A novel prediction model integrating physical information and data augmentation for fouling deposition in enhanced tubes

In traditional data center cooling systems, fouling deposition on the inner surfaces of enhanced tubes severely affects heat exchange efficiency and operational safety, leading to significant economic losses. Due to the lack of long-term fouling test data, most of the existing fouling prediction models are constant fouling factors or semi-empirical formulas established based on accelerated particulate fouling data. These models have low computational accuracy, poor generalizability, and certain limitations in engineering application constraints. To address these challenges, this study develops and validates a high-precision prediction model for combined fouling growth based on data augmentation using long-term fouling test data. First, to overcome the challenge of insufficient data, a physics-informed Wasserstein generative adversarial network with gradient penalty model is constructed in this study. The fouling thermal resistance database is expanded based on the generative adversarial network (GAN), utilizing the generated data as training sets. Simultaneously, the physical information is combined with the traditional GAN to establish a joint loss function containing physical constraints and improve the quality of the generated data. Second, a physics-informed-convolutional neural network-long short-term memory (LSTM)-Transformer model is introduced in this paper to improve prediction accuracy. To comprehensively extract the global feature information and the nonlinear relationship between each feature and the fouling thermal resistance, the Transformer is integrated with LSTM, creating a feature fusion fouling growth prediction model. Finally, SHapley Additive exPlanations were employed for interpretability analysis of the prediction model, with validation conducted using the long-term fouling test data from ASHRAE RP-1677. The results demonstrate that, compared to the baseline without data augmentation under various operating conditions, the average goodness-of-fit (R2) of the prediction model increased from −0.193 to 0.783, while the average prediction final bias decreased from 23.87% to 2.8%, confirming the superior performance of the proposed methodology.