## 2 Materials and Methods
### Feature Extraction and Multi-Feature Fusion Analysis
#### 2.4.4 Extraction of Reflectance Spectrum Features  
The reflectance spectrum was a set of data utilized to investigate the changes in reflectance at different frequencies, providing insights into the optical, electrical, and physical properties of materials. In this study, the reflectance spectrum served as an informative source concerning the reflection characteristics exhibited by TBCs within the terahertz frequency domain. Extracting feature parameters through statistical analysis and examination of the reflectance spectrum aimed to uncover the underlying patterns of reflectance variation across frequencies. Moreover, it enabled the evaluation of changes in TBCs' porosity, thereby facilitating inferences related to the heterogeneity and distribution of porosity [47]. These derived feature parameters not only offer a feasibility basis for evaluating TBCs but also lay the groundwork for exploring the relationship between variations in porosity and other performance metrics associated with TBCs.  
The extraction of the mean reflectance aimed to capture the average reflection performance of the TBC sample across the entire frequency range. The reflectance standard deviation quantified the dispersion of reflectance values, indicating the fluctuation of reflectance in the frequency domain. The maximum and minimum reflectance values represented the extreme reflection conditions observed in TBCs across different frequencies. The reflectance peak highlighted the intense reflection characteristics of the TBC sample at specific frequencies, thereby reflecting the frequency response of porosity to terahertz signals.  
The specific calculation formula is as follows:  
\[\overline{R}=\frac{\int_  
linear correlations between variables but also revealed complex patterns of relationships among multiple variables. The colors in the correlation heatmap indicated the strength of the correlations, providing insights into the associations between different feature parameters. Positive correlation indicated similar changing trends between variables, negative correlation indicated opposite changing trends, and no correlation indicated the absence of a linear relationship between two variables.  
The correlation heatmap was solely capable of illustrating the correlation between variables and does not establish a causal relationship between them. Therefore, it was necessary to consider other factors when making decisions or inferences. The \(p\)-value is a crucial statistical indicator that measures the consistency between the observed data and the null hypothesis. Additionally, \(p\)-value testing could be utilized to examine the significant differences among the feature parameters, thereby indicating that the relationships between these parameters are not coincidental and possess statistical significance. Hence, by conducting correlation analysis and \(p\)-value testing, the revealed correlations among multiple feature parameters hold essential significance in characterizing the heterogeneity of porosity. Exploring the feature parameters within the dataset bears significant application value for a comprehensive investigation of the porosity structural characteristics of TBCs.