Replacement of force-to-motion relationship with state–space model for dynamic response analysis of floating offshore structures

Abstract

The Cummins equation is commonly used to express the motion behaviour of a floating offshore structure. It is a differential equation with convolution terms, which make it inconvenient to conduct a dynamic response analysis. Moreover, the calculation of the simulation response is not highly efficient because of the presence of these convolution terms, and a serious error accumulation problem occurs when calculating the dynamic response using a numerical integration method. Therefore, a method for estimating the dynamic response of a floating offshore structure by replacing the force-to-motion relationship with a state–space model has been described in literature. One theoretical development is the translation of dynamic response calculation for a floating structure into the task of obtaining the output of the state–space model system, which is easy to implement and convenient to use for designing motion control systems. Meanwhile, this method does not require the calculation of the convolution terms, which implies that the algorithm can considerably improve the calculation efficiency of a dynamic response simulation and avoid the problem of error accumulation. Three examples were used to verify the proposed algorithm. The first was a single degree of freedom system in the form of the Cummins equation, which was used to exhibit the entire process of the proposed algorithm. Studies have shown that the dynamic response computed by the proposed method is in accordance with that of the average acceleration method, and the proposed method can avoid the error accumulation caused by large time steps. The second was a semi-submersible floating offshore wind turbine, which expanded the application of the proposed algorithm to an estimation of the dynamic response of a floating offshore structure with six degrees of freedom. The results showed that the proposed algorithm, as compared with the time domain method, could obtain an accurate response and avoid the numerical dissipation problem in the numerical integration algorithm. Meanwhile, the computational efficiency of the proposed method was significantly higher than that of the average acceleration method. The last example was a physical model of a semi-submersible platform. The heave response estimated using the proposed algorithm was good match with the experimental data.