Detection, Reconstruction, and Overheating Warning of Three-Dimensional Dynamic Temperature Fields Inside Conductive...

Conductive polymer gel materials are inherently susceptible to localized overheating during electrical heating owing to spatially nonuniform conductivity distributions, while their internal three-dimensional temperature fields remain challenging to monitor in real time through noncontact means. Traditional inversion methods, such as Tikhonov-LSQR and TV-ADMM, perform frame-by-frame spatial regularization. The former enforces global smoothness, while the latter preserves sharp edges-but neither exploits the temporal evolution of the temperature field governed by the heat conduction equation, leading to unstable reconstructions in deep regions. To address this limitation, we propose a comprehensive methodology for the calibration, reconstruction, and overheating warning of three-dimensional dynamic temperature fields based on the focused light-field infrared camera. A forward electro-thermal coupled heat conduction model is established to characterize the transient temperature evolution within the gel throughout the heating process. Concurrently, a forward imaging model and its corresponding linear system matrix are constructed for focused light-field infrared imaging, enabling the acquisition of infrared light-field images and subsequent reconstruction of the three-dimensional dynamic temperature field. Furthermore, we develop an ETP-Causal LSQR online inversion algorithm tailored for real-time overheating warning during gel heating. Unlike conventional spatial regularization methods, we incorporate a temporal physical prior: the previous reconstruction is propagated through the heat conduction equation to predict the current temperature field, and this prediction is introduced as a soft constraint into the LSQR solver. The algorithm strictly respects causality, using only current measurements and historical reconstructions. Comparative results demonstrate that the proposed method consistently outperforms conventional Tikhonov-LSQR and TV-ADMM algorithms across multiple aspects, including reconstruction accuracy, noise robustness, physical consistency, cross-operating condition generalization, and computational efficiency, thereby validating the effectiveness and broad applicability of the physically constrained causal inversion framework.