Optimisation auto-adaptative en environnement d'analyse multidisciplinaire via les modèles de krigeage combinés à la méthode PLS

Aerospace turbomachinery consists of a plurality of blades. Their main function is to transfer energy between the air and the rotor. The bladed disks of the compressor are particularly important because they must satisfy both the requirements of aerodynamic performance and mechanical resistance. Mechanical and aerodynamic optimization of blades consists in searching for a set of parameterized aerodynamic shape that ensures the best compromise solution between a set of constraints.This PhD introduces a surrogate-based optimization method well adapted to high-dimensional problems. This kind of high-dimensional problem is very similar to the Snecma's problems. Our main contributions can be divided into two parts: Kriging models development and enhancement of an existing optimization method to handle high-dimensional problems under a large number of constraints.Concerning Kriging models, we propose a new formulation of covariance kernel which is able to reduce the number of hyper-parameters in order to accelerate the construction of the metamodel. One of the known limitations of Kriging models is about the estimation of its hyper-parameters. This estimation becomes more and more difficult when the number of dimension increases.In particular, the initial design of experiments (for surrogate modelling construction) requires an important number of points and therefore the inversion of the covariance matrix becomes time consuming. Our approach consists in reducing the number of parameters to estimate using the Partial Least Squares regression method (PLS). This method provides information about the linear relationship between input and output variables. This information is integrated into the Kriging model kernel while maintaining the symmetry and the positivity properties of the kernels. Thanks to this approach, the construction of these new models called KPLS is very fast because of the low number of new parameters to estimate. When the covariance kernel used is of an exponential type, the KPLS method can be used to initialize parameters of classical Kriging models, to accelerate the convergence of the estimation of parameters. The final method, called KPLS+K, allows to improve the accuracy of the model for multimodal functions.The second main contribution of this PhD is to develop a global optimization method to tackle high-dimensional problems under a large number of constraint functions thanks to KPLS or KPLS+K method. Indeed, we extended the self adaptive optimization method called "Efficient Global Optimization, EGO" for high-dimensional problems under constraints. Several enriching criteria have been tested. This method allows to estimate known global optima on academic problems up to 50 input variables.The proposed method is tested on two industrial cases, the first one, "MOPTA", from the automotive industry (with 124 input variables and 68 constraint functions) and the second one is a turbine blade from Snecma company (with 50 input variables and 31 constraint functions). The results show the effectiveness of the method to handle industrial problems. We also highlight some importantlimitations.Les turbomachines aéronautiques sont composées de plusieurs roues aubagées dont la fonction est de transférer l'énergie de l'air au rotor. Les roues aubagées des modules compresseur et turbine sont des pièces particulièrement sensibles car elles doivent répondre à des impératifs de performance aérodynamique, de tenue mécanique, de tenue thermique et de performance acoustique. L'optimisation aéro-méca-acoustique ou aéro-thermo-mécanique des aubages consiste à chercher, pour un ensemble de formes aérodynamiques paramétrées (par plusieurs dizaines de variables), celle assurant le meilleur compromis entre la performance aérodynamique du moteur et la satisfaction de plusieurs dizaines de contraintes souvent contradictoires.Cette thèse introduit une méthode d'optimisation basée sur les métamodèles et adaptée à la grande dimension pour répondre à la problématique industrielle des aubages. Les contributions de cette thèse portent sur deux aspects : le développement de modèles de krigeage, et l'adaptation d'une stratégie d'optimisation pour la gestion du grand nombre de variables et de contraintes.La première partie de ce travail traite des modèles de krigeage. Nous avons proposé une nouvelle formulation du noyau de covariance permettant de réduire le nombre de paramètres du modèle afin d'accélérer sa construction. Une des limitations connues du modèle de krigeage concerne l'estimation de ses paramètres. Cette estimation devient de plus en plus difficile lorsque nous augmentons la dimension du phénomène à approcher. En particulier, la base de données nécessite davantage de points et par conséquent la matrice de covariance du modèle du krigeage est de plus en plus coûteuse à inverser.Notre approche consiste à réduire le nombre de paramètres à estimer en utilisant la méthode de régression des moindres carrés partiels (PLS pour Partial Least Squares). Cette méthode de réduction dimensionnelle fournit des informations sur la relation linéaire entre les variables d'entrée et la variable de sortie. Ces informations ont été intégrées dans les noyaux du modèle de krigeage tout en conservant les propriétés de symétrie et de positivité des noyaux. Grâce à cette approche, la construction de ces nouveaux modèles appelés KPLS est très rapide étant donné le faible nombre de paramètres nécessaires à estimer. La validation de ces modèles KPLS sur des cas test académiques ou industriels a démontré leur qualité de prédiction équivalente voire même meilleure que celle des modèles de krigeage classiques. Dans le cas de noyaux de covariance de type exponentiel, la méthode KPLS peut être utilisée pour initialiser les paramètres du krigeage classique, afin d'accélérer la convergence de l'estimation des paramètres du modèle. La méthode résultante, notée KPLS+K, a permis d'améliorer la qualité des modèles dans le cas de fonctions fortement multimodales.La deuxième contribution de la thèse a consisté à développer une stratégie d'optimisation globale sous contraintes pour la grande dimension, en s'appuyant sur les modèles KPLS ou les modèles KPLS+K. En effet, nous avons étendu la méthode d'optimisation auto-adaptative connue dans la littérature sous le nom "Efficient Global Optimisation, EGO" pour gérer les problèmes d'optimisation sous contraintes en grande dimension. Différents critères d'enrichissement adaptatifs ont pu être explorés. Cette stratégie a permis de retrouver l'optimum global sur des problèmes académiques jusqu'à la dimension 50.La méthode proposée a été confrontée à deux types de problèmes industriels, le cas test MOPTA issu de l'industrie automobile (124 variables d'entrée et 68 fonctions contraintes) et le cas test Snecma des aubes de turbomachines (50 variables d'entrée et 31 fonctions contraintes). Les résultats ont permis de montrer la validité de la démarche ainsi que les limites de la méthode pour une application dans un cadre industriel

