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.

This paper briefly reviews the engineering development of Modelica-based hydraulic system modeling. On this basis, it reconsiders the issue of reasonable decomposition in component-based hydraulic modeling and discusses the methodological relevance of Xu's method for the development of Modelica hydraulic model libraries. Finegrained component decomposition facilitates rapid assembly and reuse, especially for users without extensive hydraulic modeling expertise. However, excessive subdivision may also introduce duplicated pressure states, hidden volumes, artificial fast time constants, increased numerical stiffness, and ambiguous physical semantics. Through order-of-magnitude examples involving pilotoperated relief valves, pressure compensators in multiway valves, short manifold passages, hydraulic cylinder chambers, and accumulator groups, the paper illustrates that the appropriate component boundary depends on the modeling objective, the dominant physical mechanism, the available parameters, and the quantities to be validated.