Modeling and simulation techniques are today extensively used both in industry and science. Parts of larger systems are, however, typically modeled and simulated by different techniques, tools, and algorithms. In addition, experts from different disciplines use various modeling and simulation techniques. Both these facts make it difficult to study coupled heterogeneous systems. Co-simulation is an emerging enabling technique, where global simulation of a coupled system can be achieved by composing the simulations of its parts. Due to its potential and interdisciplinary nature, co-simulation is being studied in different disciplines but with limited sharing of findings. In this survey, we study and survey the state-of-the-art techniques for co-simulation, with the goal of enhancing future research and highlighting the main challenges. To study this broad topic, we start by focusing on discrete-event-based co-simulation, followed by continuous-time-based co-simulation. Finally, we explore the interactions between these two paradigms, in hybrid co-simulation. To survey the current techniques, tools, and research challenges, we systematically classify recently published research literature on co-simulation, and summarize it into a taxonomy. As a result, we identify the need for finding generic approaches for modular, stable, and accurate coupling of simulation units, as well as expressing the adaptations required to ensure that the coupling is correct.
Model-based design can shorten the development time of complex systems by the use of simulation techniques. However, it can be hard to simulate the system as a whole if it is developed in a concurrent fashion by multiple and specialized teams. Co-simulation, with the support of the Functional Mockup Interface (FMI) Standard, is proposed as a way to promote tool interoperability while protecting the intellectual property of subsystems. The standard allows uniform communication between subsystem simulators, but does not state how the inputs and outputs should be interpreted, nor how the subsystems should interact correctly. Semantic adaptations can be quickly made to correct the interactions with subsystem simulators that were produced with different assumptions, and avoid changing those subsystems, their simulators, or the orchestration algorithm that computes the co-simulation. In this work, we explore how to describe common adaptations and what their meaning is in the context of FMI co-simulation. The result is a sound language that enables the implementation of adaptations with minimal effort. A distinct feature is that it describes adaptations for groups of interconnected subsystem simulators in the same way as for a single simulator, and the implementation is itself a simulator, thanks to a sound definition of hierarchical co-simulation. This work paves the way for research into the correct combination and interfacing of different adaptations.
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Engineering modern, hybrid systems is becoming increasingly difficult due to the heterogeneity between different subsystems. Modelling and simulation techniques have traditionally been used to tackle complexity, but with increasing heterogeneity of the subsystems, it becomes impossible to find appropriate modelling languages and tools to specify and analyse the system as a whole. Co-simulation is a technique to combine multiple models and their simulators in order to analyse the behaviour of the whole system over time. Past research, however, has shown that the naïve combination of simulators can easily lead to incorrect simulation results, especially when co-simulating hybrid systems. This paper shows (i) how co-simulation of a family of hybrid systems can fail to reproduce the order of events that should have occurred (event ordering); (ii) how to prove that a co-simulation algorithm is correct (w.r.t. event ordering), and if it is incorrect, how to obtain a counterexample showing how the co-simulation fails; and (iii) how to correct an incorrect co-simulation algorithm. We apply the above method to two well known co-simulation algorithms used with the FMI Standard, and we show that one of them is incorrect for the family of hybrid systems under study, under the restrictions of the standard. The conclusion is that either the standard needs to be revised, or one of the algorithms should be avoided.
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