Q-shift dual-tree complex wavelet phase-based vibration displacement measurement for wind turbine towers

In the context of the global energy transition, wind turbine towers serve as the primary load-bearing structures of wind energy systems, and accurate measurement of their vibration-induced displacements is essential for structural health monitoring and safety assessment. Conventional contact-based measurement techniques suffer from complex installation procedures and limited spatial coverage. In contrast, existing vision-based vibration measurement methods are often highly dependent on surface texture and exhibit insufficient phase stability under challenging imaging conditions. To address these limitations, this study proposes a non-contact vibration displacement measurement method for wind turbine towers based on the phase information of the Q-shift dual-tree complex wavelet transform. The proposed approach exploits the multi-scale and multi-directional complex coefficients obtained from the Q-shift dual-tree complex wavelet decomposition to construct a phase representation with approximate shift invariance and improved inter-scale consistency. Displacement estimation is performed within regions exhibiting stable phase responses, such as structural edges, thereby enhancing robustness against complex backgrounds and noise. Furthermore, an adaptive downsampling strategy is introduced to alleviate phase wrapping effects in large-scale structural vibrations, enabling reliable displacement measurement under relatively large vibration amplitudes. Numerical simulations and wind turbine tower model experiments demonstrate that the proposed method achieves sub-pixel displacement accuracy under complex environmental conditions. Compared with conventional vision-based approaches based on phase or image intensity information, the proposed method exhibits superior overall stability, providing a high-precision and robust visual vibration measurement solution for the non-contact monitoring of tall and flexible structures.