Data fusion of spectral and acoustic signals in LIBS to improve the measurement accuracy of carbon emissions at varying gas temperatures

Laser-induced breakdown spectroscopy (LIBS) is a promising technique to monitor carbon emissions in post-combustion flue gas. However, its measurement accuracy is susceptible to variations in gas temperature. In this work, a mid-level data fusion method integrating spectral and acoustic signals generated by laser-induced plasmas (LIPs) was proposed to improve the measurement accuracy. This method utilizes the high sensitivity of acoustic signals to variations in gas temperature, enabling a correction of temperature effects. The acoustic features were extracted from both the time-domain waveforms and frequency spectra, while the spectral features were selected using a SelectKBest method. These features were fused into a new array, on whose basis multivariate regression models including Partial Least Squares (PLS), Support Vector Machines (SVM), and Random Forest (RF) were trained. Data fusion significantly improved the predictive precision and trueness of SVM and RF models, with the RF model achieving the best performance: a coefficient of determination (R²) of 0.9941, a root-mean-square error (RMSE) of 0.4864, a mean absolute error (MAE) of 0.2587, and a mean absolute deviation (MAD) of 0.0980. Shapley additive explanation (SHAP) analysis revealed that in the RF model, the acoustic features that exhibited higher temperature sensitivity could be more frequently selected in the training process and thus had greater impacts on model outputs, which can better correct for the gas temperature effect. Furthermore, the potential of this method in industrial applications was demonstrated in an unsteady flow.