Multi-Scale Analysis of Terahertz Time-Domain Spectroscopy for Inversion of Thermal Growth Oxide Thickness in Thermal Barrier Coatings

To address the inverse problem of thermal growth oxide (TGO) thickness in thermal barrier coatings (TBCs), a novel multi-scale analysis (MSA) method based on terahertz time-domain spectroscopy (THz-TDS) is introduced. The proposed method involves a MSA technique based on four wavelet basis functions (db4, sym3, haar, coif3). Informative feature parameters characterizing the TGO thickness were extracted by performing continuous wavelet transform (CWT) and max-pooling operations on representative wavelet coefficients. Subsequently, multi-linear regression and machine learning regression models were employed to predict and assess the wavelet feature parameters. Experimental results revealed a discernible trend in the wavelet feature parameters obtained through CWT and max-pooling in the MSA, wherein the visual representation of TGO thickness initially increases and then gradually decreases. Significant variations in these feature parameters with changes in both thickness and scale enabled the effective inversion of TGO thickness. Building upon this, multi-linear regression and machine learning regression prediction were performed using multi-scale data based on four wavelet basis functions. Partial-scale data were selected for multi-linear regression, while full-scale data were selected for machine learning regression. Both methods demonstrated high accuracy prediction performance. In particular, the haar wavelet basis function exhibited excellent predictive performance, as evidenced by regression coefficients of 0.9763 and 0.9840, further confirming the validity of MSA. Hence, this study effectively presents a feasible method for the inversion problem of TGO thickness, and the analysis confirms the promising application potential of terahertz time-domain spectroscopy’s multi-scale analysis in the field of TBCs evaluation. These findings provide valuable insights for further reference.