Optimization of a centrifugal turbine rotor for robustness and reliability against manufacturing tolerances

The classic approach in turbomachinery design optimization considers only nominal geometries while manufacturing tolerances are evaluated in post-processing. Without any knowledge about such deviations, the optimizer chooses the solution corresponding to the highest attainable performance. However, such a shape may require tight and expensive tolerances to maintain the expected performance in large-scale populations or even necessitate tolerances not realizable with the available manufacturing process. Therefore, the entire optimization activity would need to be re-run to look for a more robust solution. In contrast, Uncertainty Quantification (UQ) methods take into account the tolerances applicable to every design parameter and propagate those uncertainties to the output. When applied in combination with an optimizer, performance data along with information related to the robustness and reliability of every geometry become available, thus allowing to find optimal solutions that are less sensitive to the design parameters deviations. In this work, we present the development of an efficient evaluation framework through the application of the Probabilistic Collocation method, a sampling-based UQ technique generating high-fidelity statistical data of the uncertainties impact on the output solution, coupled with the Smolyak algorithm to reduce the sampling size. A metamodel-assisted approach steers the optimization using surrogate modeling to rapidly approximate the statistical data using the Monte-Carlo method. The UQ model is invoked only when the optimizer approaches convergence in order to confirm the robustness of the identified optimum or to lead the optimization to a more robust region of the design space. The methodology is applied to the robust optimization of a radial turbine rotor with 32 design variables, nine of which were affected by uncertainties. The proposed approach provides a more robust and reliable design against geometrical uncertainties, in addition to the sensitivity analysis, with an estimated overhead below 30% of the cost of a traditional design optimization.