A deposition–removal-informed hybrid temporal model for online fouling estimation of industrial heat exchangers under parameter variability and nonstationarity

Fouling-induced efficiency degradation in industrial heat exchangers poses a critical challenge to energy sustainability in process industries. This study proposes a physics-informed hybrid temporal model (PI-HTM) for online estimation of fouling resistance. The proposed model combines a physics-based deposition–removal mechanism (DRM) to represent fouling dynamics with a deep temporal neural network. The network architecture integrates temporal convolutional networks (TCN) and bidirectional gated recurrent units (BiGRU) to effectively capture multi-scale temporal dependencies. An adaptive online learning framework is introduced to improve the model’s adaptability to variations in intrinsic fouling parameters, which are driven by fluctuations in fluid composition and operating conditions. This approach mitigates the limitations of conventional methods in handling such dynamic environments. Model parameters are updated in real time using the state transition algorithm (STA) based on recent operational trajectories. Additionally, fouling discontinuities induced by cleaning actions are incorporated into the improved DRM, enabling accurate tracking of abrupt process nonstationarities. Furthermore, a monotonicity constraint is incorporated into the physics-informed component to embed prior knowledge of the progressive nature of fouling accumulation. The proposed method is evaluated on three real-world fouling datasets, encompassing both crude oil and crystalline fouling. With only 15% of the training data, it achieves $R^2$ values of 0.959, 0.989, and 0.957, demonstrating high predictive accuracy, strong generalization capability, and adherence to the underlying physical mechanisms.