Dynamic soft sensor model based on combination of GRU and TCN-Transformer for chemical process application

Soft sensor technology has been widely applied in key areas of industrial process monitoring. To address challenges such as strong nonlinearity, complex temporal dependencies, and dynamic system behavior commonly encountered in industrial soft sensor data modeling, we propose a hybrid dynamic modeling method that integrates gated recurrent unit (GRU) with temporal convolutional network-Transformer (TCN-Transformer) architecture. TCN-Transformer module is employed to extract multi-scale temporal patterns and capture long-range dependencies among auxiliary variables, while GRU network processes the historical information of target variables through its gated memory mechanism. The complementary feature representations from both components are summed before being passed into a fully connected layer for prediction. To validate the effectiveness of GRU-TCN-Transformer framework, comprehensive case studies were conducted on two typical industrial processes: the prediction of butane (C₄) concentration in a debutanizer column and the estimation of hydrogen sulfide (H₂S) and sulfur dioxide (SO₂) concentrations in a sulfur recovery unit (SRU). Experimental results demonstrate that the proposed hybrid dynamic modeling method significantly outperforms traditional dynamic modeling methods—convolutional neural network (CNN), long short-term memory (LSTM), and TCN—across multiple evaluation metrics. Specifically, for C₄ concentration estimation, the proposed method reduced root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) by 55.0%, 51.0% and 50.1%, respectively, and improved R² by 2.3% compared to the best-performing TCN-Transformer model. For H₂S estimation, it achieved reductions of 30%, 30.61% and 29.23% in RMSE, MAE, and MAPE, respectively, while increasing R² by 11.09% over the best LSTM-TCN-Transformer model. For SO₂ estimation, the proposed model reduced RMSE, MAE, and MAPE by 7.91%, 9.09% and 9.64%, respectively, with a 0.87% increase in R². These comparative results further confirm the improvements in prediction accuracy, indicating that the proposed model is capable of meeting the stringent requirements of industrial applications.