TSI metamodels-based multi-objective robust optimization

Purpose - This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account. Design/methodology/approach - ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows. Findings - First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1-T̄_TSI )× 100, where T̄_TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy. Originality/value - Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field.