Macro-step-size selection and monitoring of the coupling error for weak coupled subsystems in the frequency-domain

Abstract

A rather general approach to establish a multiphysic simulation is referred to as non-iterative co-simulation or weak coupled simulation. The involved subsystems are coupled in a weak sense and thus stepwise extrapolation of the coupling signals is required. Extrapolation is associated with an error which may influence the dynamical behavior of the coupled system. This coupling error depends significantly on the coupling step-size, i.e. the macro-step-size, and is one of the most critical parameter of a noniterative co-simulation. In practice, appropriate macro-step-sizes are determined by some numerical tests or chosen according to the experience of domain-specific engineers. But who assesses the results of a non-iterative co-simulation? Comparison between reference and co-simulation results in the time-domain is often practiced in case studies using complex subsystems to validate co-simulation performance and accuracy of the achieved results. But this approach is counter-productive and mostly not applicable in practice. In this work we consider the coupling process as single source of distortion and analyse it in the frequency-domain. As a consequence, a relation between the macro-step-size and the coupling signals is available which leads to a ’rule-of-thumb’ for a adequate macro-stepsize selection. In addition, the gained insight into the coupling process itself enables new possibilities to monitor the coupling error leading to the ability to assess the results of a weak coupled simulation. The proposed methodologies are examined using a complex mechatronic system describing a vehicle (multi-body system, MBS), which is controlled via an anti-lock braking system (ABS) during different scenarios.