Computational design of an automotive twist beam

International audienceIn recent years, the automotive industry has known a remarkable development in order to satisfy the customer requirements. In this paper, we will study one of the components of the automotive which is the twist beam. The study is focused on the multicriteria design of the automotive twist beam undergoing linear elastic deformation (Hooke's law). Indeed, for the design of this automotive part, there are some criteria to be considered as the rigidity (stiffness) and the resistance to fatigue. Those two criteria are known to be conflicting, therefore, our aim is to identify the Pareto front of this problem. To do this, we used a Normal Boundary Intersection (NBI) algorithm coupling with a radial basis function (RBF) metamodel in order to reduce the high calculation time needed for solving the multicriteria design problem. Otherwise, we used the free form deformation (FFD) technique for the generation of the 3D shapes of the automotive part studied during the optimization process

Semaine d'Etude Mathématiques et Entreprises 5 : Détection de marques de cylindres sur une ligne sidérurgique, ou comment séparer des sources périodiques dans une image bruitée

Lors de la fabrication de tôe par laminage, des défauts périodiques peuvent être marqués par les cylindres qui compressent le métal. Un contrôle automatique est incorporé dans le processus afin de détecter les défauts par traitement numérique des images prises par des capteurs. Ces images sont de grandes tailles et fortement bruitées de sorte que les défauts sont souvent à peine perceptibles. Arcelor Mittal propose ici de réfléchir sur des méthodes robustes et performantes qui permettraient l'extraction des composantes périodiques des images. Ce document est la synthèse des méthodes et pistes que nous avons explorées lors de cette cinquième édition de la SEME à l'Ecole des Mines de Nancy

Semaine d'Etude Mathématiques et Entreprises 7 : Détection d'ilôtage dans un réseau électrique

In recent years, the signiﱂcant increase in number of connections to photo- voltaic installations in the public networks has caused greater risks. Meth- ods involving in detecting situations such as islanding, damage on the trans- port network, and normal situations without special event arise have been exploited, however, each method has its disavantages. In this work, by using the statistical and signal processing tools, we can consider and appre- ciate the change of data of the simulated model. Then we apply the CART algorithm to classify the above phenomena

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Dans le domaine d’optimisation de forme de structures, la réduction des coûts et l’amélioration des produits sont des défis permanents à relever. Pour ce faire, le procédé de mise en forme doit être optimisé. Optimiser le procédé revient alors à résoudre un problème d’optimisation. Généralement ce problème est un problème d’optimisation multicritère très coûteux en terme de temps de calcul, où on cherche à minimiser plusieurs fonctions coût en présence d’un certain nombre de contraintes. Pour résoudre ce type de problème, on a développé un algorithme robuste, efficace et fiable. Cet algorithme, consiste à coupler un algorithme de capture de front de Pareto (NBI ou NNCM) avec un métamodèle (RBF), c’est-à-dire des approximations des résultats des simulations coûteuses. D’après l’ensemble des résultats obtenus par cette approche, il est intéressant de souligner que la capture de front de Pareto génère un ensemble des solutions non dominées. Pour savoir lesquelles choisir, le cas échéant, il est nécessaire de faire appel à des algorithmes de sélection, comme par exemple Nash et Kalai-Smorodinsky. Ces deux approches, issues de la théorie des jeux, ont été utilisées pour notre travail. L’ensemble des algorithmes sont validés sur deux cas industriels proposés par notre partenaire industriel. Le premier concerne un modèle 2D du fond de la canette (elasto-plasticité) et le second est un modèle 3D de la traverse (élasticité linéaire). Les résultats obtenus confirment l’efficacité de nos algorithmes développés.One of the current challenges in the domain of the multiobjective shape optimization is to reduce the calculation time required by conventional methods. The high computational cost is due to the high number of simulation or function calls required by these methods. Recently, several studies have been led to overcome this problem by integratinga metamodel in the overall optimization loop. In this thesis, we perform a coupling between the Normal Boundary Intersection -NBI- algorithm and The Normalized Normal constraint Method -NNCM- algorithm with Radial Basis Function -RBF- metamodel in order to have asimple tool with a reasonable calculation time to solve multicriteria optimization problems. First, we apply our approach to academic test cases. Then, we validate our method against two industrial cases, namely, shape optimization of the bottom of a can undergoing nonlinear elasto-plastic deformation and an optimization of an automotive twist beam. Then, in order to select solutions among the Pareto efficient ones, we use the same surrogate approach to implement a method to compute Nash and Kalai-Smorodinsky equilibria

Méthodes efficaces de capture de front de pareto en conception mécanique multicritère : applications industrielles

