Efficient Modal Decomposition and Reconstruction of Riser Response due to VIV

Vortex-Induced-Vibrations (VIV) due to ocean currents can consume a sizable portion of the allotted fatigue life of marine risers. Vibration monitoring and concurrent estimation of fatigue damage due to VIV can significantly enhance the safe and reliable operation of risers. To this end, riser response can be characterized by using sensors (e.g. accelerometers and/or angular rate sensors) to measure the motion of the riser at a few locations. Fatigue damage can be predicted along the entire length of riser from measured data using the method of modal decomposition and reconstruction. In this method the structural response of interest, such as stress and fatigue damage, is expressed by modal superposition, where the modal weights are estimated using measured data and analytical modeshapes. However the accuracy of this method declines as the sensor density (number of sensors per unit riser length) decreases, especially when the riser vibrates in high-order modes and exhibits traveling wave behavior. In this paper, an efficient frequency-domain methodology allowing for accurate reconstruction of the riser response along the entire riser using a limited number of sensors is proposed. We first identify the excited VIV modes (natural frequency and modeshape) using principal vectors of the cross spectral density. Modal decomposition and reconstruction is performed separately for each VIV band surrounding each excited mode. This allows us to use several (as many as the number of sensors) participating modes in each band, and thus improve the accuracy. Since the stress distribution is sensitive to the chosen set of participating modes, we optimize over several candidate sets, selecting the set of modes that result in the lowest prediction error. In order to improve the reconstruction of complex modes, particularly traveling waves, the modeshapes can be augmented with additional basis vectors. The additional basis vectors are obtained by shifting the phase of the normal modes by 90 degrees at every wave number using the Hilbert transform. Though developed in the context of VIV, the method can be used to estimate fatigue damage due to vibrations regardless of the excitation mechanism. The methodology is demonstrated using the NDP (Norwegian Deepwater Program) test data on a 38 meter long slender riser, using data from eight accelerometers. Results show that the proposed algorithm can reconstruct stresses and fatigue damage accurately along the length of the riser in the presence of traveling wave behavior using relatively few sensors.