An improved approach for estimating the hyperparameters of the kriging model for high-dimensional problems through the partial least squares method

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging

An adaptive optimization strategy based on mixture of experts for wing aerodynamic design optimization

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143084/1/6.2017-4433.pd

Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method

In many engineering optimization problems, the number of function evaluations is often very limited because of the computational cost to run one high-fidelity numerical simulation. Using a classic optimization algorithm, such as a derivative-based algorithm or an evolutionary algorithm, directly on a computational model is not suitable in this case. A common approach to addressing this challenge is to use black-box surrogate modeling techniques. The most popular surrogate-based optimization algorithm is the Efficient Global Optimization (EGO) algorithm, which is an iterative sampling algorithm that adds one (or many) point(s) per iteration. This algorithm is often based on an infill sampling criterion, called expected im- provement, which represents a trade-off between promising and uncertain areas. Many studies have shown the efficiency of EGO, particularly when the number of input variables is relatively low. However, its performanceon high-dimensional problems is still poor since the Kriging models used are time-consuming to build. To deal with this issue, this paper introduces a surrogate-based optimization method that is suited to high-dimensional problems. The method first uses the “locating the regional extreme” criterion, which incorporates minimizing the surrogate model while also maximizing the expected improvement criterion. Then, it replaces the Kriging models by the KPLS(+K) models (Kriging combined with the partial least squares method), which are more suitable for high-dimensional problems. Finally, the proposed approach is validated by a comparison with alternative methods existing in the literature on some analytical functions and on 12-dimensional and 50-dimensional instances of the benchmark automotive problem “MOPTA08”

New insights on the mechanism of quinoline-based DNA methyltransferase inhibitors

Among the epigenetic marks, DNA methylation is one of the most studied. It is highly deregulated in numerous diseases, including cancer. Indeed, it has been shown that hypermethylation of tumor suppressor genes promoters is a common feature of cancer cells. Because DNA methylation is reversible, the DNA methyltransferases (DNMTs), responsible for this epigenetic mark, are considered promising therapeutic targets. Several molecules have been identified as DNMT inhibitors and, among the non-nucleoside inhibitors, 4-aminoquinoline-based inhibitors, such as SGI-1027 and its analogs, showed potent inhibitory activity. Here we characterized the in vitro mechanism of action of SGI-1027 and two analogs. Enzymatic competition studies with the DNA substrate and the methyl donor cofactor, S-adenosyl-L-methionine (AdoMet), displayed AdoMet non-competitive and DNA competitive behavior. In addition, deviations from the Michaelis-Menten model in DNA competition experiments suggested an interaction with DNA. Thus their ability to interact with DNA was established; although SGI-1027 was a weak DNA ligand, analog 5, the most potent inhibitor, strongly interacted with DNA. Finally, as 5 interacted with DNMT only when the DNA duplex was present, we hypothesize that this class of chemical compounds inhibit DNMTs by interacting with the DNA substrate

