Reduced order modeling, statistical analysis and system identification for a bladed rotor with geometric mistuning

Open Access
Vishwakarma, Vinod
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
August 14, 2014
Committee Members:
  • Alok Sinha, Dissertation Advisor
  • Christopher Rahn, Committee Member
  • Hosam Kadry Fathy, Committee Member
  • George A Lesieutre, Committee Member
  • Vishal Monga, Committee Member
  • Karen Ann Thole, Committee Member
  • turbine
  • mistuning
  • system identification
  • reduced order modeling
  • force response
  • random permutation
  • monte carlo
Modified Modal Domain Analysis (MMDA) is a novel method for the development of a reduced-order model (ROM) of a bladed rotor. This method utilizes proper orthogonal decomposition (POD) of Coordinate Measurement Machine (CMM) data of blades’ geometries and sector analyses using ANSYS. For the first time ROM of a geometrically mistuned industrial scale rotor (Transonic rotor) with large size of Finite Element (FE) model is generated using MMDA. Two methods for estimating mass and stiffness mistuning matrices are used a) exact computation from sector FE analysis, b) estimates based on POD mistuning parameters. Modal characteristics such as mistuned natural frequencies, mode shapes and forced harmonic response are obtained from ROM for various cases, and results are compared with full rotor ANSYS analysis and other ROM methods such as Subset of Nominal Modes (SNM) and Fundamental Model of Mistuning (FMM). Accuracy of MMDA ROM is demonstrated with variations in number of POD features and geometric mistuning parameters. It is shown for the aforementioned case b) that the high accuracy of ROM studied in previous work with Academic rotor does not directly translate to the Transonic rotor. Reasons for such mismatch in results are investigated and attributed to higher mistuning in Transonic rotor. Alternate solutions such as estimation of sensitivities via least squares, and interpolation of mass and stiffness matrices on manifolds are developed, and their results are discussed. Statistics such as mean and standard deviations of forced harmonic response peak amplitude are obtained from random permutations, and are shown to have similar results as those of Monte Carlo simulations. These statistics are obtained and compared for 3 degree of freedom (DOF) lumped parameter model (LPM) of rotor, Academic rotor and Transonic rotor. A state - estimator based on MMDA ROM and Kalman filter is also developed for offline or online estimation of harmonic forcing function from measurements of forced response. Forcing function is estimated for synchronous excitation of 3DOF rotor model, Academic rotor and Transonic rotor from measurement of response at few nodes. For asynchronous excitation forcing function is estimated only for 3DOF rotor model and Academic rotor from measurement of response. The impact of number of measurement locations and accuracy of ROM on the estimation of forcing function is discussed.