Theoretical Reconstruction of Xu's Digital Twin Modeling Method and Its Integration with the Modelica Environment

Abstract

Digital twin technology is central to Cyber-Physical Systems, yet purely data-driven approaches demand high computational resources and expensive validation. Xu's Modular Modeling Method for Performance Parameters of Large-scale Hydraulic Systems ("Xu's Modeling Method")—a physical modeling technology from the 1980s implemented in the PERSIM software—shares structural similarities with Modelica, though their algorithms differ. We extend Xu's method to mechanismbased digital twin modeling, creating a grey-box approach that combines physical models with data. Using Modelica, we implement XAP (Xu's Algorithm Package), unifying simulation and digital twin modeling. A key contribution is an inverse operation framework that recovers physical fault indicators from measured step-response data. Numerical validation shows that identifiable fault parameters—single, dual, and crosschamber multi-parameter combinations—are recovered with errors below 1%, and the identifiability limit of joint estimation within a chamber pair is characterized. The resulting grey-box method offers interpretable, efficient digital twin modeling for motion control systems.