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

Abstract 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.