Physics-Informed Reduced-Order Digital Twin for Edge Deployment: Online Tracking of Heat Transfer Dynamics Under Variable Loads and Strong Noise

Large-scale shell-and-tube heat exchangers operate for extended periods, critically affecting the energy efficiency and safety of hydrogen production processes. However, online condition monitoring on industrial distributed control systems (DCSs) is often hindered by an engineering trilemma: high-fidelity mechanistic models incur prohibitive computational latency; static constant-parameter models suffer from severe systematic bias; and purely data-driven models risk yielding non-physical predictions under out-of-distribution scenarios such as variable-load operations. To address these challenges, this study proposes a physics-guided adaptive digital twin tailored to high-noise industrial DCS environments. Energy conservation and the counterflow logarithmic mean temperature difference (LMTD) relation are embedded as hard constraints in a lightweight reduced-order model (ROM). On this basis, a closed-loop online adaptation strategy—comprising physical-bound checking, window-wise inverse estimation, anomaly rollback, and exponentially weighted moving average (EWMA) smoothing—treats the overall heat transfer coefficient U as an equivalent time-varying parameter that co-evolves with operating regimes. Validation on real plant DCS data under variable-load conditions shows that, compared with a conservative fixed-U baseline, the proposed online update eliminates massive systematic overestimations (up to tens of degrees Celsius) and suppresses inversion oscillations caused by small cold-side temperature differences and sensor noise. Relative to an overfitting-prone data-driven baseline, the framework retains millisecond-level inference latency while enforcing thermodynamic feasibility, thereby establishing a dynamic healthy baseline. This baseline provides a proxy indicator for distinguishing load-induced reversible variations from potential degradation-related residual trends.