Engineering computer codes are often computationally expensive. To lighten this load, we exploit new covariance kernels to replace computationally expensive codes with surrogate models. For input spaces with large dimensions, using the kriging model in the standard way is computationally expensive because a large covariance matrix must be inverted several times to estimate the parameters of the model. We address this issue herein by constructing a covariance kernel that depends on only a few parameters. The new kernel is constructed based on information obtained from the Partial Least Squares method. Promising results are obtained for numerical examples with up to 100 dimensions, and significant computational gain is obtained while maintaining sufficient accuracy.

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Surrogate models are often used to reduce the cost of design optimization problems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by surrogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality constraints. The proposed algorithm-super efficient global optimization coupled with mixture of experts (SEGOMOE)can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained problems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization.

In order to reduce the CO2 emissions, a disruptive concept in aircraft propulsion has to be considered. As studied in the past years hybrid distributed electric propulsion is a promising option. In this work the feasibility of a new concept aircraft, using this technology, has been studied. Two different energy sources have been used: fuel based engines and batteries. The latters have been chosen because of their flexibility during operations and their promising improvements over next years. The technological horizon considered in this study is the 2035: thus some critical hypotheses have been made for electrical components, airframe and propulsion. Due to the uncertainty associated to these data, sensivity analyses have been performed in order to assess the impact of technologies variations. To evaluate the advantages of the proposed concept, a comparison with a conventional aircraft (EIS 2035), based on evolutions of today's technology (airframe, propulsion, aerodynamics) has been made.

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 improvement, 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 performance

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.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is a publisher-deposited version published in: http://oatao. Any correspondence concerning this service should be sent to the repository administrator:staff-oatao@inp-toulouse.fr Surrogate modeling approximation using a mixture of experts based on EM joint estimation Dimitri Bettebghor · Nathalie Bartoli · Stéphane Grihon · Joseph Morlier · Manuel Samuelides Abstract An automatic method to combine several local surrogate models is presented. This method is intended to build accurate and smooth approximation of discontinuous functions that are to be used in structural optimization problems. It strongly relies on the Expectation−Maximization (EM) algorithm for Gaussian mixture models (GMM). To the end of regression, the inputs are clustered together with their output values by means of parameter estimation of the joint distribution. A local expert is then built (linear, quadratic, artificial neural network, moving least squares) on each cluster. Lastly, the local experts are combined using the Gaussian mixture model parameters found by the EM algorithm to obtain a global model. This method is tested over both mathematical test cases and an engineering optimization problem from aeronautics and is found to improve the accuracy of the approximation.

A new approach is considered to construct effective boundary conditions for the solution of problems related to the scattering of electromagnetic waves by perfectly conducting cylinders coated by a thin dielectric shell. These boundary conditions aim to be both robust and of high order while remaining set in terms of surface differential operators involving at most second-order derivatives. Error estimates yield a theoretical basis for the use of these boundary conditions in practical computations. Some numerical experiments at frequencies beyond the range of validity of the usual impedance boundary conditions validate the efficiency of the approach.