Exploration of the Optimal Model for Raman Spectral Characterization of Bituminous Coal Structure: Based on Multipeak Function Optimization and Statistical Information Validation

Abstract

Raman spectroscopy, as a powerful analytical technique, holds significant applications in the characterization of coal structure. However, there is currently no consensus on the selection of peak-fitting models for Raman spectroscopy. Specifically, there is a lack of unified standards regarding the choice of mathematical functions and the determination of the number of subpeaks. This leads to inconsistencies in analytical results and may lead to overfitting, thereby undermining the physical significance of the results. In this study, two bituminous coal samples with different metamorphic grades were selected to compare the peak-fitting effects of four mathematical models─GaussAmp function, Gaussian-LorenCross (GLC) function, Lorentz function, and Voigt function─under two to five subpeak models. Comprehensive evaluation was conducted using statistical indicators such as the nested model F-test, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), along with the physical reasonableness of the fitting parameters. The results indicate that increasing the number of subpeaks significantly improves the statistical goodness of fit. However, the five-peak model produces abnormal parameters across all fitting functions, indicating overfitting. In contrast, the GLC four-peak model achieves a goodness-of-fit R2 greater than 0.999, with a residual sum of squares (RSS) as low as 0.089. All fitting parameters fall within the typical range for bituminous coal, and its shape factor s further confirms mixed line-shape characteristics that cannot be described by pure Gaussian or pure Lorentzian functions. The GLC four-peak model represents the optimal method for Raman spectroscopy analysis of the two bituminous coal samples in this study. Additionally, this study proposes an analytical framework that combines statistical rigor with physical interpretability. Future work will extend to a broader range of coal samples with varying metamorphic grades.