DNV is a global assurance and risk management company, and our research division has been involved in co-simulation efforts in the Norwegian maritime industry for more than 10 years, since the inception of the Open Simulation Platform initiative. In this time, we have worked with several challenges inherent to co-simulation, and its application to model-based assurance and secure industry collaboration. For the past three years, we have had a central role in the SEACo (Safer, Easier, and more Accurate Co-simulations) research project, from which we will present some of the results that we find relevant to the FMI community.

The coupling problem in co-simulations encompasses not only the challenge of correctly connecting the different simulation models in a larger system but also dealing with the coupling errors that are introduced during the data exchange [2] [3]. In recent work, the concept of power bonds, introduced in bond graph modelling of physical systems, has been applied to co-simulations, resulting in several experimental methods for error quantification and control. In particular, the energy-conservation-based co-simulation method (ECCO) [1] is attractive for co-simulation as it relies only on the coupling signals as power bonds and assumes no additional constraints on the models, co-simulation solver, or FMI version in use. The impact of this approach is highest for couplings with large numerical contributions, where the simplistic discretization found in many co-simulation solvers leads to correspondingly large numerical errors. For stiff couplings, where we here refer to stiffness in the numerical sense, this is of particular interest as an error reducing step size control algorithm may be used to identify a suitable step size for integrating the system equations based on minimizing the observed coupling error for each timestep.

As a part of case-study in the SEACo project, the ECCO algorithm is applied to the connection between a deck crane and hull. This system is known to be poorly suited for co-simulation because of the large inertias inherent to this coupling. We look at the effect of applying ECCO to such a system, starting with a simplified configuration of two connected masses that can be actuated in one degree of freedom, before considering the same problem under multiple degrees of freedom.

In SEACo, we also consider assuring complex operations based on simulations. This requires building trust in the chosen simulation methods, the system models, as well as the system integration as a co-simulation. The value of assurance in such a context can only be realized with sufficiently efficient and practical methods, which are currently lacking. We will present from the assurance activities performed in the project, centered on a case study involving a marine lifting operation between two floating structures. We will also connect this work to our recommended practice for the assurance of simulation models, and connected methodology for model qualification, verification, and validation.

References [1] Sadjina, S., Kyllingstad, L. T., Skjong, S. and Pedersen, E. “Energy Conservation and Power Bonds in Co-Simulations: Non-Iterative Adaptive Step Size Control and Error Estimation”. Engineering with Computers 33(3), 607–620 (2017).

[2] Sadjina, S., Pedersen, E. “Energy conservation and coupling error reduction in non-iterative co-simulations”. Engineering with Computers 36, 1579–1587 (2020).

[3] Sadjina, S., Kyllingstad, L. T., Pedersen, E. and Skjong, S. “Energy Conservation and Co-simulation: Background and Challenges”. Proceedings of the 2024 International Conference on Bond Graph Modeling and Simulation (ICBGM’24). Simulation Series Vol 56(2). San Diego, CA, USA. July 1–3, 155–168 (2024).

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