High-fidelity displacement reconstruction method for offshore wind turbines under extreme sea conditions and high noise

Conventional methods, such as modal expansion, orthogonal basis superposition, and the inverse finite element method, struggle with poor noise robustness when reconstructing wind turbine tower responses under non-stationary wind loads and high measurement noise in complex sea conditions. A reconstruction methodology integrating dynamic-static hybrid basis functions with an augmented Kalman filter (DS-HB-AKF) is developed herein as a resolution to these identified limitations. The DS-HB-AKF method inherently improves reconstruction accuracy under high measurement noise through a three-step framework. First, the method constructs a hybrid basis using fourth-order modal and second-order quasi-static basis functions to establish the observation matrix and initial system model. Second, a sequential greedy algorithm minimizes the observation matrix's condition number, directly optimizing sensor placement. Finally, the augmented Kalman filter applies optimal recursive estimation to synchronously track and precisely decouple unknown quasi-static coefficients and modal coordinates from noisy observation sequences. Validation across 27 finite element simulation cases demonstrated the method's high fidelity. The relative root-mean-square error (RRMSE) of the full-field displacement reconstruction remained strictly below 18.5%, even under the most adverse combination of a 10 dB signal-to-noise ratio and a 24 m/s wind speed. The proposed method offers a potential underlying algorithm for the full-field state awareness of large offshore wind structures using limited physical measurement points.