Supervised deep slow feature extraction enhanced time–frequency fusion network for industrial quality prediction

Accurate prediction of difficult-to-measure quality variables is essential for monitoring and control of complex industrial processes. Existing deep models do not explicitly distinguish persistent process-driving dynamics from transient fluctuations and measurement noise. Moreover, time-domain models may fail to characterize localized periodic and abrupt variations in nonstationary process data. To address these limitations, we propose a supervised deep slow feature extraction (SDSFE) enhanced time–frequency fusion framework for industrial quality prediction. A time–frequency fusion network, termed TF2-Net, preserves the frame order of the short-time Fourier transform (STFT) representation, aligns the resulting spectral sequence with the bidirectional gated recurrent unit (BiGRU) temporal sequence, and fuses the two domains through cross-domain attention. The fused representation is then projected into a task-supervised slow-feature space, where temporal slowness, unit-variance, and decorrelation constraints are jointly optimized with the quality-prediction loss. Consequently, the learned slow representation is directly adapted to the prediction target. Experiments on a numerical example, an industrial froth-flotation benchmark, and a real-world alumina digestion process (ALDP) demonstrate the competitive predictive accuracy and robustness of the proposed framework.