Optimisation multi-objectif sous incertitudes de phénomènes de thermique transitoire

Abstract : The resolution of multi-objective problems under uncertainties in the presence of costly numerical simulations requires the development of parsimonious optimization and uncertainty propagation techniques. Because the aimed application is a transient thermal engineering one, we have also developed spatio-temporal surrogate models. First of all, we study a multi-objective optimization algorithm capable of returning a complete Pareto front by only using few calls to the objective functions. The proposed algorithm is based on Gaussian processes and on the EGO method. In order to return a uniformly discretized Pareto front, the maximization of the multi-objective expected improvement is processed thanks to the NSGA-II genetic algorithm, applied on the Kriging prediction of the objectives. In particular, this allows to improve the input space exploration ability of the method. The optimization problem under uncertainties is then studied by considering the worst case and a probabilistic robustness measure. The worst case strategy considers the maximum of the value attained by the objective function, no matter the value taken by the uncertainties. Less conservative solutions can be found with a probabilistic criterion. Among these, the superquantile also gives an information on the weight of the distribution tail by integrating every events on which the output value is between the quantile and the worst case. Those risk measures require an important number of calls to the uncertain objective function. This number can be reduced thanks to a coupling with the multi-objective algorithm which enables to reuse previously computed evaluations. Few methods give the possibility to approach the superquantile of the output distribution of costly functions. To this end, we have developed a superquantile estimator based on the importance sampling method and Kriging surrogate models. It enables to approach superquantiles with few error and using a limited number of samples. The application of those two risk measures on the industrial test case has highlighted that a Pareto optimal solution for the worst case may not be Pareto optimal for the superquantile. It has also led to innovative and competitive solutions. In the last part, we build spatio-temporal surrogate models. They are necessary when the execution time of the uncertain objective function is too large. In order to answer to the framework imposed by the transient thermal industrial application, the surrogate model has to be able to predict dynamic, long-term in time and non linear phenomena with few learning trajectories. Recurrent neural network are used and a construction facilitatingthe learning is implemented. It is based on cross validation and on a weights computation performed by multi-level optimization. Sensitivity analysis techniques are also applied to lower the input dimension of the neural network.
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Jonathan Guerra. Optimisation multi-objectif sous incertitudes de phénomènes de thermique transitoire. Algorithme et structure de données [cs.DS]. INSTITUT SUPERIEUR DE L’AERONAUTIQUE ET DE L’ESPACE (ISAE), 2016. Français. ⟨tel-01416394⟩

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