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Research Papers

Determination of Modal Parameters in Complex Nonlinear Systems

[+] Author and Article Information
Peter F. Skjoldan

Loads, Aerodynamics, and Control, Siemens Wind Power A/S, 2630 Taastrup, Denmarkpeter.skjoldan@siemens.com

Olivier A. Bauchau

Georgia Institute of Technology, School of Aerospace Engineering, Atlanta, GA 30332-0150olivier.bauchau@ae.gatech.edu

J. Comput. Nonlinear Dynam 6(3), 031017 (Mar 02, 2011) (10 pages) doi:10.1115/1.4002975 History: Received March 23, 2010; Revised October 27, 2010; Published March 02, 2011; Online March 02, 2011

This paper describes a methodology for evaluating the modal parameters of complex nonlinear systems. It combines four different tools: the Coleman post-processing, the partial Floquet analysis, the moving window analysis, and the signal synthesis algorithm. The approach provides a robust estimation of the linearized modal parameters and qualitative information about the nonlinear behavior of the system. It operates on one or multiple discrete time signals and is able to deal with both time-invariant and periodic systems. The method is computationally inexpensive and can be used with multiphysics computational tools, and in principle, with experimental data. The proposed approach is validated using a simple, four degree of freedom model of a wind turbine. The predictions for the linear system are validated against an exact solution of the problem. For the nonlinear system, it is demonstrated that qualitative information concerning the nonlinear behavior of the system is obtained using the proposed method. Finally, the nonlinear behavior of a realistic, three-bladed horizontal axis wind turbine model is investigated.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Selecting various windows for a signal

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Figure 2

Simplified model of a three-bladed wind turbine

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Figure 3

Simplified model frequencies. Reference solution: dashed lines; PFA for periodic system: symbols “●;” and PFA with CPP: symbols “×.”

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Figure 4

Simplified model frequencies. Reference solution: dashed lines; and PFA for time-invariant system: symbols “○.”

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Figure 5

Largest singular values in decreasing order for the three approaches. Periodic PFA: symbols “●;” time-invariant PFA: symbols “○;” and PFA with CPP: symbols “×.”

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Figure 6

Signals from the window starting at time 0. Original signals (top) and signals after applying CPP (bottom). Computed signals: solid line; and reconstructed signals: dashed line.

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Figure 7

System frequencies (top) and damping ratios (bottom) for the MWA

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Figure 13

Frequency identification using the MWA for the moderate (M) and high (H) excitation level

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Figure 14

Damping ratio identification using the MWA

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Figure 15

Modal amplitudes from MWA for signal ua0

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Figure 16

Modal amplitudes from MWA for signal ua1

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Figure 20

Modal amplitudes from MWA for signal ua1

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Figure 21

Modal amplitudes from MWA for signal ut

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Figure 8

Amplitudes of the modes contained in the θa1 signal

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Figure 9

Damping ratio versus modal amplitude

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Figure 10

Damping ratio versus modal amplitude. (γ¯t=−0.002,  γ¯b=−0.01).

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Figure 11

Largest singular values in decreasing order for complex wind turbine model

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Figure 12

Identified frequencies as function of rank number

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Figure 18

Damping ratio identification using the MWA

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Figure 19

Modal amplitudes from MWA for signal ua0

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Figure 17

Modal amplitudes from MWA for signal ut

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