Modal identification of wind turbine tower based on optimal fractional order statistical moments

In vibration testing of civil engineering structures, the first two vibration modes are crucial in representing the global dynamic behavior of the structure measured. In the present study, a comprehensive method is proposed to identify the first two vibration modes of wind turbine towers, which is based on the analysis of fractional order statistical moments (FSM). This study offers novel contributions in two key aspects: (1) theoretical derivations of the relationship between FSM and vibration mode; and (2) successful use of 32/7-order displacement statistical moment $(M_d^{32/7})$ as the optimal FSM to identify wind turbine tower modes, by combining with noise resistance analysis, sensitivity analysis, and stability analysis, respectively. Using the proposed method, the FSM was first used to identify the modal vibration of wind turbine towers. By obtaining the response of the structure on the same vertical line, FSM was then calculated to estimate the corresponding structural modal vibration. Considering other influencing factors in the field test, the modal identification results of this index under different excitation forms and noise conditions were analyzed based on numerical simulation and verified with field wind tower test data. The results of the evaluation show that the proposed statistical moments of $M_d^{32/7}$ can accurately identify the first two vibration modes of wind turbine towers. This presents a new robust method for modal vibration identification, that is, simple and effective in its implementation.