Transformer-based deep learning models for quantification of La, Ce, and Nd in rare earth ores using laser-induced...

Rare earth elements like lanthanum (La), cerium (Ce), and neodymium (Nd) are vital for high-tech industries, and their real-time quantitative analysis is crucial for refining rare earth ores. Laser induced breakdown spectroscopy (LIBS) is an effective tool for such analysis but faces challenges due to the matrix effects and spectral overlaps. This paper proposes a LIBS quantitative analysis model based on the iTransformer-Bidirectional long short-term memory (iTBi) deep learning algorithm, and further integrates the iTBi model with the random forest (RF) algorithm to form the iTBi-RF-LIBS ensemble model. These methods uses 35 samples, with concentration ranges for La, Ce, and Nd from 0wt% to 1.924wt%, 0wt% to 2.917wt%, and 0wt% to 1.492wt%, respectively. Compared to univariate analysis, BiLSTM, RF, and backpropagation neural network models, the iTBi-LIBS and iTBi-RF-LIBS models show significant advantages. The iTBi-LIBS model achieves calibration coefficients (R²) of 0.989, 0.983, and 0.994 for La, Ce, and Nd, respectively, with mean absolute prediction errors (MAEP) of 0.075wt%, 0.167wt%, and 0.067wt%, and root mean square prediction errors (RMSEP) of 0.095wt%, 0.225wt%, and 0.083wt%, respectively. The R² values for the iTBi-RF-LIBS model are improved to 0.993, 0.992, and 0.996 for La, Ce, and Nd, respectively, with MAEP reduced to 0.059wt%, 0.135wt%, and 0.053wt%, and RMSEP reduced to 0.075wt%, 0.184wt%, and 0.069wt%, respectively. These results indicate that both the iTBi-LIBS model and the iTBi-RF-LIBS ensemble model effectively reduce matrix effects and spectral overlap interferences, providing a feasible technical pathway for the precise determination of La, Ce, and Nd element concentrations in rare earth ores.