sensor-specific static bias causes the strongest reconstruction degradation, whereas common-mode bias and thermal-response lag have weaker effects. QR-pivoting retains a lower cross-condition mean RMSE than classical DEIM within the examined perturbation ranges. Online reconstruction requires less than 10 ms per full-field estimate. These results demonstrate the feasibility of POD-based sparse reconstruction for rapid thermal-state estimation in dynamically controlled immersion-cooled battery systems.