To ensure the thermal stability of aero-engine blades under high temperature and harsh service environments, it is necessary to quickly and accurately evaluate the thickness of thermal barrier coatings (TBCs). In this work, it was proposed to use the terahertz nondestructive testing (NDT) technique combined with the hybrid machine learning algorithm to measure the thickness of TBCs. The finite difference time-domain (FDTD) method was used to model the optical propagation characteristics of TBC samples with different thicknesses (101–300 μm) in the frequency band. To make the terahertz time-domain signal obtained simulation more realistic, uniform white noise was added to the simulation data and wavelet denoising was conducted to mimic the real testing environment. Principal components analysis (PCA) algorithm and whale optimization algorithm (WOA) combined with an optimized Elman neural network algorithm was employed to set up the hybrid machine learning model. Finally, the hybrid thickness regression prediction model shows low error, high accuracy, and an exceptional coefficient of determination R² of 0.999. It was demonstrated that the proposed hybrid algorithm could meet the thickness evaluation requirements. Meanwhile, a novel, efficient, safe, and accurate terahertz nondestructive testing method has shown great potential in the evaluation of structural integrity of thermal barrier coatings in the near future.

Thermal barrier coatings (TBCs) play a crucial role in safeguarding aero-engine blades from high-temperature environments and enhancing their performance and durability. Accurate evaluation of TBCs’ porosity is of paramount importance for aerospace material research. However, existing evaluation methods often involve destructive testing or lack precision. In this study, we proposed a novel nondestructive evaluation method for TBCs’ porosity, utilizing terahertz time-domain spectroscopy (THz-TDS) and a machine learning approach. The primary objective was to achieve reliable and precise porosity evaluation without causing damage to the coatings. Multiple feature parameters were extracted from THz-TDS data to characterize porosity variations. Additionally, correlation analysis and p-value testing were employed to assess the significance and correlations among the feature parameters. Subsequently, the dung-beetle-optimizer-algorithm-optimized random forest (DBO-RF) regression model was applied to accurately predict the porosity. Model performance was evaluated using K-fold cross-validation. Experimental results demonstrated the effectiveness of our proposed method, with the DBO-RF model achieving high precision and robustness in porosity prediction. The model evaluation revealed a root-mean-square error of 1.802, mean absolute error of 1.549, mean absolute percentage error of 8.362, and average regression coefficient of 0.912. This study introduces a novel technique that presents a dependable nondestructive testing solution for the evaluation and prediction of TBCs’ porosity, effectively monitoring the service life of TBCs and determining their effectiveness. With its practical applicability in the aerospace industry, this method plays a vital role in the assessment and analysis of TBCs’ performance, driving progress in aerospace material research.

Accurate measurement of porosity is crucial for comprehensive performance evaluation of thermal barrier coatings (TBCs) on aero-engine blades. In this study, a novel data-driven predictive method based on terahertz time-domain spectroscopy (THz-TDS) was proposed. By processing and extracting features from terahertz signals, multivariate parameters were composed to characterize the porosity. Principal component analysis, which enabled effective representation of the complex signal information, was introduced to downscale the dimensionality of the time-domain data. Additionally, the average power spectral density of the frequency spectrum and the extreme points of the first-order derivative of the phase spectrum were extracted. These extracted parameters collectively form a comprehensive set of multivariate parameters that accurately characterize porosity. Subsequently, the multivariate parameters were used as inputs to construct an extreme learning machine (ELM) model optimized by the sparrow search algorithm (SSA) for predicting porosity. Based on the experimental results, it was evident that the predictive accuracy of SSA-ELM was significantly higher than the basic ELM. Furthermore, the robustness of the model was evaluated through K-fold cross-validation and the final model regression coefficient was 0.92, which indicates excellent predictive performance of the data-driven model. By introducing the use of THz-TDS and employing advanced signal processing techniques, the data-driven model provided a novel and effective solution for the rapid and accurate detection of porosity in TBCs. The findings of this study offer valuable references for researchers and practitioners in the field of TBCs inspection, opening up new avenues for improving the overall assessment and performance evaluation of these coatings.