Contributions à la planification d'expériences robuste à l'erreur structurelle

Abstract : We deal with the problem of model robust design of experiments for regression, when the regression model is parametric, linear with respect to parameters. The model error is modelled by a stochastic process, Gaussian or more generally which possess a second order moment. The case of standard least squares estimation for the regression parameters with the integrated squared prediction error (ISPE) as performance criterion for the predictor is mainly considered, but the approach remains valid for weighted least squares and for all linear functional of the prediction error as performance criterion. The optimality criteria defined are based on total expectation (with respect to the joint distribution of noise and model error) of the ISPE and quantile of the ISPE, which are optimized for exact designs by a particle swarm method. Optimization of the quantile criterion required to develop an efficient numerical method to approximate the quantile of a sum of squares of correlated Gaussian variables. The problem of dependence of optimal designs with respect to hyperparameters (introduced by the process covariance function) is treated by a maximin approach, and leads to the definition of a new optimality criterion, whose optimization is made possible by using an interpolation for criterion evaluation. Resulting optimal designs are proven to be efficient with respect to other criteria and compare favorably to other designs from the literature. Application of the approach to the design of a flowmeter robust to pipe singularities illustrates how to introduce precise a priori knowledge about the nature of the model error, here some data computed by a finite elements code.
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Traitement du signal et de l'image. Université Paris Sud - Paris XI, 2007. Français
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Morgan Roger. Contributions à la planification d'expériences robuste à l'erreur structurelle. Traitement du signal et de l'image. Université Paris Sud - Paris XI, 2007. Français. 〈tel-00274258〉

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