Reconstruction Optimization Algorithm of 3D Temperature Distribution Based on Tucker Decomposition

For the purpose of solving the large temperature field reconstruction error caused by different measuring point arrangements and the problem that the prior dataset cannot be built due to data loss or distortion in actual measurement, a three-dimensional temperature profile reconstruction optimization algorithm is proposed to repair the empirical dataset and optimize the arrangement of temperature measuring points based on Tucker decomposition, the minimum condition number method, the greedy algorithm, and the hill climbing algorithm. We used the Tucker decomposition algorithm to repair the missing data and obtain the complete prior dataset and the core tensor. By optimizing the dimension of the core tensor and the number and position of the measuring points calculated by the minimum condition number method, the greedy algorithm, and the mountain climbing algorithm, the real-time three-dimensional distribution of the temperature field is reconstructed. The results show that the Tucker decomposition optimization algorithm could accurately complete the prior dataset, and compared with the original algorithm, the proposed optimal placement algorithm improves the reconstruction accuracy by more than 20%. At the same time, the algorithm has strong robustness and anti-noise, and the relative error is less than 4.0% and 6.0% with different signal-to-noise ratios. It indicates that the proposed method can solve the problem of building an empirical dataset and 3D temperature distribution reconstruction more accurately and stably in industry.