arXiv subjects

Yohan Eguillon

Publications and source records attributed to Yohan Eguillon.

4 recordsLinked to original sources

arXiv2022

COSTARICA estimator for rollback-less systems handling in iterative co-simulation algorithms

Co-simulation is widely used in the industry due to the emergence of modular dynamical models made up of interconnected, black-boxed systems. Several co-simulation algorithms have been developed, each with different properties and different levels of accuracy and robustness. Among them, the most accurate and reliable ones are the iterative ones, although they have a main drawback in common: the involved systems are required to be capable of rollback. The latter denotes the ability of a system to integrate over a co-simulation time step that has already been simulated. Non-rollback-capable system can only go forward in time and every integrated step is definitive. In practice, the industrial modelling and simulation platforms rarely produce rollback-capable systems. This paper proposes a solution that slightly changes the co-simulation methodology and that enables to use iterative co-simulation methods on a modular model which contains non-rollback-capable systems in case the latter represent ordinary differential equations. The idea is to replace such a system by a simplified version, which is used to estimate the results of the integrations instead of integrating the real system. Once the co-simulation method's surrogate iterations on these estimators predict the convergence on the co-simulation step, the non-rollback-capable systems genuinely integrate the step using the estimated solution on the other systems before moving forward, transforming the iterative co-simulation method into a non-iterative one.

eess.SY↗

arXiv2022

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

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.

math.NA↗

arXiv2021

F3ORNITS: A Flexible Variable Step Size Non-Iterative Co-simulation Method handling Subsystems with Hybrid Advanced Capabilities

This paper introduces the F3ORNITS non-iterative co-simulation algorithm in which F3 stands for the 3 flexible aspects of the method: flexible polynomial order representation of coupling variables, flexible time-stepper applying variable co-simulation step size rules on subsystems allowing it and flexible scheduler orchestrating the meeting times among the subsystems and capable of asynchronousness when subsystems constraints requires it. The motivation of the F3ORNITS method is to accept any kind of co-simulation model, including any kind of subsystem, regardless on their available capabilities. Indeed, one the major problems in industry is that the subsystems usually have constraints or lack of advanced capabilities making it impossible to implement most of the advanced co-simulation algorithms on them. The method makes it possible to preserve the dynamics of the coupling constraints when necessary as well as to avoid breaking C1 smoothness at communication times, and also to adapt the co-simulation step size in a way that is robust both to zero-crossing variables (contrary to classical relative error-based criteria) and to jumps. Two test cases are presented to illustrate the robustness of the F3ORNITS method as well as its higher accuracy than the non-iterative Jacobi coupling algorithm (the most commonly used method in industry) for a smaller number of co-simulation steps.

math.NA↗

arXiv2021

IFOSMONDI Co-simulation Algorithm with Jacobian-Free Methods in PETSc

IFOSMONDI iterative algorithm for implicit co-simulation of coupled physical systems (introduced by the authors in july 2019 during the Simultech conference, p.176-186) enables us to solve the nonlinear coupling function while keeping the smoothness of interfaces without introducing a delay. Moreover, it automatically adapts the size of the steps between data exchanges among the systems according to the difficulty of the solving of the coupling constraint. The latter was solved by a fixed-point algorithm in the original implementation whereas this paper introduces the JFM version (standing for Jacobian-Free Methods). Most implementations of Newton-like methods require a jacobian matrix which can be difficult to compute in the co-simulation context, except in the case where the interfaces are represented by a Zero-Order-Hold (ZOH). As far as IFOSMONDI coupling algorithm uses Hermite interpolation for smoothness enhancement (up to Third-Order-Hold), we propose hereafter a new formulation of the non-linear coupling function including both the values and the time-derivatives of the coupling variables. This formulation is well designed for solving the coupling through jacobian-free Newton type methods. Consequently, successive function evaluations consist in multiple simulations of the systems on a co-simulation time step using rollback. The orchestrator-workers structure of the algorithm enables us to combine the PETSc framework on the orchestrator side for the non-linear Newton-type solvers with the parallel integrations of the systems on the workers side thanks to MPI processes. Different nonlinear methods will be compared to one another and to the original fixed-point implementation on a newly proposed 2-systems academic test-case (mass-spring-damper type) with direct feedthrough on both sides.

math.NA↗