## 4 Conclusions  
In this study, an efficient solution was proposed for the nondestructive evaluation and prediction of TBCs' porosity, based on the terahertz multi-feature fusion and machine learning approach. The extraction of multiple terahertz feature parameters was carried out, and subsequent correlation and significance analyses facilitated the fusion of these parameters for the nondestructive evaluation of porosity variations. Moreover, a robust random forest regression model, optimized using the dung beetle algorithm, was successfully developed to ensure accurate prediction of TBCs' porosity.  
Based on the analysis of the experimental results, it was observed that the approach of terahertz multi-feature fusion comprehensively characterized the TBCs' porosity and effectively revealed the internal pore structure's characteristics. Subsequently, the DBO-RF model was employed, utilizing the fused feature parameters as inputs and porosity as the output. The experimental findings demonstrated the precise prediction of TBCs' porosity. Furthermore, through the implementation of five-fold cross-validation and analysis of evaluation indicators, the superior performance of the DBO-RF model in porosity prediction was confirmed. The mean error values of RMSE, MAE, and MAPE were 1.802, 1.549, and 8.362, respectively. The mean regression coefficient was 0.912, indicating the model's high accuracy and robustness in accurately predicting porosity in TBCs.  
In conclusion, our study proposes an efficient solution for the nondestructive evaluation and prediction of TBCs' porosity. This solution is based on a quantitative characterization method that integrates terahertz multi-feature fusion and machine learning. The results demonstrate a porosity prediction accuracy exceeding 90%, highlighting its significant potential for practical applications in evaluating and analyzing the microstructure of TBCs. This method enables effective monitoring of the thermal barrier coating's service life and determination of its validity. Additionally, our research paves the way for expanding the application of this method to assess other aerospace materials, contributing to the advancement of materials science and related fields. Looking ahead, the continuous development and refinement of nondestructive techniques for evaluating various materials hold great promise. Further research in this direction has the potential to drive advancements in material characterization methodologies and contribute to a more scientific understanding of material performance and reliability.  
Conceptualization, D.Y.; data curation, R.L. and D.Y.; funding acquisition, D.Y. and J.P.; investigation, R.L., Q.Z. and J.X.; methodology, R.L., D.Y., Q.Z. and J.X.; project administration, D.Y.; resources, D.Y.; supervision, D.Y. and J.P.; visualization, Q.Z. and J.X.; writing--original draft, R.L.; writing--review and editing, D.Y. and J.P. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (52205547), Key Research and Development Projects in Anhui Province (2022a05020004, 202104a05020002), the Open Research Fund of Fujian Provincial Key Laboratory of Terahertz Functional Devices and Intelligent Sensing, Fuzhou University (FPKLTFDS20301), the Open Research Fund of Huzhou Key Laboratory of Terahertz Integrated Circuits and Systems (HKLTICY23 KF05), the Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices (JCKJ2022A08), the Anhui Institute of Future Technology Enterprise Cooperation Project (2023 tyhz04), and the Scientific Research Starting Foundation of Anhui Polytechnic University (2021 YQQ029).