Data-driven sensor placement for efficient thermal field reconstruction

Complete temperature field estimation from limited local measurements is widely desired in many industrial and scientific applications of thermal engineering. Since the sensor configuration dominates the reconstruction performance, some progress has been made in designing sensor placement methods. But these approaches remain to be improved in terms of both accuracy and efficiency due to the lack of comprehensive schemes and efficient optimization algorithms. In this work, we develop a data-driven sensor placement framework for thermal field reconstruction. Specifically, we first tailor the low-dimensional model from the prior thermal maps to represent the high-dimensional temperature distribution states by virtue of proper orthogonal decomposition technique. Then, on such subspace, a recursive greedy algorithm with determinant maximization as the objective function is developed to optimize the sensor placement configuration. Furthermore, we find that the same sensor configuration can be yielded faster by the standard procedures of column-pivoted QR factorization, which allows concise software implementation with readily available function packages. When the sensor locations are determined, we advocate using the data-based closed-form estimator to minimize the reconstruction error. Real-time thermal monitoring on the multi-core processor is employed as the case to demonstrate the effectiveness of the proposed methods for thermal field reconstruction. Extensive evaluations are conducted on simulation or experimental datasets of three processors with different architectures. The results show that our method achieves state-of-the-art reconstruction performance while possessing the lowest computational complexity when compared with the existing methods.