Global optimization in inverse problem of scatterometry

International audienceIn the current work, we consider the inverse problem in scatterometry which consists in determining the feature shape from an experimental ellipsometric signature. The reformulation of the given nonlinear identification problem was considered as a parametric optimization problem using the Least Square criterion. In this work, a design procedure for global robust optimization is developed using Kriging and global optimization approaches. Robustness is determined by Kriging model to reduce the number of real functional calculations of Least Square criterion. The technical of the global optimization methods is adopted to determine the global robust optimum of a surrogate model

Optimal control for a two-sidedly degenerate aggregation equation

In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming. We establish the wellposedness (existence and uniqueness) for the weak solution of the direct problem by means of an auxiliary nondegenerate aggregation equation, the Faedo–Galerkin method (for the existence result) and duality method (for the uniqueness). Moreover, for the adjoint problem, we prove the existence result of minimizers and first-order necessary conditions. The main novelty of this work concerns the presence of a control to our nonlocal degenerate aggregation model. Our results are complemented with some numerical simulations

Coupled complex boundary method for a geometric inverse source problem

This work deals with a geometric inverse source problem. It consists in recovering the characteristic function of an unknown inclusion based on boundary measurements. We propose a new reconstruction method based on the CCBM and the shape gradient method, the inverse problem is formulated as a shape optimization one, corresponding to a coupled complex boundary state problem. Well posedness and existence results are presented. A computed expression for the shape gradient is used to implement a gradient algorithm. The efficiency and accuracy of the reconstruction algorithm are illustrated by some numerical results, and a comparison between CCBM, Least-squares and Kohn-Vogeluis methods is presented

Application of the Kriging method to the reconstruction of ellipsometric signature

International audienceThe inverse problem in scatterometry which consists in determining the feature shape from an experimental ellipsometric signature is very difficult to solve. On one hand, the problem is ill-posed; on the other hand, due to equipment limitation and the presence of noise in the measurement, the number of experimental signature acquisition is limited to a few measurements. The efficient resolution of the inverse problem requires a more comprehensive signature. To deal with this problem, we use a new approach based on the Kriging interpolation method to enrich the number of usable data. This method is inherently providing the best linear unbiased optimal estimation

Les techniques d'optimisation de forme pour résoudre le problème inverse de la tomographie d'impédance électrique

Le but de cette thèse est l'étude d'un problème inverse en tomographie, il s'agit de l'identification d'une inclusion située à l'intérieur d'un domaine de conductivités différentes à partir d'une paire de mesures frontières. Nous résolvons le problème du point de vu de l'optimisation de forme. Nous considérons deux fonctionnelles coûts, la première est de type classique de moindres carrés, quant à la deuxième, il s'agit de minimiser l'écart énergétique entre la solution d'un problème de Dirichlet et un problème de Neumann (fonctionnelle coût de type Kohn-Vogelius). Afin de résoudre numériquement le problème d'optimisation, nous prouvons l'existence et calculons les gradients des deux fonctionnelles coûts en introduisant un problème adjoint pour la méthode de moindres carrés. Nous montrons que le gradient de la fonctionnelle coût de Kohn-Vogelius dans une direction donnée dépend uniquement de la solution d'état et non pas de ses dérivées. Concernant la procédure d'optimisation, nous utilisons la méthode des équations intégrales frontières pour la résolution du problème direct et la méthode de Quasi-Newton "BFGS" pour la minimisation. Par ailleurs, pour analyser la stabilité du problème, nous étudions la dérivée seconde d'état et nous calculons la Hessienne de forme associée aux fonctionnelles coûts considérées. Nous prouvons que l'opérateur de Riesz associé à la Hessienne est compact, ce qui nous permet de déduire que la forme quadratique associée aux dérivées secondes des fonctionnelles coûts n'est pas coercive. Comme conséquence de cette étude, nous montrons que le problème inverse est sévèrement mal posé et que les fonctionnelles coûts considérées sont plates. Le constat précédent nous a amené à introduire un paramètre de régularisation afin de rendre possible la résolution numérique.The goal of this work is to study the inverse problem in tomography : it acts of the identification of an inclusion located inside a domain that have different conductivities based on the boundary measurements. We solve the problem by the shape optimization method. In fact, we proposed two identification s methods : the first one consists of minimizing the cost functional of the Least Squares. The second method concerns the cost functional of the Kohn-Vogelius. For dealing with the problem numerically, we proved the existence and calculated the gradients of the two cost functionals. Then, we used the integral equations method to solve direct problems. Concerning the optimization s procedure, we used the Quasi-Newton method "BFGS". In order to analyze the stability of the problem, we studied the second derivative of the state and we calculated the shape Hessian of the cost functional. Then, we proved that the Riesz operator associated to the Hessian is compact, consequently, the associated quadratic form of the second derivative of the cost functional is not coercive. To overcome this difficulty, we regularized the problem.COMPIEGNE-BU (601592101) / SudocSudocFranceF

A Connected farm Metamodeling Using Advanced Information Technologies for an Agriculture 4.0

The agriculture 4.0 revolution is an opportunity for farmers to meet the challenges in food production. It has become necessary to adopt a set of agricultural practices based on advanced technologies following the agriculture 4.0 revolution. This latter enables the creation of added value by combining innovative technologies: precision agriculture, information and communication technology, robotics, and Big Data. As an enterprise, a connected farm is also highly sensitive to strategic changes like organizational changes, changes in objectives, modified variety, new business objects, processes, etc. To strategically control its information system, we propose a metamodeling approach based on the ISO/IS 19440 enterprise meta-model, where we added some new constructs relating to new advanced digital technologies for Smart and Connected agriculture