Geometric Parameterization of Reduced-Order Models and Applications to Rotating Systems

The present thesis focuses on parameterized reduced-order models (pROMs). These lower-order models are derived from full-order models that are parameter-dependent. Examples of parameters include geometry configurations, material properties, initial conditions, and operating or loading conditions. This work proposes both geometric and operating conditions parametrization of a physical model whose system matrices are expressed in an affine representation. From the Finite Element Method formulation, affine parameter dependencies of full-order system matrices were derived for both geometric and operating conditions parameterizations. Affine dependency is advantageous, as it preserves its functional form in the reduced matrices, meaning that the same type of relationship as in the full matrices is retained. Subsequently, different reduction techniques were employed to identify one capable of maintaining the master-slave structure while preserving affine parameter dependence. This phase results in the generation of a parameterized reduced-order model. Finally, these reduced-order models were validated on models of varying complexity. Special focus was placed on the accuracy of the dynamic features, such as natural frequencies and mode shapes, computed by the parameterized reduced-order model compared to the full-order model.