How knowledge discovery and embedded paradigm transform industrial process management: exploring pipeline hydraulic dynamic identification

An effective hydraulic parameter identification underpins process simulation for pipeline optimization. However, current studies often overlook the hydraulic spatiotemporal dynamics and multi-frequency variations of simulation parameters, limiting accuracy and interpretability. Here, by leveraging the exceptional dynamic representation capability of scientific machine learning for complex system, we propose a knowledge discovery and embedded framework to identify optimal friction coefficient and capture multi-frequency online variations of friction. The proposed framework identifies the optimal friction coefficient by discovering hydraulic spatiotemporal dynamics based on partial derivative differences within pipeline hydraulic state matrices. By embedding explicit hydraulic physical theory into forward propagation, a physics-constrained autoregressive neural network is developed as an efficient, interpretable surrogate model. Then, a self-coordination framework is designed for synchronous friction updating. The proposed framework can achieve precise online hydraulic simulation by performing knowledge-discovery identification and knowledge-embedded modeling. Results confirm accuracy and robustness of the proposed framework across varying pipeline and fluid properties. By integrating bottom-up knowledge discovery with top-down embedding, this approach forms a self-improving loop, offering strong potential for industrial pipeline digital twins and efficient decision-making.