9 Operational Vibration-Based Response Estimation for Offshore Wind Lattice Structures 95 Fig. 9.11 Time signal representation of the strain response estimation with erroneous design model at two lattice members: (a) node 21 and (b) node 246 Fig. 9.12 Frequency domain representation of the strain response estimation with erroneous design model at two lattice members: (a) node 21 and (b) node 246 and states are estimated from measurements with a noise level of 5 % with a finite element model in the absence of modelling errors. From this, the strain response at chosen locations on the lattice structure is estimated, which could eventually serve the estimation of the accumulated fatigue damage. Subsequently, a design finite element model is constructed by adjusting the main natural frequencies. This design model is applied to estimate the strain response in the lattice structure on the basis of the true response measurements. The response estimates show that the main frequency content can be captured relatively accurately. The estimations with the design model, with a 20 % error on the first and second natural frequency, do show a small bias with respect to the real response, resulting from the invalidity of the zero-mean assumption used for the process noise. This bias, however, will not harm the quality of the accumulated fatigue damage estimation, since for this only the magnitude of the strain cycles is of interest. Nevertheless, the strain response estimates do contain some high frequency disturbance in which the sixth natural frequency of the system is most pronounced. The occurrence of this disturbance can be related to the ill-conditioning of the observability matrix. The analysis illustrated the trade-off between the accuracy of the reduced-order finite element model and the illconditioning of the observability matrix. The modal basis of the finite element model should account for a sufficient number of modes to describe the dynamic response sufficiently accurate. Certain modes, however, can be hardly observable, implying ill-conditioning of the observability matrix. In this particular case, the observability of mode 6 is small, resulting in the noisy disturbance of the estimated response. Excluding mode 6 from the modal basis would decrease the ill-conditioning of the observability matrix and, of course, result in strain estimates without the disturbance from the sixth natural frequency. On the other hand, further reduction of the modal basis would increase the modelling error in the design model.
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