One of the current challenges in the domain of the multiobjective shape optimization is to reduce the calculation time required by conventional methods. The high computational cost is due to the high number of simulation or function calls required by these methods. Recently, several studies have been led to overcome this problem by integratinga metamodel in the overall optimization loop. In this thesis, we perform a coupling between the Normal Boundary Intersection -NBI- algorithm and The Normalized Normal constraint Method -NNCM- algorithm with Radial Basis Function -RBF- metamodel in order to have asimple tool with a reasonable calculation time to solve multicriteria optimization problems. First, we apply our approach to academic test cases. Then, we validate our method against two industrial cases, namely, shape optimization of the bottom of a can undergoing nonlinear elasto-plastic deformation and an optimization of an automotive twist beam. Then, in order to select solutions among the Pareto efficient ones, we use the same surrogate approach to implement a method to compute Nash and Kalai-Smorodinsky equilibria.Dans le domaine d’optimisation de forme de structures, la réduction des coûts et l’amélioration des produits sont des défis permanents à relever. Pour ce faire, le procédé de mise en forme doit être optimisé. Optimiser le procédé revient alors à résoudre un problème d’optimisation. Généralement ce problème est un problème d’optimisation multicritère très coûteux en terme de temps de calcul, où on cherche à minimiser plusieurs fonctions coût en présence d’un certain nombre de contraintes. Pour résoudre ce type de problème, on a développé un algorithme robuste, efficace et fiable. Cet algorithme, consiste à coupler un algorithme de capture de front de Pareto (NBI ou NNCM) avec un métamodèle (RBF), c’est-à-dire des approximations des résultats des simulations coûteuses. D’après l’ensemble des résultats obtenus par cette approche, il est intéressant de souligner que la capture de front de Pareto génère un ensemble des solutions non dominées. Pour savoir lesquelles choisir, le cas échéant, il est nécessaire de faire appel à des algorithmes de sélection, comme par exemple Nash et Kalai-Smorodinsky. Ces deux approches, issues de la théorie des jeux, ont été utilisées pour notre travail. L’ensemble des algorithmes sont validés sur deux cas industriels proposés par notre partenaire industriel. Le premier concerne un modèle 2D du fond de la canette (elasto-plasticité) et le second est un modèle 3D de la traverse (élasticité linéaire). Les résultats obtenus confirment l’efficacité de nos algorithmes développés

A Radial basis function Metamodel Assisted Nor- mal Boundary Intersection, Nash and Kalai-Smorodinsky equilibria algorithms for Multiobjective Design Optimization.

International audienc

A Radial basis function Metamodel Assisted Nor- mal Boundary Intersection, Nash and Kalai-Smorodinsky equilibria algorithms for Multiobjective Design Optimization.

International audienc

A metamodel-based multicriteria shape optimization process for an aerosol can

International audienceIn this paper, we study a multicriteria shape design of a highly nonlinear mechanical 2D structure, namely the shape optimization of the aerosol can bottom. In fact, it is made depending on two criteria, the dome growth DG and the dome reversal pressure DRP, that define the resistance of the bottom against the internal pressure. This two criteria are known to be conflicting; therefore, a multicriteria optimization problem is formulated to represent the trade-offs among the design parameters. Due to the expensive time-consuming cost to solve this kind of optimization problems (e.g., capturing the Pareto front), the use of a surrogate model (e.g., metamodel) cheap to evaluate is mandatory. For this reason, we have developed an algorithm which is a coupling between the normalized normal constraint method (NNCM) and the radial basis function metamodel (RBF). The NNCM-RBF coupling was tested for several academic test cases and for our industrial problem and the obtained results clearly show the efficiency of our coupling to solve all the problems treated with a remarkable gain in the computational time

A case study of multicriteria shape optimization of thin structures

International audienceAerosol cans are usually made of thin high performance steel and are fi lled with fluid at high pressure. For these two reasons, and considering usage and packaging requirements, the structural stability of their ends, top and bottom is then delicate to maintain. In the present work, we address the problem of shape optimization of the bottom of a can, in order to control the dome growth DG (e.g. displacement of can base) at a proof pressure as well as the dome reversal pressure DRP, a critical pressure at which the can bottom looses stability (e.g. initiates buckling). We fi rst implemented and validated an RBF-like metamodel to have at hand cheap criteria surrogates (DG,DRP) using a 2D spline representation in an axi-symmetric setting. Then, we implemented a Normal Boundary Intersection -NBI- with fi ltering for- mulation in order to capture the -approximate- Pareto Front, using an FSQP method for the NBI-related sub-optimizations. The obtained approximate Pareto Fronts corroborate the antagonistic behavior of the DG and DRP criteria, and are successfully compared to the projection on the exact cost evaluations. We also identify Pareto-optimal solutions which lie in a restrictive industrial-prescribed acceptable interval for the DG- DRP costs. We then consider the problem of selection of solutions among the Pareto Front. We model the selection problem as a Nash game played by the two costs DG and DRP, and show that an arbitrary splitting of the shape parameters among the two players may lead to ine fficient solutions (strictly dominated by Pareto-optimal ones)

Multicriteria shape design of an aerosol can

One of the current challenges in the domain of the multicriteria shape optimization is to reduce the calculation time required by conventional methods. The high computational cost is due to the high number of simulation or function calls required by these methods. Recently, several studies have been led to overcome this problem by integrating a metamodel in the overall optimization loop. In this paper, we perform a coupling between the Normal Boundary Intersection – NBI – algorithm with Radial Basis Function – RBF – metamodel in order to have a simple tool with a reasonable calculation time to solve multicriteria optimization problems. First, we apply our approach to academic test cases. Then, we validate our method against an industrial case, namely, shape optimization of the bottom of an aerosol can undergoing nonlinear elasto-plastic deformation. Then, in order to select solutions among the Pareto efficient ones, we use the same surrogate approach to implement a method to compute Nash and Kalai–Smorodinsky equilibria