## 3 Results and Discussion  
### Nondestructive Evaluation of Porosity  
In this study, the terahertz time-domain spectra were processed using the fast independent component analysis (Fast ICA) algorithm, yielding a set of kurtosis values for  
Figure 9: Cross-validation schematics. 20 samples. Kurtosis, a statistical metric quantifying the sharpness and peakedness of signal waveforms, was employed to describe the signal characteristics. The extracted kurtosis values were then analyzed in association with the corresponding porosity and visually presented. As shown in Figure 10a, after ICA treatment of individual components, it was observed that the waveform, amplitude, and frequency of each component were significantly different. It was evident that these components exhibited complex and redundant characteristics, making it challenging to discern clear patterns that could effectively represent porosity. To address this issue, we proceeded to calculate the kurtosis of each component, which served as a representative feature parameter for porosity assessment. As shown in Figure 10b, a decreasing trend in kurtosis values was observed with increasing porosity. This indicated that as the TBCs' porosity increased, the waveform of its terahertz time-domain spectra became smoother. This phenomenon can be attributed to the structural changes occurring within the thermal barrier coatings due to the increasing porosity, which consequently led to variations in the internal permittivity and refractive indicators of the samples. More precisely, the augmentation of voids and pore quantity caused the propagation path of the terahertz signal within the coating to become more intricate and convoluted, thereby diminishing the sharpness and steepness of the waveform. As the porosity varied, the complexity and heterogeneity within the TBCs became more prominent, consequently causing the interaction between the terahertz wave and the medium to exhibit a greater degree of complexity and diversity. Correspondingly, the kurtosis feature parameter values of the spectra also underwent changes. Hence, the fluctuations in kurtosis can serve as a reflection and evaluation of the porosity. Furthermore, as shown in Figure 11, the spectrum was subjected to a smoothing process, followed by Gaussian fitting of the main peak to extract additional feature parameters, including center frequency, bandwidth, and APSD. These feature parameters provided crucial information about the frequency components and energy distribution of the signal, which were then correlated with the porosity. As shown in Figure 12a, where the small figure was a curved representation of the smooth spectrum, it was another form of Figure 11. The center frequency was the extreme point of the smoothed curve, and the center frequency decreased with the increase in porosity. As shown in Figure 12b, the frequency bandwidth was the frequency broadening when the peak dropped to half, and the frequency bandwidth increased with the increase in porosity. The changes in center frequency and frequency bandwidth with porosity showed strong regularity, which was the result of Gaussian fitting. Figure 13a shows a single power spectrum used to calculate  
Figure 10: Results of Fast ICA: (**a**) ICA separation visualization; (**b**) kurtosis evaluation of porosity. More precisely, the variation in porosity led to changes in the dielectric properties within the TBCs. As porosity increased, scattering effects were enhanced, resulting in a decrease in the dielectric constant and a reduction in wave velocity. Consequently, the overall frequency decreased, causing the center frequency to shift towards lower frequencies. Moreover, an increased porosity introduced more scattering and multipath effects, making the signal transmission more complex. This broadened the signal spectrum, indicating a wider distribution of energy across a range of frequencies, thus increasing the bandwidth.