19 April 2013 Cyclo-stationary linear parameter time-varying subspace realization method applied for identification of horizontal-axis wind turbines
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Wind energy is becoming increasingly important worldwide as an alternative renewable energy source. Economical, maintenance and operation are critical issues for large slender dynamic structures, especially for remote offshore wind farms. Health monitoring systems are very promising instruments to assure reliability and good performance of the structure. These sensing and control technologies are typically informed by models based on mechanics or data-driven identification techniques in the time and/or frequency domain. Frequency response functions are popular but are difficult to realize autonomously for structures of higher order and having overlapping frequency content. Instead, time-domain techniques have shown powerful advantages from a practical point of view (e.g. embedded algorithms in wireless-sensor networks), being more suitable to differentiate closely-related modes. Customarily, time-varying effects are often neglected or dismissed to simplify the analysis, but such is not the case for wind loaded structures with spinning multibodies. A more complex scenario is constituted when dealing with both periodic mechanisms responsible for the vibration shaft of the rotor-blade system, and the wind tower substructure interaction. Transformations of the cyclic effects on the vibration data can be applied to isolate inertia quantities different from rotating-generated forces that are typically non-stationary in nature. After applying these transformations, structural identification can be carried out by stationary techniques via data-correlated Eigensystem realizations. In this paper an exploration of a periodic stationary or cyclo-stationary subspace identification technique is presented here by means of a modified Eigensystem Realization Algorithm (ERA) via Stochastic Subspace Identification (SSI) and Linear Parameter Time-Varying (LPTV) techniques. Structural response is assumed under stationary ambient excitation produced by a Gaussian (white) noise assembled in the operative range bandwidth of horizontal-axis wind turbines. ERA-OKID analysis is driven by correlation-function matrices from the stationary ambient response aiming to reduce noise effects. Singular value decomposition (SVD) and eigenvalue analysis are computed in a last stage to get frequencies and mode shapes. Proposed assumptions are carefully weighted to account for the uncertainty of the environment the wind turbines are subjected to. A numerical example is presented based on data acquisition carried out in a BWC XL.1 low power wind turbine device installed in University of California at Davis. Finally, comments and observations are provided on how this subspace realization technique can be extended for modal-parameter identification using exclusively ambient vibration data.
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Antonio Velazquez, R. Andrew Swartz, "Cyclo-stationary linear parameter time-varying subspace realization method applied for identification of horizontal-axis wind turbines", Proc. SPIE 8692, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2013, 86921I (19 April 2013); doi: 10.1117/12.2011723; https://doi.org/10.1117/12.2011723

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