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Co-simulation: State of the art

Cláudio Gomes, Casper Thule, David Broman, Peter Gorm Larsen, Hans Vangheluwe

arXiv:1702.00686v1eess.SY

TL;DR

Co-simulation addresses the need to integrate independently developed models from different disciplines while preserving specialized tools and limited model disclosure. This survey bridges heterogeneous research communities by reviewing approaches, applications, challenges, and a five-year taxonomy, identifying modularity, stability, accuracy, and correct coupling adaptations as central research needs.

  • Problem

    No existing survey covered the heterogeneous communities studying co-simulation, limiting sharing of techniques and findings across disciplines.

  • Method

    The paper presents a survey and taxonomy that bridges, relates, and classifies co-simulation approaches and the state of the art.

  • Results

    The review identifies a lack of approaches that combine discrete-event and continuous-time bases while leveraging simulation-unit capabilities.

  • Takeaways & Limitations

    The main research needs are generic coupling approaches that are modular, stable, and accurate, plus explicit adaptations that ensure coupling correctness.

Abstract

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It is essential to find new ways of enabling experts in different disciplines to collaborate more efficient in the development of ever more complex systems, under increasing market pressures. One possible solution for this challenge is to use a heterogeneous model-based approach where different teams can produce their conventional models and carry out their usual mono-disciplinary analysis, but in addition, the different models can be coupled for simulation (co-simulation), allowing the study of the global behavior of the system. Due to its potential, co-simulation is being studied in many different disciplines but with limited sharing of findings. Our aim with this work is to summarize, bridge, and enhance future research in this multidisciplinary area. We provide an overview of co-simulation approaches, research challenges, and research opportunities, together with a detailed taxonomy with different aspects of the state of the art of co-simulation and classification for the past five years. The main research needs identified are: finding generic approaches for modular, stable and accurate coupling of simulation units; and expressing the adaptations required to ensure that the coupling is correct.

1 Introduction

Co-simulation addresses the difficulty of integrating heterogeneous, independently developed models while preserving domain-specific tools and intellectual property. The survey bridges previously separated research communities, reviews approaches and applications, and organizes the field through a taxonomy.

  • Complex engineered systems require concurrent, distributed development across specialized teams, followed by earlier and more frequent integration of partial solutions.
  • Conventional modeling and simulation do not easily integrate models from different tools, while externally supplied models may contain protected intellectual property.
  • Co-simulation composes black-box simulators so suppliers can use their own tools and protect IP while integrators evaluate designs and perform early conformance checks.
  • The work responds to limited exchange across heterogeneous co-simulation communities by presenting a survey and taxonomy intended to bridge and classify existing approaches.
  • The taxonomy spans discrete-event, continuous-time, and hybrid co-simulation, alongside numerical analysis, algebraic systems, hybrid systems, optimization, hierarchy, verification, and testing.

2 Modeling, Simulation, and Co-simulation

This section defines models, behavior traces, simulators, and simulation units, then explains how coupled simulation units produce co-simulations. It emphasizes that predictive validity and simulation accuracy depend on explicit assumptions and approximation choices.

  • A dynamical system models a real system through state values and evolution rules, while its behavior trace records state and output trajectories over a time base.
  • Simulated time t differs from wall-clock time τ; their relationship distinguishes real-time, analytical, and interactive simulation modes.
  • Validity measures the difference between a dynamical system’s behavior and the real system’s behavior under assumptions specified by an experimental frame.
  • The survey focuses on operational simulation using solvers, rather than translating dynamical systems into another model before computing their traces.
  • Simulators compute behavior traces from dynamical systems, typically approximately, with errors arising from continuum trajectories and finite numerical representations.
  • A simulation unit combines a simulator with a dynamical system, and coupled simulation units exchange inputs and outputs to generate a co-simulation of the global system.
  • An orchestrator advances simulated time and transfers outputs to inputs according to a co-simulation scenario, while black-box composition may require relaxing strict information hiding for correctness.

3 Discrete Event Based Co-simulation

Discrete-event co-simulation couples passive, event-driven black-box simulation units through timestamped events and coordinated transitions. Its semantics support predictable scheduling, simultaneous-event ordering, and hierarchical composition.

