Displacement estimation from measured acceleration for fixed offshore structures

For offshore structures in service such as offshore platforms and offshore wind turbines, their displacements are expected but can be difficult to measure directly due to the lacking of fixed reference points in ocean. Aiming at obtaining displacements of offshore structures from accelerations which can be easily measured by accelerometers, a new non-integration displacement reconstruction method is proposed in this paper. The complex exponential series is adopted to establish a relationship between the measured acceleration and the targeted displacement. Compared to direct-integral or high-pass filtering methods, one theoretical development in the present approach is that the reconstructed displacement is derived from the estimated complex exponential parameters of measured acceleration signal with a form of fraction, and the components that cause the drift could be identified and removed, thus significantly reducing the drift issue typically experienced by traditional methods. Additionally, a challenging problem involving the estimation of velocity and displacement at the measured starting moment is solved, which implies that the noises contained in the measured acceleration signal will not be amplified during the conversion from acceleration to velocity and displacement. To investigate the performance of the proposed method, one numerical example and two physical experiments are carried out sequentially. The selected numerical example is a 4-dof system, which aims at verifying the correctness and investigating the robustness of the proposed method. Numerical results show: (1) velocities and displacements can be accurately reconstructed from noise-free acceleration signals with an obvious baseline offset; (2) even when the acceleration signals are contaminated with 15% Gaussian noise, a good estimation of velocities and displacements can still be obtained. Subsequently, a steel beam fixed on a shaking table is tested, and two accelerometers and two laser displacement sensors are used to measure the dynamic responses of the table as well as the top of the beam, respectively. The experimental results show a good agreement between the reconstructed displacements and the measured data from the laser displacement sensors. Finally, a four-leg offshore platform is investigated experimentally to assess the potential application of the present method in ocean engineering. It is observed from the experimental results that the maximum absolute difference in the amplitude between the reconstructed and measured displacements is 0.47 mm with the computed peak displacement error of 0.3166, which further confirms the feasibility and correctness of the proposed method.