9 Operational Vibration-Based Response Estimation for Offshore Wind Lattice Structures 93 Fig. 9.8 Corrective force estimation at node 283 with erroneous design model, based on measurements with and without measurements noise, presented in (a) the frequency-domain and (b) the time-domain Fig. 9.9 Corrective force estimation at node 155 with erroneous design model, based on measurements with measurements noise, presented in (a) the frequency-domain and (b) the time-domain 9.3.2 Response Estimation with an Erroneous Model A second response estimation is performed, this time with a design model that does not exactly represent the true structure. Process noise is deliberately introduced in the design model, by increasing the first and second natural frequency with 20 %. The first and second natural frequency of the design model are 0.437 and 1.21 Hz, instead of 0.364 and 1.07 Hz of the model with which the data is generated. Again, the measurement data is polluted with 5 % measurement noise. The inclusion of process noise complicates the estimation of the true forces and states. Instead, the joint inputstate estimator enables the estimation of equivalent forces and states, which combined enable the response estimation at unmeasured structure locations. To lesser extent, this was already observed in the previous section, where only measurement noise was accounted for. To optimize the functioning of the estimation algorithm, the entries of the Qmatrix are adjusted. The covariance of the process noise cannot be as easily estimated as the covariance of the measurement noise. By choosing the square roots of the process noise covariance entries of the same order of magnitude as a small percentage of the states, the covariance matrix entries can be made to correspond with what they represent [24]. When considering the frequency content of the estimated corrective forces, see Figs. 9.8 and 9.9, the force signals clearly compensate for the unmodelled dynamics. The corrective forces contain frequency peaks at the true natural frequencies The corresponding time signals illustrate the deviation of the estimated force from the true force. The effect of the measurement
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