High-Dimensional Constrained Multiobjective Optimization of a Fan Stage

Abstract

A high-dimensional design space, different objectives, many constraints and a time-consuming process chain result in a complex task for any optimization tool. This paper shows methods and strategies used at DLR, Institute of Propulsion Technology, to handle this kind of problem. The present optimization task is a rotor-stator configuration with more than two hundred free design variables, two objective functions (efficiency, stall margin) and mechanical and aerodynamic constraints (mass flow, eigenfrequencies, etc.). The process chain consists of geometry and mesh generation, FEM-and 3D-CFD calculations for different operating points. After defining the setup and explaining the initial already 3-D-preoptimized configuration, the CFD/FEM optimization tool is described. This tool calculates the complete CFD/FEM process chain and creates new designs (also called members) by using an evolutionary algorithms. Parallel to the CFD/FEM optimization a program based on surrogate models is running. By using surrogate models a fast evaluation of new members is enabled. So a database of new members can be created quickly. Based on this database a set of new members is built. This is send to the CFD/FEM optimization tool, where the complete CFD/FEM process chain is applied. After the CFD/FEM evaluation process, these member are used to train the surrogate models again. This procedure repeats until the optimization goals are reached. In the next part of this paper the implemented surrogate models are discussed. Both neural networks and Kriging models have advantages and disadvantages compared to each other. It is important to understand them to choose the right model at the right time of optimization. The main focus of this paper is on the selection criterion for new members. This criterion has two targets: push the performance of the fan stage and enhance the surrogate models. At first sight these targets seem to be contrary, but the surrogate models do not predict a single mean value for an objective. They offer a density distribution of the potential objective values. That allows calculation of the Paretofront enhancement (ParetoEnSet) for a set of new members. ParetoEnSet is the expected area gain of a set of members to the current Paretofront. This criterion based on the already known expected improvement. It is shown, that ParetoEnSet can rise, when the uncertainty of an prediction increases. The uncertainty is estimated by a surrogate model. So new members tend to explore the design space, where the predicted uncertainty is huge. These members are favorable for improving the surrogate models. In addition, it is easy to couple constraints with ParetoEnSet. In the last section the results of the optimization are illustrated. Compared to baseline design the optimized stage accomplishes a notable improvement in efficiency by obtaining the stall margin and fulfilling multi aerodynamical and mechanical constraints.