An optimized partial rollback co-simulation approach for heterogeneous FMUs

Cyber-physical systems (CPS) are generally defined as systems with integrated physical components and computational components. To simulate heterogeneous components of CPS, the Functional Mock-up Interface (FMI) standard provides the co-simulation technology to generate simulation traces. It play significant roles in analyzing and verifying behaviors of CPS. However, the FMI-based co-simulation algorithm called Master Algorithm with Step Revision (SRMA) is inefficient in some common scenarios. To improve the efficiency of SRMA, we propose an optimized Partial Rollback Co-simulation approach, which decreases the number of the rollback operations effectively. The novelty of our approach has two aspects. First, the Key FMUs Extractor and the Input/Output dependencies classification rules are proposed. They help to determine the minimum set of FMUs which are used to rollback for correcting the simulation error. Second, an optimized Master Algorithm with Partial Step Revision (PSRMA) is also proposed. To implement our approach, we also propose an extension for the FMI standard to check whether an FMU implements the function of the threshold crossing detector. The formal definition of the Zero Crossing Detector (ZCD) is presented to guide the construction of ZCD FMUs and evaluate the simulation error of the whole system. To illustrate the feasibility of our approach, two case studies are also discussed.