Hierarchical Kriging for multi-fidelity aero-servo-elastic simulators-application to extreme loading on wind turbines

Abstract : In the present work, we consider multi-fidelity surrogate modelling to fuse the output of multiple aeroservo-elastic computer simulators of varying complexity. In many instances, predictions from multiple simulators for the same quantity of interest on a wind turbine are available. In this type of situation, there is strong evidence that fusing the output from multiple aero-servo-elastic simulators yields better predictive ability and lower model uncertainty than using any single simulator. A computer simulator of a physical system requires a high number of runs in order to establish how the model response varies due to the variations in the input variables. Such evaluations might be expensive and time consuming. One solution consists in substituting the computer simulator with a mathematical approximation (surrogate model) built from a limited but well chosen set of simulations output. Hierarchical Kriging is a multi-fidelity surrogate modelling method in which the Kriging surrogate model of the cheap (low-fidelity) simulator is used as a trend of the Kriging surrogate model of the higher fidelity simulator. We propose a parametric approach to Hierarchical Kriging where the best surrogate models are selected based on evaluating all possible combinations of the available Kriging parameters candidates. The parametric Hierarchical Kriging approach is illustrated by fusing the extreme flapwise bending moment at the blade root of a large multi-megawatt wind turbine as a function of wind velocity, turbulence and wind shear exponent in the presence of model uncertainty and heterogeneously noisy output. The extreme responses are obtained by two widely accepted wind turbine specific aero-servo-elastic computer simulators, FAST and Bladed. With limited high-fidelity simulations, Hierarchical Kriging produces more accurate predictions of validation data compared to conventional Kriging. In addition, contrary to conventional Kriging, Hierarchical Kriging is shown to be a robust surrogate modelling technique because it is less sensitive to the choice of the Kriging parameters and the choice of the estimation error.
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[Research Report] ETH Zurich, Chair of Risk, Safety and Uncertainty Quantifi- cation, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland. 2017
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Imad Abdallah, Stefano Marelli, Bruno Sudret. Hierarchical Kriging for multi-fidelity aero-servo-elastic simulators-application to extreme loading on wind turbines. [Research Report] ETH Zurich, Chair of Risk, Safety and Uncertainty Quantifi- cation, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland. 2017. 〈hal-01902006〉

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