Model Order Reduction for Prediction of Turbine Engine Rotor Vibration Response in Presence of Parametric Uncertainties

Statistical inhomogeneity of material properties, variations in nominal geometry, manufacturing tolerances, operational wear lead to uncertainties in the parameters associated with FE models of turbine engine rotors and consequently to uncertainties in their vibration response. Reliable assessment of the rotor system behavior cannot be made unless the effects of such uncertainties are understood and quantified. In practical situations the parametric probabilistic approach is the first choice to employ in that context yielding efficient algorithms with feasible implementations. A set of measured or estimated experimentally random parameters is repeatedly propagated through rotor models in Monte-Carlo simulations, which would pose a formidable computational task if the full order high-fidelity finite element (FE) models were utilized. The objective of this dissertation is to decrease the expense of analyzing systems modified in the parametric space by developing accurate model reduction computational techniques suitable for repeated analysis, in particular addressing the problem of large variations in nominal geometry. The first part of the dissertation is concerned with the structural blade mistuning problem. The existing projection based model order reduction techniques capable to numerically characterize variations in nominal geometry of periodic structures are examined, a method generating very compact reduced order models (ROM) based on correction, as opposed to expansion, of the modal subspace is selected and its limitations are analyzed. A new algorithm drawing on optimal preconditioned iterative methods for generalized eigenvalue problem is introduced to address its deficiencies. Both techniques are combined in a stochastic simulation framework to analyze the effect of random mistuning on geometrically modified bladed disks, where random parameter variation in blade properties is introduced in modal space at component level. A family of benchmark problems on an industrial scale bladed disk model are utilized in a comparative study assessing the amount of computational effort and storage, scalability and accuracy as well as providing insight on underlying physical phenomena. In the second part of dissertation a new computational technique is proposed focusing on prediction of the effects of uncertainty in rotor assembly inter-stage geometry on global vibration response. The algorithm stands apart from the traditional modal projection based framework employing harmonic truncation only. It is shown that decent performance can be achieved due to reliance on sparse matrix linear algebra and sampling of small parametric space. Particular emphasis is given to the computational efficiency of ROM update. Accuracy and performance of the technique is illustrated with representative simulation examples over a practical range of geometrical parameter variations and operational conditions.