Robust optimization of a 2D air conditioning duct using kriging

Janis Janusevskis (1, 2, 3) , Rodolphe Le Riche (1, 2, 3, 4, 5)

1 CROCUS-ENSMSE - Equipe : Calcul de Risque, Optimisation et Calage par Utilisation de Simulateurs
2 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
3 FAYOL-ENSMSE - Institut Henri Fayol
4 FAYOL-ENSMSE - Département Génie mathématique et industriel
5 CNRS - Centre National de la Recherche Scientifique

The design of systems involving fluid flows is typically based on computationally intensive Computational Fluid Dynamics (CFD) simulations. Kriging based optimization methods, especially the Efficient Global Optimization (EGO) algorithm, are now often used to solve deterministic optimization problems involving such expensive models. When the design accounts for uncertainties, the optimization is usually based on double loop approaches where the uncertainty propagation (e.g., Monte Carlo simulations, reliability index calculation) is recursively performed inside the optimization iterations. We have proposed in a previous work a single loop kriging based method for minimizing the mean of an objective function: simulations points are calculated in order to simultaneously propagate uncertainties, i.e., estimate the mean objective function, and optimize this mean. In this report this method has been applied to the shape optimization of a 2D air conditioning duct. For comparison purposes, deterministic designs were first obtained by the EGO algorithm. Very high performance designs were obtained, but they are also very sensitive to numerical model parameters such as mesh size, which suggests a bad consistency between the physics and the numerical model. The 2D duct test case has then been reformulated by introducing shape uncertainties. The mean of the duct performance criteria with respect to shape uncertainties has been maximized with the simultaneous optimization and sampling method. The solutions found were not only robust to shape uncertainties but also to the CFD model numerical parameters. These designs show that the method is of practical interest in engineering tasks.

Mots clés: Kriging; Gaussian process; EGO; Efficient Global Optimization; Expected improvement; Robust optimization; Optimization under uncertainty; Uncertainty Propagation; CFD; Computational Fluid Dynamics

Domaines: Ingénierie assistée par ordinateur; Machine Learning [stat.ML]; Optimisation et contrôle [math.OC]

Janis Janusevskis, Rodolphe Le Riche. Robust optimization of a 2D air conditioning duct using kriging. [Research Report] Mines Saint-Etienne. 2011. ⟨hal-00566285⟩