Kriging is increasingly used in metamodel-assisted design optimization. For expensive simulations; however, one can afford only a few samples to build the Kriging model, which consequently lacks prediction accuracy. We propose a bounded Kriging able to handle optimization problems with a small initial database. During the optimization, the proposed Kriging suggests designs close to database samples and finds optimal designs while staying in a feasible region (with respect to mesh and CFD convergence). The bounded Kriging is applied along with the ordinary Kriging to a multidisciplinary design optimization of a radial compressor. The shape of the compressor blades is optimized by considering the aero performance at different operating points and the mechanical stresses. The objective of the optimization is to maximize the efficiency at two operating points, while constraints are imposed on the maximum stress level in the material, the choke mass flow, the pressure ratio and the momentum of inertia of the impeller. While ordinary Kriging stopped prematurely because of many failing design evaluations, the bounded Kriging satisfied all constraints and reached an improvement of 2.59% in efficiency over the baseline design that does not comply with any constraints. The bounded Kriging covers a special need for robust methods in optimization able to deal with challenging geometries and a small database, which is the case for most industrial design optimizations.
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