  • DE co-simulation treats simulation units as black boxes that exchange timestamped events while simulated time may remain stopped.Units can evolve internal state and exchange values under orchestrator control; outputs may be absent when no event occurs.
  • Each DE simulation unit uses discrete states, input and output events, external and internal transitions, an output function, and a time-advance function.The time-advance function determines when the next state change occurs if no external event arrives.
  • A coordinator processes either the next internal transition or an earlier external event, processing simultaneous events before simulated time advances.Superdense time can order simultaneous events and state changes so trajectories remain identifiable.
  • Co-simulation scenarios couple multiple DE units by mapping one unit’s output events into external input events of other units.The traffic-light and police-officer example maps a police output to the traffic light’s external event, changing it from automatic operation to off.
  • A resulting co-simulation unit behaves exactly as a DE unit, enabling execution with the same orchestration algorithm and hierarchical composition.Hierarchical scenarios can represent hierarchical systems and provide a way to address system complexity.

4 Continuous Time Based Co-simulation

Continuous-time co-simulation couples numerical simulation units through a communication step size, while orchestration choices govern accuracy, parallelism, modularity, convergence, and stability. The section illustrates these trade-offs with mass-spring-damper examples and shows how algebraic constraints can complicate modular coupling.

  • CT simulation units: Continuous-time simulation units model state evolution with differential equations and can compute behavior traces analytically or through numerical solvers such as Forward Euler.The state-space form uses state x, input u, output y, and initial state x0; Forward Euler approximates the evolving trace using micro-steps.
  • CT co-simulation orchestration: A communication step size H defines when independently advancing simulation units exchange input and output values.Each unit may use its own micro-step size, so H provides the communication grid for the coupled scenario.
  • CT co-simulation orchestration: Gauss-Seidel orchestration orders unit advances so inputs can use values from units already at time t + H, improving accuracy through interpolation but reducing parallelization potential.This contrasts with parallel communication approaches that do not impose the same sequential order.
  • Modular composition – algebraic constraints: Adding an extra simulation unit can transform a non-trivial algebraic constraint into a simpler one, separating constraint handling from orchestration.The added unit may use a smaller internal micro-step size to meet stability and accuracy criteria.
  • Modular composition – algebraic constraints: Rigid, protected simulation units make some couplings difficult because their inputs and outputs do not directly match the constraints imposed by the physical connection.For a massless link, the units’ states and forces must satisfy shared-position and equal-and-opposite-force conditions.
  • Accuracy, convergence, and stability: Extrapolation introduces coupling error that generally grows with communication step size, while convergence can hold under stated assumptions and stability depends on system characteristics.For one parameterization, H = 0.001 gives spectral radius ρ(A) = 0.9992 and stability; with damping dk = 6.0E6, ρ(A) ≈ 76.43 and instability results. The compared co-simulation trace also shows error at H = 0.1.
  • Accuracy, convergence, and stability: Repeatedly retrying small micro-steps can preserve acceptable results but impose a large performance cost because simulated time does not advance during retries.This highlights a practical trade-off between numerical robustness and computational efficiency.

5 Hybrid Co-simulation Approach

Hybrid co-simulation combines continuous-time and discrete-event simulation units, whose differing assumptions about signals and timing require specialized orchestration and adaptation. No wrapper strategy fits every scenario, and algebraic loops may require iterative correction that can fail to converge.

  • Hybrid co-simulation scenarios: Hybrid scenarios mix continuous-time units, with continuously evolving states, and discrete-event units, whose states and outputs can change abruptly.These differences create fundamental challenges when the two kinds of units are combined.
  • Hybrid co-simulation scenarios: In the thermostat example, a continuous temperature model and a discrete controller exchange signals to keep room temperature within a comfort region.The controller reacts to tooHot and tooCold threshold events by switching the radiator input on or off.
  • Hybrid co-simulation approaches: Hybrid CT and Hybrid DE approaches use wrappers to reconcile continuous signals with event signals at the simulation-unit interfaces.A Hybrid DE wrapper can convert threshold crossings into output events and controller events into a continuous radiator signal.
  • Hybrid co-simulation approaches: Extrapolation and signal conversion must preserve constituent-system properties, because making a discontinuous signal continuous may violate the coupled system’s behavior.The paper therefore emphasizes that domain and simulation-unit knowledge remain important for selecting adaptations.
  • Hybrid co-simulation approaches: There is no best wrapper for all scenarios because adaptations depend on the concrete coupling and the simulation units’ features.More sophisticated adaptations can use predicted threshold-crossing times, while adaptive alternatives may monitor conditions such as quantized output spaces.
  • Algebraic loops: Algebraic loops can be solved by fixed-point iteration, but failure to converge can cause the orchestrator to exchange infinitely many values at one simulation time.Feedthrough information can detect these non-causal dependencies before the iteration is attempted.

6 Classification

The survey classifies co-simulation approaches through a feature-model taxonomy and reviews papers from 2011–2016. Its classification identifies accuracy as prominent, while extensibility and combined discrete-event/continuous-time capabilities remain underdeveloped.

