Complex coupling representation in low-dimensional space for control-oriented energy-consuming industries modeling

In energy-consuming industries, developing soft-sensing models for key performance indicators is essential for improving production efficiency and reducing emissions. However,existing industrial soft-sensing models often struggle to achieve real-time tracking of state variable in system, making them hard to meet the requirements in simulation experiments based on control algorithms. To address this challenge, this paper proposes a novel coupled mapping framework based on element-wise multiplication (CMF-EWM), specifically designed for control-oriented modeling. First, we propose a feature selection method, CC-MI, that combines Pearson correlation coefficients and stationary-high frequency mutual information to capture both linear and nonlinear variable coupling. Subsequently, an end-to-end soft-sensing framework using element-wise multiplication is constructed to represent high-dimensional implicit relationships. The model is validated using designed linear systems, nonlinear systems, and an actual sintering process. Experimental results demonstrate that the proposed framework not only delivers exceptional performance in standalone soft-sensing tasks, but also effectively substitutes the controlled object in control algorithm simulation experiments.