Raman Spectroscopy–Machine Learning Integration: Advancing High-Precision Quantitative Analysis of Na ₂ SO ₄ and CaCO ₃ in Simulated Mural Surface White Pigments

Numerous precious ancient murals have seriously degraded due to long-term environmental impact and human damage. Prolonged environmental exposure renders them susceptible to salt-induced deterioration (exfoliation and cracking), damaging their physical integrity and artistic significance. In this study, Raman spectroscopy combined with partial least squares (PLS) was proposed for quantitatively analyzing the concentrations of sodium sulfate (Na₂SO₄) and calcium carbonate (CaCO₃) of the surface white pigment of simulated mural samples. According to the salt concentration range of authentic murals, the particle size and gelatin concentration of pigments were optimized; 30 simulated mural samples were prepared; and Raman spectra were collected. Subsequently, the PLS calibration model was optimized by different spectral pretreatment methods and variable selection methods, and the predictive performance was evaluated using multiple statistical metrics, such as high coefficient of determination (<i>R</i>²), low values for root-mean-square error (RMSE), mean relative error (MRE), relative standard deviation (RSD), and satisfactory residual prediction deviation (RPD). The results demonstrated that two PLS calibration models of MSC-biPLS-PLS (<i>R</i>_p² = 0.9635, RMSE_p = 0.0024, MRE_p = 0.0709, RSD = 4.14%, and RPD = 8.6) and MSC-siPLS-PLS (<i>R</i>_p² = 0.9891, RMSE_p = 0.0125, MRE_p = 0.0449, RSD = 3.59%, and RPD = 10.9) showed superior predictive performance for the quantitative analysis of Na₂SO₄ and CaCO₃, respectively. Additionally, the recovery of the two salts in a random sample was 106.7% and 111.3%, respectively. It enhances the efficiency and accuracy of mural microregion quantitative analysis and provides innovative technical support for cultural heritage preservation.