VIV Force Identification Using Classical Optimal Control Algorithm

Due to the difficulty of direct force measurements in vortex induced vibration (VIV) experiments with long elastic cylinders, accelerometer and bending strain measurement are available. Still, obtaining information on the force is of great interest to researchers. The work presented in this paper follows the same principle as Mainc¸on (2004), who estimated external forces acting on a riser subjected to VIV from measured response by using a classical optimal tracking algorithm. The objective of this study is to first present a method for extracting VIV forces from measured data with long elastic riser models subjected to current. The second objective is to extract first order (primary) cross-flow force coefficients by a combined use of modal filtering. The algorithm minimizes the sum of the squares of the discrepancies between measured and predicted response plus a constant times the sum of squares of the external forces, while satisfying the system’s dynamic equilibrium equation. FEM discretization of the riser with Euler beam elements leads to a stiffness and mass matrix. The dimension of these matrixes is reduced by eliminating the rotation degree of freedom using master-slave condensation, which greatly facilitates the matrix iteration. Displacement is used in this study as input to the algorithm to identify forces. The method is verified against synthetic measurement data. The results showed the algorithm’s capability to accurately estimate the input forces from noisy measurement data. The method is applied to the data from a rotating rig test to identify hydrodynamic forces in primary cross-flow vortex shedding frequency range. The emphasis is on extracting force coefficient database. One important finding is that the high mode component of the force contributed little to the response, while it resulted in complication of the coefficient data base. Therefore, they are neglected by filtering the measurement with modal analysis before the use of inverse force estimation. The excitation and added mass coefficients are calculated and their contour plots are generated. Comparisons with existing data are investigated.