Title: Design of a matrix hydraulic turbine using a metamodel-assisted evolutionary algorithm with PCA-driven evolution operators

Authors: Stylianos A. Kyriacou; Simon Weissenberger; Kyriakos C. Giannakoglou

Addresses: Andritz HYDRO, RD, Lunzerstrasse 78, 4031 Linz, Austria; National Technical University of Athens, Parallel CFD and Optimisation Unit, P.O. Box 64069, Athens 15710, Greece. ' Andritz HYDRO, RD, Lunzerstrasse 78, 4031 Linz, Austria. ' National Technical University of Athens, Parallel CFD and Optimisation Unit, P.O. Box 64069, Athens 15710, Greece

Abstract: To overcome the excessive CPU cost of evolutionary algorithms (EAs) which make use of demanding evaluation models, metamodel-assisted EAs (MAEAs) have been devised and used in either single-objective (SOO) or multi-objective (MOO) problems. MAEAs are based on low-cost surrogate evaluation models that screen out non-promising individuals during the evolution and exclude them from the expensive, problem-specific evaluation. This paper proposes a new technique that further reduces the computational cost of MAEAs. This technique is based on the principal-component-analysis (PCA) of the non-dominated individuals (in MOO) within each generation, to identify dependences among the design variables and, through appropriate rotations, use this piece of information to efficiently |drive| the application of the evolution operators. The proposed technique is used to perform the multi-operating point design of a matrix hydraulic turbine, where each evaluation is based on a 3D computational fluid dynamics (CFD) code; this is a highly constrained optimisation problem with many objectives, which is herein handled as a two-objective one. Some convincing mathematical function minimisation problems are also worked out using PCA-driven EAs; it is, thus, shown that the PCA-driven evolution operators can be used with or without metamodels.

Keywords: optimisation; evolutionary algorithms; EAs; metamodelling; correlated design variables; hydraulic turbines; turbine design; principal component analysis; PCA; computational fluid dynamics; CFD; constrained optimisation.

DOI: 10.1504/IJMMNO.2012.044713

International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.1/2, pp.45 - 63

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 04 Jan 2012 *

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