Cross-instrument coal quality spectral analysis via a PDS-assisted fine-tuning calibration transfer method

Device-related variations in X-ray fluorescence (XRF) instruments often lead to spectral inconsistencies, which significantly degrade the accuracy and generalization of quantitative coal quality models, particularly for ash content prediction. Conventional calibration transfer methods or single-stage transfer learning approaches struggle to effectively handle large inter-instrument spectral discrepancies, especially under limited sample conditions.

In this study, a two-stage transfer learning framework integrating piecewise direct standardization (PDS) with feature fine-tuning (FT), termed PDS-FT, is proposed to enhance cross-instrument ash content prediction. Using 140 coal samples measured on two different XRF instruments, five approaches-PDS, FT, Domain-Adversarial Neural Network (DANN), PDS-DANN, and PDS-FT-were systematically evaluated. The results show that standalone PDS and FT exhibit limited test-set performance, achieving average R² values of 0.33 and 0.51 with root mean square error (RMSE) of 1.86% and 1.55%, respectively. DANN improves cross-domain prediction performance (R² = 0.74, RMSE = 1.36%) but is constrained by training instability. The hybrid PDS-DANN method further enhances performance, reaching R² = 0.78 and RMSE = 1.0%. In contrast, the proposed PDS-FT framework achieves the best performance, with a test-set R² of 0.95 and a substantially reduced RMSE of 0.59%, demonstrating superior accuracy, robustness, and cross-device generalization capability.

By combining spectral-level physical correction with feature-level model adaptation, the proposed PDS-FT framework establishes a hierarchical domain alignment mechanism that progressively mitigates inter-instrument discrepancies. This dual-stage strategy significantly enhances the transferability and reliability of XRF-based ash content models, providing a practical and generalizable solution for coal quality analysis across heterogeneous XRF instruments in industrial applications.