Conventional amplitude-based indicators may be insufficient to characterise the effects of varying crack elevation in offshore wind turbine towers. To address this limitation, a bidirectional multi-feature sensitivity analysis was conducted using a finite element model based on the NREL 5 MW reference wind turbine. Transient dynamic analyses were performed in ANSYS under combined stochastic wind–wave loading. One intact case and five cracked cases with identical crack dimensions but different elevations were considered. Acceleration responses in the X and Y directions were extracted at eight measurement points. The root-mean-square value, peak absolute acceleration, dominant frequency, and frequency-band energy indices were calculated, and their sensitivities to variations in crack elevation were quantified using the absolute relative change with respect to the intact case. Under the adopted loading conditions, the X-direction response exhibited a larger overall amplitude. However, the RMS and frequency-band energy indices exhibited higher relative sensitivities in the Y direction, whereas the peak-value sensitivity was higher in the X direction. No detectable change in dominant frequency was observed at the adopted frequency resolution. Among the investigated features, the frequency-band energy in the 0–0.05 Hz band exhibited the highest sensitivity in both directions. Among the eight candidate measurement points, P1 showed the highest sensitivity under the considered loading and crack cases, and the sensitivity generally decreased with increasing measurement height. These findings provide a basis for damage-sensitive feature selection and sensor-layout optimisation in crack monitoring of offshore wind turbine towers.

Abstract
1. Introduction
2. Finite element modelling of the offshore wind turbine tower and load application
    2.1 Basic specifications of the NREL 5 MW reference wind turbine
    2.2 Establishment of the finite element model
    2.3 Application of wind and wave loads
    2.4 Modal analysis of the tower
    2.5 Transient dynamic analysis settings
3. Crack cases and arrangement of measurement points
    3.1 Crack case settings
    3.2 Arrangement of measurement points
4. Feature extraction methods and bidirectional sensitivity analysis
    4.1 Feature extraction methods
    4.2 Sensitivity analysis of X/Y bidirectional features
5. Discussion
6. Conclusions
References

• Kexin Zhang(School of Naval Architecture and Port Engineering, Shandong Jiaotong University, Weihai 264209, China)
• Zhuoyi Yang(School of Naval Architecture and Port Engineering, Shandong Jiaotong University, Weihai 264209, China) Corresponding author
• Jingkai Bi(School of Naval Architecture and Port Engineering, Shandong Jiaotong University, Weihai 264209, China)
• Pengfei Ge(School of Naval Architecture and Port Engineering, Shandong Jiaotong University, Weihai 264209, China)
• Jiaxin Zhang(School of Naval Architecture and Port Engineering, Shandong Jiaotong University, Weihai 264209, China)