Temperature field reconstruction from the partial measurement data using the gappy proper orthogonal decomposition

Fast reconstruction of the temperature field from the partial temperature measurement data is highly desirable in the field of thermal engineering, in which reconstruction algorithms play a crucial role in real applications. Based on the gappy proper orthogonal decomposition technique, a promising approach that integrates the numerical simulation information and the measurement information is proposed in this study for the temperature field reconstruction from the partial measurement data, where the original reconstruction problem is formulated into an optimisation problem. An objective functional, which simultaneously considers the outliers in the measurement data and the model approximation distortions, is presented. Based on the split Bregman iteration technique, an iterative scheme is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the feasibility and effectiveness of the proposed algorithm.