A Pre-Step Stabilization Method for Non-Iterative Co-Simulation and Effects of Interface-Jacobians Identification

Co-Simulation of complex subsystems can lead to stiff problems, where, especially for applied explicit numerical schemes, small communication step sizes are mandatory to obtain stable and accurate results. Due to the utilization of subsystem information, i.e. interface-jacobians or partial derivatives, it is possible to increase the stability and accuracy of the overall co-simulation. The herein proposed co-simulation coupling method therefore performs three major steps: a global approximation of the monolithic solution utilizing an introduced Error Differential Equation; a global model-based extrapolation over the next communication step and, finally, a local pre-step input optimization is carried out for all subsystems. This method is validated along a two degree-of-freedom oscillator benchmark example. As for realistic use cases it is difficult to access interface-jacobians, system identification methods are applied for approximation. Associated interface-jacobian approximation errors are investigated with respect to the performance and especially the stability of the overall co-simulation.