In power electronics applications, embedded mechatronic systems (MSs) must meet the severe operating conditions and high levels of thermomechanical stress. The thermal fatigue of the solder joints remains the main mechanism leading to the rupture and a malfunction of the complete MS. It is the main failure to which the lifetime of embedded MS is often linked. Consequently, robust and inexpensive design optimization is needed to increase the number of life cycles of solder joints. This paper proposes an application of metamodel-assisted evolution strategy (MA-ES) which significantly reduces the computational cost of ES induced by the expensive finite element simulation, which is the objective function in optimization problems. The proposed method aims to couple the Kriging metamodel with the covariance matrix adaptation evolution strategy (CMA-ES). Kriging metamodel is used to replace the finite element simulation in order to overcome the computational cost of fitness function evaluations (finite element model). Kriging is used together with CMA-ES and sequentially updated and its fidelity (quality) is measured according to its ability in ranking of the population through approximate ranking procedure (ARP). The application of this method in the optimization of MS proves its efficiency and ability to avoid the problem of computational cost.

RÉSUMÉ. Face aux exigences concurrentielles et économiques actuelles dans le secteur industriel, Les outils de simulation numérique, tels que les méthodes des éléments finis, sont de plus en plus largement appliqués aux problèmes de conception des systèmes mécatroniques. De nombreux problèmes nécessitent un grand nombre de simulations pour évaluer une fonction objectif. Cependant, pour de nombreux cas, une seule simulation peut prendre plusieurs minutes, heures, ou même des jours pour converger. Par conséquent, les tâches à forte intensité de simulations, telles que l'analyse de sensibilité, l'analyse de fiabilité, l'optimisation, et l'optimisation fiabiliste deviennent impraticables ou presque impossibles, car elles nécessitent des centaines, des milliers ou même des millions de simulations. La construction des modèles d'approximation devient la méthode la plus robuste pour remédier à ce problème. Ces modèles connus sous le nom de métamodèles, permettent de rapprocher le plus possible la relation entrée-sortie (input-output) du modèle de simulation élément finis, tout dans le but de réduire le coût d'évaluation. Finalement les tâches à grand nombre de simulations peuvent être mises en oeuvre en utilisant le métamodèle construit. Cet article présente les métamodèles les plus populaires, leurs méthodes de validation, ainsi que des exemples d'étude comparative pour un choix optimal du métamodèle convenable au problème. ABSTRACT. In the face of current competitive and economic demands in the industrial sector, numerical simulation tools, such as finite element methods, are increasingly applied to the design problems of mechatronic systems. Many problems require a large number of simulations to evaluate an objective function. However, for many cases, a single simulation can take several minutes, hours, or even days to converge. As a result, simulation-intensive tasks such as sensitivity analysis, reliability analysis, optimization, and reliability based design optimization become impractical or almost impossible, as they require hundreds, thousands or even millions of simulations. The construction of the approximation models becomes the most robust method to remedy this problem. These models, known as metamodels, make it possible to approximate as much as possible the input-output relation of the finite element simulation model, all with the aim of reducing the evaluation cost. Finally, tasks with large number of simulations can be implemented using the meta model built. This article present the most popular metamodeling techniques, their validation methods, as well as examples of comparative studies for an optimal choice of the metamodel suitable for the problem. MOTS-CLÉS. Systèmes mécatroniques, Plans d'expériences, Métamodèle, Modèle numérique.

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