## 1 Introduction
Quantitative measurements of pore size, shape, and distribution can be obtained through image processing and analysis techniques, enabling the calculation of porosity. However, these microscopic observation methods are considered destructive, requiring sample embedding and polishing procedures. Therefore, nondestructive testing (NDT) methods present a superior choice. NDT is a vital technology that could be applied to the evaluation of various materials and components. Utilizing various testing techniques detects surface and internal defects, damages, or structural changes without causing sample destruction. Due to its ability to provide timely and accurate information, NDT has found extensive applications in industries such as aerospace, automotive, marine, nuclear, and construction, facilitating quality control and fault diagnosis, as well as ensuring preventive maintenance, structural safety, and reliability [20; 21]. Furthermore, NDT methods hold significant potential for the evaluation of porosity in TBCs. For instance, NDT of the coatings can be achieved using ultrasonic waves [22], infrared thermography [23], and X-rays [24]. These methods offer advantages such as rapid assessment, non-contact measurement, and comprehensive evaluation of the coatings. However, they still encounter complex challenges in signal processing and data analysis during practical application. Ultrasonic testing has limited resolution and cannot accurately detect micro-sized pores. Infrared thermography requires thermal cycling of the samples, which can affect the detection results. As the sample undergoes heating and subsequent cooling cycles, it experiences expansion and contraction, which can affect its thermal conductivity, heat capacity, and thermal diffusivity. X-ray technology involves radiation and poses certain safety risks to operators. Despite these challenges, the methods utilized for NDT of thermal barrier coatings are still quite accurate. In recent years, many scholars have employed machine learning techniques to further enhance the accuracy of NDT for thermal barrier coatings. Utilizing machine learning in NDT has further improved accuracy, enabling more efficient and precise evaluation of critical components such as TBCs in aerospace applications [25; 26; 27]. Therefore, combining a superior NDT method with machine learning techniques enables higher accuracy in detecting the TBCs' porosity. The terahertz time-domain spectroscopy (THz-TDS) technique offers unique advantages in the evaluation of TBCs' porosity [28; 29]. When the terahertz pulse interacts with the sample, it undergoes changes in amplitude and phase due to the sample's material properties, such as its refractive index and absorption characteristics. The altered terahertz pulse is then combined with the reference pulse at the detector, and the resulting electric field is measured as a function of time. Operating within the frequency range of 0.1 THz to 10 THz, corresponding to wavelengths ranging from 30 \(\upmu\)m to 3 mm, terahertz waves occupy an intermediate position between infrared light and microwaves. This nondestructive technique provides high resolution, sensitivity, and real-time capabilities and the ability to conduct comprehensive analyses of multiple parameters. Moreover, it can penetrate non-metallic ceramic layers without causing material damage or altering their properties, making it suitable for continuous and repeatable testing of TBCs. For instance, [PERSON] et al. [30] proposed a nondestructive evaluation method using THz-TDS to assess the dielectric constant of Al\({}_{2}\)O\({}_{3}\) ceramic samples, allowing for the evaluation of critical parameters such as porosity, grain size, and impurity content. This demonstrates the potential application of terahertz radiation in the field of ceramics with high dielectric constants. Some researchers have already started exploring the application of machine learning as an advanced signal-processing method in the field of nondestructive testing [31; 32]. [PERSON] et al.