The gradual growth of oxides inside thermal barrier coatings is a key factor leading to the degradation of thermal barrier coating performance until its failure, and accurate monitoring of the growth stress during this process is crucial to ensure the long-term stable operation of engines. In this study, terahertz time-domain spectroscopy was introduced as a new method to characterize the growth stress in thermal barrier coatings. By combining metallographic analysis and scanning electron microscope (SEM) observation techniques, the real microstructure of the oxide layer was obtained, and an accurate simulation model of the oxide growth was constructed on this basis. The elastic solutions of the thermally grown oxide layer of thermal insulation coatings were obtained by using the controlling equations in the rate-independent theoretical model, and the influence of the thickness of the thermally grown oxide (TGO) layer on the stress distribution was explored. Based on experimental data, multidimensional 3D numerical models of thermal barrier coatings with different TGO thicknesses were constructed, and the terahertz time-domain responses of oxide coatings with different thicknesses were simulated using the time-domain finite difference method to simulate the actual inspection scenarios. During the simulation process, white noise with signal-to-noise ratios of 10 dB to 20 dB was embedded to approximate the actual detection environment. After adding the noise, wavelet transform (WT) was used to reduce the noise in the data. The results showed that the wavelet transform had excellent noise reduction performance. For the problems due to the large data volume and small sample data after noise reduction, local linear embedding (LLE) and kernel-based extreme learning machine (KELM) were used, respectively, and the kernel function was optimized using the gray wolf optimization (GWO) algorithm to improve the model’s immunity to interference. Experimental validation showed that the proposed LLE-GWO-KELM hybrid model performed well in predicting the TGO growth stress of thermal insulation coatings. In this study, a novel, efficient, nondestructive, online, and high-precision measurement method for the growth in TGO stress of thermal barrier coatings was developed, which provides reliable technical support for evaluating the service life of thermal barrier coatings.

Modern turbine engines, when operating at high temperatures, can inhale calcium–magnesium–alumina–silicate particles (CaO-MgO-Al₂O₃-SiO₂, CMAS) from the air, which can erode the thermal barrier coatings on the blade surface, affecting the service life of the thermal barrier coatings and, in severe cases, leading to premature blade failure. Therefore, it is of great significance to effectively detect the thickness of CMAS deposited on the surface of the thermal barrier coatings at an early stage of CMAS erosion to ensure the high-temperature structural integrity of the hot-end components of aeroengines. Based on this, this study proposes a method combining terahertz time-domain spectroscopy technology and a hybrid machine learning algorithm for the quantitative detection of the thickness of CMAS on the surface of thermal barrier coatings. Firstly, the terahertz time-domain spectroscopy experimental data of CMAS were obtained using a terahertz experimental system, and the refractive index and absorption coefficient of CMAS in the terahertz frequency band were calculated. The FDTD method, Gaussian noise addition, and wavelet denoising processing were combined to further simulate the terahertz detection process of thermal barrier coatings with different thicknesses of CMAS attached to the surface under high-temperature conditions, and the terahertz simulation detection data were obtained. Principal component analysis (PCA) was used to reduce the dimensionality of the original experimental and simulation data, and a support vector machine (SVM) model integrating PCA and bacterial foraging optimization (BFO) algorithm was constructed. The research results show that the integrated model exhibits excellent performance in predicting the thickness of CMAS, with a correlation coefficient of 0.95, and the mean absolute error (MAE) and root mean square error (RMSE) are 0.13 μm and 0.46 μm, respectively. This study provides a new high-precision method for non-destructive detection of the thickness of CMAS on the surface of thermal barrier coatings, which has certain engineering application value for ensuring the service performance of thermal barrier coatings under harsh service conditions. Although the current method is based on simulated and experimental data under controlled conditions, it has the potential to be developed into an in situ monitoring strategy in the future, enabling real-time assessment of CMAS thickness on the coating surface during engine operation.

Accurate determination and prediction of pickling time are essential for preventing under-pickling and over-pickling and for improving the surface quality of hot-rolled high-strength steel. In this study, an electrochemical endpoint detection method combined with hybrid machine-learning models was developed to predict the pickling time of hot-rolled automotive high-strength steel. The variation in open-circuit potential during hydrochloric-acid pickling was monitored using an electrochemical workstation, and a potential-derivative near-zero method was proposed to determine the completion of oxide-scale removal. Based on repeated experiments under ten representative process conditions, a potential-derivative threshold of −5 × 10⁻⁴ V/s was adopted as the operational criterion for identifying the pickling endpoint. The effects of oxide-scale thickness, HCl concentration, pickling temperature, and accelerator concentration on pickling time were subsequently investigated. To describe the nonlinear relationship between these variables and pickling time, BP, GA-BP, ELM, and PSO-ELM regression models were established. The 48-observation dataset was evaluated using leakage-free grouped nested six-fold cross-validation repeated ten times, with all observations from the same strip group kept within the same fold. Among the investigated models, PSO-ELM exhibited the best prediction performance, achieving R² = 0.85 ± 0.05, MAE = 7.27 ± 1.01 s, MAPE = 0.14 ± 0.02, and RMSE = 9.65 ± 1.48 s. These quantities are regression-performance statistics and are not interpreted as the percentage prediction accuracy. The proposed endpoint criterion and regression framework provide a laboratory-scale basis for data-driven pickling-time estimation within the investigated material and process ranges, and broader industrial application requires validation using larger multi-grade production datasets.