Shape sensing of a wind turbine tower based on a one-sided four-node quadrilateral inverse shell element with a coupling functional

With the development of renewable energy, wind power became a reliable solution. The inverse finite element method (iFEM) achieved shape sensing of wind turbine towers based on finite strain data, which demonstrated significant potential for applications in real-time structural health monitoring (SHM). However, in practical engineering, the implementation of the measurement method with double-sided strain placement presented certain challenges that were difficult to overcome. A single-sided four-node quadrilateral inverse shell element method with coupled functional (iQS4_S_C) was proposed based on the coupling relationship between single-sided measured strain, membrane strain, and bending strain. The method was employed for shape sensing of a wind turbine tower to enable efficient monitoring under single-sided measurement conditions. An improved method with reduced sensor placement (iQS4_S_C_R) was introduced to optimize sensor placement schemes and still achieved effective shape sensing with fewer strain sensors. The sensing results based on virtual strain measurement indicated that the iQS4_S_C method exhibited excellent performance in shape sensing and demonstrated strong robustness. For the critical node at the top of the tower, the average error of the iQS4_S_C method under noise-free condition was 1.95 %, and under a 20 dB signal-to-noise ratio (SNR), no significant increase was observed, with the error remaining approximately 1.95 %. The robustness of iQS4_S_C_R was also superior to that of iQS4.