  • Methodology: The review classified collected papers from 2011 through 2016 after iteratively developing and revising the taxonomy.The initial taxonomy was based on approximately 30 papers and was later applied systematically to the collected interval.
  • Taxonomy: The taxonomy organizes co-simulation into non-functional, simulation-unit, and framework requirements, with mandatory and optional features.Examples include accuracy, IP protection, information exposed, causality, rollback, adaptive step sizes, and strong coupling.
  • Observed requirements: Accuracy was the most frequently observed non-functional requirement, with 31 reports, followed by IP protection and performance.Fault tolerance, hierarchy, and extensibility were the least observed non-functional requirements.
  • Observed requirements: Extensibility was identified as needing greater importance because heterogeneous simulation units can provide a large combination of capabilities.The survey connects extensibility with accommodating new semantic adaptations.
  • Observed approaches: Few approaches use nominal state and output values or support a-causal modeling, despite their relevance to validity detection and modularity.The survey notes that these capabilities are supported by the FMI Standard but remain scarce in observed approaches.
  • Observed approaches: Dynamic structure, interactive visualization, multi-rate, algebraic coupling, and strong coupling were among the least observed framework features.The survey attributes their limited presence to dependencies on simulation-unit capabilities that may not yet be mature.
  • Cross-feature discussion: Feature interactions reveal limited support for approaches combining discrete-event and continuous-time domains, IP protection, and accuracy across larger co-simulations.Only one approach was identified as supporting both continuous-time and discrete-event simulation for any number of simulation units, while accuracy and IP protection remained limited in several combined settings.
  • Discussion: Overall, the classification indicates a research gap in approaches that combine discrete-event and continuous-time simulation while exploiting additional simulation-unit features.The survey specifically identifies this combination as insufficiently studied.

7 Concluding Remarks

Co-simulation research has advanced through many applications, but most reported scenarios remain small and ad hoc. The survey identifies major needs in semantic adaptation and modular, stable, accurate coupling.

  • Most reported applications use ad-hoc couplings between two simulators from different domains, leaving larger co-simulation scenarios underexplored.
  • The survey separately examines continuous-time, discrete-event, and combined co-simulation, then classifies five years of research with a proposed taxonomy.
  • Key challenges include semantic adaptation, modular coupling, stability, accuracy, and standardization for hybrid co-simulation.
  • Adaptations needed to combine simulators from different formalisms are difficult to generalize across co-simulation scenarios.
  • The classification finds insufficient research on modular, stable, and accurate coupling for dynamic-structure scenarios.
  • The document aims to summarize, bridge, and support future research in co-simulation.

A Historical Perspective of Co-simulation

The survey provides an historical perspective linking major co-simulation concepts to when they emerged in the literature.

  • The historical perspective relates major co-simulation concepts to their recognition in the surveyed state of the art and summarizes them in table 1.

A.1 One Formalism and Dynamic Iteration

Early co-simulation decomposed systems into independently integrated subsystems, later expanding across formalisms, abstraction levels, and heterogeneous tools. These developments improved efficiency but introduced approximation and coupling challenges.

  • A.1 One Formalism and Dynamic Iteration: A.1 One Formalism and Dynamic Iteration: Large systems were decomposed into coupled constituent systems whose outputs and inputs defined the coupling.
  • A.1 One Formalism and Dynamic Iteration: A.1 One Formalism and Dynamic Iteration: Decomposition improved simulation speed by up to two orders of magnitude through independent subsystem integration.
  • A.1 One Formalism and Dynamic Iteration: A.1 One Formalism and Dynamic Iteration: Dynamic iteration integrates each subsystem using extrapolated neighbor outputs, then repeats integration with corrected outputs until convergence.
  • A.1 One Formalism and Dynamic Iteration: A.1 One Formalism and Dynamic Iteration: Subsystems communicate only at interval boundaries and can integrate independently in parallel with separate numerical methods and step-size policies.
  • A.1 One Formalism and Dynamic Iteration: A.1 One Formalism and Dynamic Iteration: Independent step-size control avoids forcing slow components to use the smallest step required by faster components.
  • A.1 One Formalism and Dynamic Iteration: A.1 One Formalism and Dynamic Iteration: Early coordination methods supported multiple subsystems but assumed a common differential-equation formalism.
  • A.2 Two Formalisms: Digital and Analog Co-simulation: A.2 Two Formalisms: Digital and Analog Co-simulation: Co-simulation enabled concurrent software and hardware development while reducing the need for prototype circuit validation.
  • A.3 Multi-abstraction/Multi-Formalism Co-simulation: A.3 Multi-abstraction/Multi-Formalism Co-simulation: Research introduced multiple abstraction levels, heterogeneous formalisms, common coupling interfaces, and specialized simulation units for physical systems.

