An improved time-domain response estimation method for floating structures based on rapid solution of a state-space model

Abstract

The proposed time-domain response estimation method aims to improve computational efficiency of the traditional step-by-step techniques by considering convolution item with a state-space model for floating structures. Different from the present three techniques of estimating state-space model matrices, which are the impulse response curve fitting, the realization theory and the regression in the frequency domain, a more accurate and efficient algorithm has been developed by constructing these matrices with poles and residues of retardation functions. One theoretical development is that the poles and residues are estimated by using the state-space model, not directly by solving ordinary differential equations, which implies that the traditional ill-conditioned issue can be reduced significantly. Meanwhile, this algorithm is a direct estimation procedure and also does not require initial values during the process of computing state-state model matrices, which means that a better computational efficiency can be expected. To investigate the performance of the proposed method, three examples are employed. The first example is a numerical retardation function that is based on a purely analytical relationship, and this function satisfies all the properties of the convolution terms in math. By comparing the approach with the three techniques of estimating state-space model matrices, one can draw the conclusion that the approach provides accuracy similar to that of the regression method but outperforms the curve fitting and the realization methods, obviously because of the improperly used initial values. The second example is a single-degree-of-freedom system excited by different forms of external load. Numerical results show that a dynamic response analysis using replacement of convolution with the proposed method is in accordance with the traditional frequency and time domain method. However, the proposed method is insensitive to the step size of the calculation, which means that the proposed method is more stable. To extend the proposed method to a system with multiple degrees of freedom and investigate the capacity for computational efficiency, a semi-submersible platform was used. Conclusions from the numerical and experimental studies can be drawn: (1) the estimated response of the platform by using the proposed method to replace convolution items with a state-space model matches well with the traditional Newmark-β method; (2) the calculation time is reduced significantly using the proposed method when the number of calculation steps is large; and (3) the heave response of semi-submersible physical model calculated by the proposed method is in good agreement with the experimental data.