Geometric Mistuning Reduced Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

Abstract

Abstract By design, Integrally Bladed Rotors (IBRs) are meant to be tuned, rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, referred to as mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned-structure analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model. To overcome this expense, Reduced Order Models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. This method, referred to as the Surrogate Modal Analysis for Geometry Mistuning Assessments (SMAGMA), will propagate the uncertainties of the surrogate prediction to the forced response. Assessments of the ROM accuracy are made by comparing results to the true forced response levels and results computed by a frequency-based ROM.