Permeability Index Modeling with Multiscale Time Delay Characteristics Excavation in Blast Furnace Ironmaking Process

The permeability index (PI) is a key comprehensive indicator that reflects the smoothness of internal gas flow in pig iron production via blast furnace. An accurate prediction for it is essential for forecasting abnormal furnace conditions and preventing potential faults. However, developing an early prediction model for PI has been neglected in existing research, and it faces massive challenges due to the strong nonlinearity, undesirable nonstationarity, and significant multiscale time delays inherent in the blast furnace data. To bridge this gap, a new modeling paradigm for PI is proposed to explore the inherent time delay characteristics among multiple variables. First, the data are progressively decomposed into multiple components using wavelet decomposition and spike separation. Then, a novel delay extraction method based on wavelet coherence analysis is developed to obtain accurate multiscale time delay knowledge. Furthermore, the integration of Orthonormal Subspace Analysis (OSA) and wavelet neural network (WNN) achieves comprehensive modeling across time and frequency domains, incorporating global and local features. A Gauss–Markov-based fusion framework is also utilized to reduce the output error variance, ultimately enabling the early prediction of PI. Mechanism analysis and a practical case study on blast furnace production verify the effectiveness of the proposed target-oriented prediction framework.