FGOSNET+: A Frequency-Guided Online Sequential Learning Framework for Robust Prediction of Nonstationary Gas Utilization Ratio

Accurate prediction of the gas utilization ratio (GUR) is critical for ensuring the safe, stable, and efficient operation of the ironmaking process in a blast furnace. However, the complex, dynamic, and nonstationary nature of GUR severely undermines the reliability of time-domain features, increases the risk of spurious regression, and reduces the efficiency of current deep-learning models. To address these challenges, this article presents a frequency-guided online sequential learning framework. The proposed framework incorporates a dual-layer feature extraction strategy designed to capture the underlying variation trends of GUR, which integrates multiscale dilated convolution and supervised principal component analysis to extract cross-frequency and multiresolution interactions in the frequency domain and long-term temporal dependencies in the time domain, respectively. Subsequently, a new online sequential kernel-based random vector functional-link network learning architecture is presented, which utilizes the extracted frequency-domain features as privileged information during training, mitigating time-domain feature limitations and improving model generalization. Furthermore, an adaptive forgetting factor adaptively adjusts the sensitivity to dynamic conditions, while ensuring computational efficiency. Experimental outcomes validate the effectiveness of the proposed model in GUR prediction across various forecasting horizons.