Martin Benedikt

Modelling and analysis of the non-iterative coupling process for co-simulation

Concerning non-iterative co-simulation, stepwise extrapolation of coupling signals is required to solve an overall system of interconnected subsystems. Each extrapolation is some kind of estimation and is directly associated with an estimation error. The introduced disturbance depends significantly on the macro-step size, i.e. the coupling step size, and influences the entire system behaviour. In addition, for synchronization purposes, sampling of the coupling signals can cause aliasing. Instead of analysing the coupling effects in the time domain, as it is commonly practised, we concentrate on a model-based approach to gain more insight into the coupling process. In this work, we consider commonly used polynomial extrapolation techniques and analyse them in the frequency domain. Based on this system-oriented point of view of the coupling process, a relation between the coupling signals and the macro-step size is available. In accordance to the dynamics of the interconnected subsystems, the model-based relation is used to select the most critical parameter, i.e. the macro-step size. Besides a ‘rule of thumb’ for meaningful step-size selection, a co-simulation benchmark example describing a two degree of freedom (2-DOF) mechanical system is used to demonstrate the advantages of modelling and the efficiency of the proposed method.

An Adaptive Coupling Methodology for Fast Time-Domain Distributed Heterogeneous Co-Simulation

An adaptive Coupling Methodology for Fast Time-Domain distributed heterogeneous CoSimulation In the automotive industry well-established different simulation tools targeting different needs are used to mirror the physical behavior of domain specific components. To estimate the overall system behavior coupling of these components is necessary. As systems become more complex, simulation time increases rapidly by using traditional coupling approaches. Reducing simulation time by still maintaining accuracy is a challenging task. Thus, a coupling methodology for co-simulation using adaptive macro step size control is proposed. Convergence considerations of the used algorithms and scheduling of domain specific components are also addressed. Finally, the proposed adaptive coupling methodology is examined by means of a cross-domain co-simulation example describing a hybrid electric vehicle. Considerable advantages in terms of simulation time reduction are presented and the trade-off between simulation time and accuracy is depicted.

Guidelines for the Application of a Coupling Method for Non-iterative Co-simulation

Modular simulation requires efficient coupling of the involved subsystems. Subsystems are independently solved and synchronized at coupling time instants. By the commonly used non-iterative coupling approach the extrapolation of some coupling quantities is necessary because of bidirectional dependencies between subsystems. Thus, a coupling step-size dependent coupling error is introduced. Required sampling of the coupling signals may lead to aliasing effects and unintentional discontinuities at coupling time instants occur. A recently developed coupling error compensation approach seems to be able to solve the typical problems concerning non-iterative co-simulation. However, for adequate usage of the available functionalities proper settings of the proposed coupling scheme are mandatory. In this work, the basic nearly energy-preserving coupling approach is explained and significant extensions are proposed. Especially, the resulting enhanced coupling performance enables smoothing of the coupling signals without degradation of the overall system behavior. The resulting effects as well as the specific adjustments are discussed, which leads to supporting parameterization guidelines.