Here, we study the flow of energy between coupled simulators in a co-simulation environment using the concept of power bonds. We introduce energy residuals which are a direct expression of the coupling errors and hence the accuracy of co-simulation results. We propose a novel EnergyConservation-based Co-Simulation method (ECCO) for adaptive macro step size control to improve accuracy and efficiency. In contrast to most other co-simulation algorithms, this method is noniterative and only requires knowledge of the current coupling data. Consequently, it allows for significant speed ups and the protection of sensitive information contained within simulator models. A quarter car model with linear and nonlinear damping serves as a co-simulation benchmark and verifies the capabilities of the energy residual concept: Reductions in the errors of up to 93 % are achieved at no additional computational cost.

Abstract-Both marine surface vehicles and underwater vehicles are often equipped with cranes, robotic manipulators or similar equipment. Much attention is given to modeling of both the dynamics of marine vehicles and the dynamics of manipulators, cranes and other equipment. However, less attention is given to the interconnected behaviour of the vehicle and the equipment, even though such equipment may have a considerable impact on the vehicle dynamic behaviour, and therefore risk, or conversely, the vehicle may have a considerable impact on the equipment dynamic behaviour. With main focus on ships equipped with cranes, this paper presents a framework for modeling the interconnected dynamics of rigid body systems, based on Lagrangian dynamics. The resulting equations of motion are implemented as a bond graph template to which any subsystem of interest, such as actuators, hydrodynamics, and controllers may be interfaced. An example on how this framework can be used in order to develop a high fidelity simulator of an offshore installation vessel with a heavy duty crane is presented. This work represents the first bond graph implementation of crane and vessel dynamics where the interconnections are modeled according to true physical rigid body principles without non-physical limitations such as diagonal mass-inertia matrix.

Abstract-In this work we demonstrate the use of co-simulation technology in the maritime industry through four relevant examples of applications based on the outcome of the knowledgebuilding project Virtual Prototyping of Maritime Systems and Operations (ViProMa). Increasing computational capabilities opens for extended use of simulators in the design processes. Even complex systems can now be analyzed at an early stage of the design process and even in real time using distributed simulation technology. We conduct an assessment of the need for co-simulation technology in the industry, present a short background in co-simulation technology, and provide a short summary of the major findings and deliverables in the ViProMa project (http://viproma.no). The four case studies presented in this work pinpoint different advantages of using co-simulations in the industry, such as combining different modeling and simulation tools, improving collaboration without revealing sensitive information by using black-box models, testing conceptual designs in a fast and consistent manner before initiating building processes, and verifying the interplay between hardware and software in the simulation environment in hardware in the loop (HIL) tests. All the case studies are simulated using the open source co-simulation software Coral developed in the project, using the Functional Mock-up Interface (FMI) standard, and the co-simulation software can be downloaded from the project's web site.

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