Co-Simulation: Error Estimation and Macro-Step Size Control

Meyer, Tobias; Kraft, Jan; Schweizer, Bernhard

doi:10.1115/1.4048944

Cited by 14 publications

(11 citation statements)

References 35 publications

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“…In a second round of simulations, the energy correction method was evaluated; in these, the coefficient μ was adjusted using the relations obtained for the linear oscillator shown in Eqs. (20) and (21). In most examples it was necessary to introduce an additional correction by means of the removal of the accumulated energy difference, as done in Eq.…”

Section: Resultsmentioning

confidence: 99%

“…The values of μ calculated with Eqs. (20) and (21) were used as reference for the cosimulation of the rest of cases in Table 1 and the benchmark examples. Figure 22 shows the effect of the energy correction on the position η 2 of the mass m 2 of the double linear oscillator in case 7 with a corrective factor μ = 0.5, corresponding to single-rate co-simulation.…”

Section: Resultsmentioning

confidence: 99%

“…Some methods to quantify the errors introduced in the co-simulation results have been put forward nonetheless. In general, these require some information about the subsystem internals, either directly obtained [20] or provided by the directional derivatives of the subsystems [15].…”

Section: Energy-based Indicators For Explicit Co-simulationmentioning

confidence: 99%

“…The subsystem M integrates the multibody system dynamics using as Fig. 20 Double linear oscillator: Mechanical energy in the multi-rate co-simulation of case 1 with ZOH extrapolation: H = h M1 = 1 ms, h M2 = 0.1 ms, μ = 0.725, the correction force was limited to 100 % of the original coupling force input the force f exerted by the piston and returns as output x M the displacement s c and rate ṡc of the cylinder. The hydraulic subsystem H, in turn, integrates its dynamics to obtain the pressures in the cylinder and evaluates the hydraulic force using Eq.…”

Section: Hydraulic Cranementioning

confidence: 99%

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Energy-based monitoring and correction to enhance the accuracy and stability of explicit co-simulation

Rodríguez

Sputh

et al. 2022

Multibody Syst Dyn

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The simulation of complex engineering applications often requires the consideration of component-level dynamics whose nature and time-scale differ across the elements of which the system is composed. Co-simulation offers an effective approach to deal with the modelling and numerical integration of such assemblies by assigning adequate description and solution methods to each component. Explicit co-simulation, in particular, is frequently used when efficient code execution is a requirement, for instance in real-time setups. Using explicit schemes, however, can lead to the introduction of energy artifacts at the discrete-time interface between subsystems. The resulting energy errors deteriorate the accuracy of the co-simulation results and may in some cases develop into the instability of the numerical integration process. This paper discusses the factors that influence the severity of the energy errors generated at the interface in explicit co-simulation applications, and presents a monitoring and correction methodology to detect and remove them. The method uses only the information carried by the variables exchanged between the subsystems and the co-simulation manager. The performance of this energy-correction technique was evaluated in multi-rate co-simulation of mechanical and multiphysics benchmark examples.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Energy-based Indicators For Explicit Co-simulationmentioning

confidence: 99%

Section: Hydraulic Cranementioning

confidence: 99%

See 2 more Smart Citations

Energy-based monitoring and correction to enhance the accuracy and stability of explicit co-simulation

Rodríguez

Sputh

et al. 2022

Multibody Syst Dyn

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“…A sketch of it is presented on figure5. It is a very common benchmark for co-simulation methods[23] [14][24].…”

mentioning

confidence: 99%

MISSILES: an Efficient Resolution of the Co-simulation Coupling Constraint on Nearly Linear Differential Systems through a Global Linear Formulation

Yohan¹,

Lacabanne²,

Tromeur-Dervout³

2022

Preprint

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In a co-simulation context, interconnected systems of differential equations are solved separately but they regularly communicate data to one another during these resolutions. Iterative co-simulation methods have been developed in order to enhance both stability and accuracy. Such methods imply that the systems must integrate one or more times per co-simulation step (the interval between two consecutive communications) in order to find the best satisfying interface values for exchanged data (according to a given coupling constraint). This requires that every system involved in the modular model is capable of rollback: the ability to re-integrate a time interval that has already been integrated with different input commands. In a paper previously introduced by Eguillon et al. in 2022, the COSTARICA process is presented and consists in replacing the non-rollback-capable systems by an estimator on the non-last integrations of the iterative process. The MISSILES algorithm, introduced in this paper, consists in applying the COSTARICA process on every system of a modular model simulated with the IFOSMONDI-JFM iterative co-simulation method (introduced by Eguillon et al. in 2021). Indeed, in this case, the iterative part on the estimators of each system can be avoided as the global resolution on a co-simulation step can be written as a single global linear system to solve. Consequently, MISSILES is a non-iterative method that leads to the same solution than the IFOSMONDI-JFM iterative co-simulation method applied to systems using the COSTARICA process to emulate the rollback.

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F$$_3$$ORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilities

Éguillon

Lacabanne

Tromeur-Dervout

2022

Engineering with Computers

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Co-Simulation: Error Estimation and Macro-Step Size Control

Cited by 14 publications

References 35 publications

Energy-based monitoring and correction to enhance the accuracy and stability of explicit co-simulation

Energy-based monitoring and correction to enhance the accuracy and stability of explicit co-simulation

MISSILES: an Efficient Resolution of the Co-simulation Coupling Constraint on Nearly Linear Differential Systems through a Global Linear Formulation

F$$_3$$ORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilities

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