Non-intrusive probabilistic collocation method for operational, geometrical, and manufacturing uncertainties in engineering practice

Abstract

An industry-ready uncertainty quantification tool chain is developed and successfully applied to both simultaneous operational and geometrical uncertainties and uncertainties resulting from manufacturing variability, which are characterized by correlations of the measured coordinates. The non-intrusive probabilistic collocation method is combined with a sparse grid approach to drastically reduce the computational cost. This is one of the key features that make UQ in industrial applications feasible. A second required element is the automatization of the entire simulation chain, from uncertainty definition, simulation setup, post-processing and in case of geometrical uncertainties, geometry modification, and re-meshing. This process is fully automated including the post-processing of the UQ simulations, which consists of output PDF reconstruction and the calculation of scaled sensitivity derivatives. This tool chain is applied to the rotor 37 configuration with imposed uncertainties, demonstrating its capability of handling many simultaneous operational and geometrical or correlated manufacturing uncertainties in turnaround times significantly below the UMRIDA quantitative objectives of less than 1000CPUh for 10 simultaneous uncertainties. It is found that a level 1 sparse grid approach is sufficient if the mean and variance of output quantities are needed and a level 2 sparse grid is sufficient for the reconstructed PDF shape for most engineering applications. For manufacturing uncertainties, it is shown that a level 1 sparse grid can be used for the propagation of manufacturing uncertainties and that a surface reconstruction accuracy of 99% seems necessary for the purpose of UQ studies on manufacturing variability.