A.4 Black-box Co-simulation

Co-simulation supports distributed development by allowing suppliers and integrators to exchange executable system representations without disclosing sensitive implementation information.

  • IP protection enables suppliers and integrators to exchange co-simulation units without disclosing sensitive information or accepting vendor lock-in contracts.

A.5 Real-time Co-simulation

Co-simulation spans development stages from early system validation to X-in-the-Loop, where hard real-time constraints add to the challenge set.

  • X-in-the-Loop co-simulation introduces hard real-time constraints alongside the challenges of earlier development stages.

A.6 Many simulation units: Large Scale Co-simulation

As co-simulation targets larger systems of systems, scale and distribution become inherent challenges.

  • Larger systems of systems make scale and distribution inherent co-simulation challenges.

B State of the Art in Co-simulation Frameworks

The surveyed state of the art classifies co-simulation references by approaches, simulator properties, coupling choices, domains, and reported outcomes across varied frameworks and applications.

  • The section classifies references into categories and lists the publications assigned to each category.
  • Reported approaches include co-simulation masters, time-step selection, multi-rate simulation, asynchronous coupling, and semi-implicit Jacobian-based correction.
  • The taxonomy records nonfunctional concerns such as performance, accuracy, intellectual-property protection, parallelism, distribution, and platform independence.
  • Frameworks use coupling schemes including Jacobi, Gauss-Seidel, explicit, and implicit algorithmic loops, with fixed or variable simulation step sizes.
  • Accuracy-oriented work reports close agreement between DACCOSIM co-simulation and Dymola simulation, using output examination to estimate deviation from exact values.
  • The surveyed scenarios span continuous-time, discrete-event, and mixed simulator domains, with examples from automotive, maritime, power production, and smart-grid applications.

C Co-Simulation Scenario Categorization

This section describes the categories used for the co-simulation scenario classification and identifies the references assigned to each category.

  • Each category is described together with the references classified into it.

C.1.1 Fault Tolerance

The taxonomy characterizes co-simulation frameworks by capabilities including fault tolerance, configurability, performance, protection, distribution, abstraction, scalability, portability, extensibility, and accuracy. These properties describe how frameworks handle failures, resources, model exposure, execution environments, and simulation fidelity.

  • Fault Tolerance: Fault-tolerant co-simulation can replace a failed simulation unit by restoring stored state and replaying recorded inputs.Periodic state storage and input recording support pausing, restoring, and continuing long-running simulations.
  • Configuration Reuse: Reusable external configurations reduce the time and errors involved in setting up co-simulations.Configurations can be reused without altering the co-simulation application binaries.
  • Performance: Performance combines substantial simulation throughput with low resource use through variable-step integration, extrapolation, and parallelism.Variable-step methods and signal extrapolation improve speed, while parallelism primarily reduces elapsed time.
  • IP Protection: IP protection limits the structural and variable information exposed by participating models, including through web services or FMI binaries.These mechanisms can let component suppliers provide simulations while retaining control over model details and use.
  • Distribution: Distributed frameworks allow remote simulation units across wide-area networks, with distribution supported by parallelism techniques and fault tolerance.Web-based availability can give suppliers more control over how simulation units are used.
  • Other Framework Properties: Framework capabilities also include hierarchical abstraction, support for many simulation units, platform independence, extensibility, and accuracy through error control.Hierarchical frameworks can represent a co-simulation scenario as a black-box simulation unit, while platform-independent coordination and higher-level languages support portability and extension.

C.3.9 Results Visualization

The taxonomy distinguishes when simulation results become available and identifies iterative coupling schemes used across co-simulation approaches. It also records standard terminology for simulation domains, interfaces, requirements, and related concepts.

  • Results Visualization: Results may be available postmortem, live during execution, or interactively, distinguishing when users can observe a co-simulation.The supplied classification lists references under postmortem, live, and interactive result availability.
  • Coupling Schemes: Jacobi and Gauss-Seidel are both represented as co-simulation coupling schemes across the surveyed approaches.The taxonomy provides separate reference lists for each scheme.
  • Terminology: The paper defines abbreviations spanning cyber-physical systems, time and event formalisms, interfaces, requirements, and differential-equation problems.The glossary includes CPS, CT, DE, DEVS, DTSS, FMI, FR, GVT, IP, IVP, NFR, ODE, and SR.
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