Calorific value measurement of large-particle coal using NIRS–XRF fusion spectroscopy and nonlinear residual correction: a PLS–AE–RR model framework

This study addresses the on-site challenge posed by large-particle (0-6 mm) coal samples, which are difficult to mill and exhibit pronounced matrix effects and strong nonlinearities that degrade the accuracy of online calorific-value prediction. We propose an NIRS-XRF fused-spectra framework-PLS-AE-RR (Partial Least Squares - Autoencoder - Ridge Regression)-for coal-quality prediction. The principal novelty of the framework is a three-tier hybrid architecture combining a linear baseline (PLS), nonlinear feature extraction (AE), and residual correction (RR). By confining complex nonlinear modeling to the residual domain of the linear model, employing an autoencoder to learn deep latent features, and applying ridge regression for precise residual correction, the approach substantially enhances robustness while preserving interpretability and facilitating engineering deployment. Using a custom NIRS-XRF dual-spectroscopy system, the method was validated on 153 mixed-particle coal samples collected from two power plants. Results demonstrate a marked improvement in calorific-value prediction for coarse coal: the PLS-AE-RR model achieved test-set R² values of 0.974 and 0.938 for lignite and bituminous coal, respectively, with MAE values of 0.233 MJ kg^-1 and 0.216 MJ kg^-1. PLS-AE-RR also consistently outperformed alternative nonlinear correction schemes (PLS-AE-RF and PLS-AE-SVR), yielding the lowest MAE and RMSE and thereby underscoring the generalization advantage of ridge regression for residual fitting. The proposed method offers coal-fired power plants a high-accuracy, high-reliability online tool for raw-coal calorific-value measurement that obviates labor-intensive sample pretreatment and supports refined fuel management and coal-blending optimization.