Multi-fidelity efficient global optimization : Methodology and application to airfoil shape design

Predictions and design engineering decisions can be made using a variety of informa- tion sources that range from experimental data to computer models. These information sources could consist of different mathematical formulations, different grid resolutions, dif- ferent physics, or different modeling assumptions that simplify the problem. This leads to information sources with varying degrees of fidelity, each with an associated accuracy and querying cost. In this paper, we propose a novel and flexible way to use multi-fidelity informa- tion sources optimally in the context of airfoil shape optimization using both Xfoil and ADflow. The new developments are based on Bayesian optimization and kriging metamodeling and allow the aerodynamic optimization to be sped up. In a constrained optimization example with 15-design variables problem, the proposed approach reduces the total cost by a factor of two compared to a single Bayesian based fidelity optimization and by a factor of 1.5 compared to sequential quadratic programming

A Python surrogate modeling framework with derivatives

The surrogate modeling toolbox (SMT) is an open-source Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to training data. It also includes unique surrogate models: kriging by partial least-squares reduction, which scales well with the number of inputs; and energy- minimizing spline interpolation, which scales well with the number of training points. The efficiency and effectiveness of SMT are demonstrated through a series of examples. SMT is documented using custom tools for embedding automatically tested code and dynamically generated plots to produce high-quality user guides with minimal effort from contributors. SMT is maintained in a public version control repository

11β-hydroxysteroid dehydrogenase type 1 deficiency in bone marrow-derived cells reduces atherosclerosis

11β-Hydroxysteroid dehydrogenase type-1 (11β-HSD1) converts inert cortisone into active cortisol, amplifying intracellular glucocorticoid action. 11β-HSD1 deficiency improves cardiovascular risk factors in obesity but exacerbates acute inflammation. To determine the effects of 11β-HSD1 deficiency on atherosclerosis and its inflammation, atherosclerosis-prone apolipoprotein E-knockout (ApoE-KO) mice were treated with a selective 11β-HSD1 inhibitor or crossed with 11β-HSD1-KO mice to generate double knockouts (DKOs) and challenged with an atherogenic Western diet. 11β-HSD1 inhibition or deficiency attenuated atherosclerosis (74–76%) without deleterious effects on plaque structure. This occurred without affecting plasma lipids or glucose, suggesting independence from classical metabolic risk factors. KO plaques were not more inflamed and indeed had 36% less T-cell infiltration, associated with 38% reduced circulating monocyte chemoattractant protein-1 (MCP-1) and 36% lower lesional vascular cell adhesion molecule-1 (VCAM-1). Bone marrow (BM) cells are key to the atheroprotection, since transplantation of DKO BM to irradiated ApoE-KO mice reduced atherosclerosis by 51%. 11β-HSD1-null macrophages show 76% enhanced cholesterol ester export. Thus, 11β-HSD1 deficiency reduces atherosclerosis without exaggerated lesional inflammation independent of metabolic risk factors. Selective 11β-HSD1 inhibitors promise novel antiatherosclerosis effects over and above their benefits for metabolic risk factors via effects on BM cells, plausibly macrophages.—Kipari, T., Hadoke, P. W. F., Iqbal, J., Man, T. Y., Miller, E., Coutinho, A. E., Zhang, Z., Sullivan, K. M., Mitic, T., Livingstone, D. E. W., Schrecker, C., Samuel, K., White, C. I., Bouhlel, M. A., Chinetti-Gbaguidi, G., Staels, B., Andrew, R., Walker, B. R., Savill, J. S., Chapman, K. E., Seckl, J. R. 11β-hydroxysteroid dehydrogenase type 1 deficiency in bone marrow-derived cells reduces atherosclerosis

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques