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Modeling and control of industrial processes are essential for product quality, energy efficiency, and operational stability. With growing sensor availability and computational power, machine learning (ML) has emerged as a powerful tool. However, purely data-driven models often lack interpretability and robustness, especially under varying conditions. A key example is the wire section of a tissue machine, where basis weight is determined but not directly measurable in real time. To address this challenge, we propose a hybrid modeling framework that integrates a first-principles model (FPM) with a one-dimensional convolutional neural network (Conv1D) in a parallel structure. A secondary gated recurrent unit (GRU) network dynamically adjusts the weighting between the two predictions. Evaluated on seven months of industrial data, the hybrid model achieved a root mean square error (RMSE) of 2.12 g/m 2 , outperforming standalone FPM (4.72 g/m 2 ) and ML (2.68 g/m 2 ) models. Designed for real-time deployment, the approach provides a scalable soft-sensor solution, enabling earlier intervention and more adaptive operation in tissue manufacturing.

Hybrid soft sensor modeling for the wire section in tissue manufacturing: integrating first-principles and machine learning models