A Temporal Convolutional-Based Kolmogorov-Arnold Network for Industrial Soft Sensor Modeling

Multitimescale characteristics, nonlinearity, and dynamic features exist extensively in modern industrial processes, impairing the predictive performance and accuracy of soft sensor modeling for primary variables. To address this challenge, a multitimescale neural network-based soft sensor model, consisting of two modules, is designed for complex industrial processes. The designed temporal convolutional module, which integrates two attention mechanisms with multiple parallel temporal convolutional layers using dilated causal convolution, efficiently enhances feature extraction at different timescales. Then, bidirectional long short-term memory (BiLSTM) networks are developed to capture time series features from the designed temporal convolutional module. The extracted feature variables are fed into the Kolmogorov–Arnold network (KAN) using B-spline functions, effectively addressing nonlinear data characteristics and improving prediction performance. The superiority of the designed soft sensor model is validated through practical applications in wastewater treatment process and flue gas desulfurization, demonstrating promising potential for real-world applications.