## 5 Conclusions and Outlook  
In this study, a novel 3D temperature field reconstruction algorithm based on Tucker's decomposition and acoustic temperature measurement is proposed, which greatly improves the accuracy and reliability of acoustic temperature measurements in complex 3D temperature fields and reduces the reconstruction error by 10-20% compared to the traditional method, and by about 6% compared to the fixed-measurement Tucker's decomposition reconstruction algorithm. The reconstruction process takes about 4 s and is suitable for real-time industrial applications. The algorithm is robust to Gaussian noise and performs well in temperature fields beyond the range of the previous dataset, demonstrating its adaptability to various operating conditions. The method provides a cost-effective solution for three-dimensional temperature monitoring in coal-fired power plants, supporting combustion optimization and flexible load adjustment under carbon-neutral targets.  
Although the proposed algorithm provides significant improvements in 3D temperature field reconstruction, some limitations should be recognized: the algorithm relies heavily on CFD-generated a priori datasets, which may not fully capture the stochastic variations (e.g., coal particle fluctuations, ash deposition) in the actual boiler environment. This may limit its generalizability to real-world applications. The study assumes that the distribution of acoustic measurement points is ideal. In industrial environments, the placement of sensors may be limited by physical space, resulting in sparse data coverage in certain areas and reduced reconstruction accuracy. Noise immunity tests are limited to Gaussian  
Figure 13: Reconstruction of 3D temperature distribution in experimental condition 5.  
noise. In the real world, noise may exhibit spatial correlation or non-stationary behavior (e.g., local high-temperature distortion), which may affect the robustness of the algorithm.  
To address limitations and further improve the applicability of the proposed methodology, future research directions include conducting field experiments at an operating coal-fired power plant to validate the algorithm's performance under realistic noise and interference conditions, developing strategies to optimize sensor locations to maximize data coverage and minimize reconstruction errors in space-constrained environments; combining Tucker decomposition with deep learning models (e.g., CNNs or transformers) to improve detail preservation and robustness to complex noise patterns; investigating the applicability of the algorithm in other industrial scenarios, such as for 3D temperature monitoring critical waste incinerators and aerospace combustion chambers.  
Conceptualization, L.A.; methodology, S.Z.; investigation, P.Y. and G.S.; writing--original draft preparation, J.Y. and P.Y.; writing--review and editing, J.Y. and P.Y. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
Dataset available upon request from the authors.  
The authors declare no conflicts of interest.