A study on full-domain transient temperature reconstruction and backward sensor placement for distributed heat source systems

Online estimation of the full-domain temperature field from sparse local measurements is widely desired in effective analysis of thermal behavior, closed-loop control, and state tracking for heat-source systems. Despite advances in inversion techniques, these methods mainly focus on steady-state conditions and are often application-dependent. Moreover, existing forward sensor placement methods only yield a single sub-optimal combination. For efficient online thermal monitoring based on limited observations, a transient-state reconstruction technique and sensor placement for complex heat-source systems are described. In offline preparation, proper orthogonal decomposition (POD) is employed to identify dominant eigenvectors from representative high-fidelity temperature fields, capturing the distribution and evolutionary patterns of heat-source systems. Subsequently, a novel intelligent method, Improved Coral Reef Optimization (ICRO), which provides a new and reliable option for solving sophisticated optimization problems, and two associated backward sensor placement strategies with objective criterion of cross-validation L₂ norm error, are proposed for diverse sensor layouts and high-quality reconstruction. During online phase, coefficients of dominant eigenvector set are dynamically and robustly solved based on least squares estimator and sparse measurements, allowing for real-time inference of global thermal state. Addressing the lack of references regarding performance improvement, the influence of key parameters on reconstruction was firstly investigated with analytical models, and sensor placement optimization strategy was preliminarily validated. Finally, comprehensive evaluations of proposed sensor placement and reconstruction were conducted in two typical cases of complex heat-source systems under various operating conditions: the simulation of multi-chip printed circuit board (PCB) with anisotropic conductivity, and the experimental case of variable heat-source system. These assessments demonstrated the effectiveness and reliability of the sensor placement strategy and online reconstruction.