Stochastic response control of 2D jacket structure using MR damper

Abstract

The jacket structure is one of the most important structures in the offshore industry. It is mainly installed in relatively shallow water conditions. The jacket structures are subjected to continuous wave forces, which severely affect the life of the offshore platform. Generally, the jacket structures are designed such that their response is small under its environmental loads, but it also increases the cost. So, controlling its response is a good alternative to increase its life span. In this study, a 2D jacket structure in a water depth of 120m is studied for its response control using Magneto-Rheological damper (MR damper). MR dampers have been successfully implemented in semi-active control of civil structures. They have been well proven in controlling the structural responses subjected to multiple frequency excitations. The MR damper's semi-active control algorithm requires the calculation of optimal force by assuming the structure to be linear. This optimal force can be obtained using various methods, and one such widely used method is the Linear Quadratic Regulator (LQR) strategy. The ocean waves are random, and hence the stochastic LQR Linear Quadratic Gaussian (LQG) has to be used to compute the optimal control force on the structure. This optimal force calculated can further be used by the MR damper's semi-active control algorithm to obtain the controlled response. From the theory of the LQG method, the input excitation has to be a white noise process, but the ocean waves that excite the offshore platforms are a narrow band process. So, the spectral content of the input excitation is captured using the shaping filters. The shaping filters are designed to obtain the required narrow banded spectrum of the water particle kinematics at different points of the structure. The filters are designed such that the cross-correlation of the excitation at various offshore platform points is maintained. The Cholesky factorization of the spectral matrix at various grid points degenerates the problem into a single input multiple output problem. Thus, individual fitting of the factorized spectral matrix components is sufficient to obtain the correct cross-correlation along with the depth. The 2D jacket requires the water particle kinematics to be calculated at different horizontal locations also. This horizontal propagation problem requires developing an ‘All-Pass’ filter, which allows one to design the phase shift at different frequency components while maintaining the unit magnitude transfer function. The developed filter equations are then augmented to the original jacket structure, and LQR gains are computed for the stochastic regulator problem. A Kalman filter is designed, and the state estimate is obtained for each time step, which is further used in the calculation of the optimal force. It is shown that stochastic structural control works for an offshore structure like the jacket, and control efficiencies and limitations under various conditions are discussed.