Fushun Liu

Pole-Residue Method for Numerical Dynamic Analysis

AbstractSystems of second-order linear ordinary differential equations (ODEs) to arbitrary input functions appear in many fields of physics and engineering. Numerical methods for solving these kinds of problems have been mainly performed in the time and frequency domains. In contrast, this paper develops an efficient, seminumerical pole-residue method implemented in the Laplace domain. In this article, a key concept and development is on how to compute the poles and residues of the output from those of the input and system transfer functions. Once the poles and residues of the output are known, the corresponding time history of the output is readily obtained. Even though the correctness of the new method has been verified by using a step-by-step time-domain solution, the accuracy of the new method in theory is higher than that of any time-domain approach, partially because the output obtained from the new method is a continuous function of time.

Spectrum response estimation for deep-water floating platforms via retardation function representation

The key concept of spectrum response estimation with commercial software, such as the SESAM software tool, typically includes two main steps: finding a suitable loading spectrum and computing the response amplitude operators (RAOs) subjected to a frequency-specified wave component. In this paper, we propose a nontraditional spectrum response estimation method that uses a numerical representation of the retardation functions. Based on estimated added mass and damping matrices of the structure, we decompose and replace the convolution terms with a series of poles and corresponding residues in the Laplace domain. Then, we estimate the power density corresponding to each frequency component using the improved periodogram method. The advantage of this approach is that the frequency-dependent motion equations in the time domain can be transformed into the Laplace domain without requiring Laplace-domain expressions for the added mass and damping. To validate the proposed method, we use a numerical semi-submerged pontoon from the SESAM. The numerical results show that the responses of the proposed method match well with those obtained from the traditional method. Furthermore, the estimated spectrum also matches well, which indicates its potential application to deep-water floating structures.

Mode shape identification using residues of measured offshore structure data

Compared to traditional mode shape identification methods such as eigensystem realization algorithm (ERA), this article proposes a mode shape identification method based on estimated residues of measured data and the theoretical relationship between the estimated residues and the mode shapes from the state space model is obtained by defining a coefficient matrix. A mass-spring model with five degrees of freedom (DOFs) is utilized to demonstrate the approach. The numerical results indicate that the estimated residues are the mode shapes of structures, but with a coefficient matrix to maintain consistency with the mode shapes from the ERA. Using MATLAB a complicated numerical jacket platform is built to further study the proposed method. The results show that mode shapes consistent with those from the ERA could be obtained by taking the defined coefficient matrix into account, which is also demonstrated by a physical beam model that was built at Ocean University of China.

An improved lower order method of modal parameter estimation for offshore structures using reconstructed signals

For modal parameter estimation of offshore structures, one has to deal with two challenges: 1) identify the interested frequencies, and 2) reduce the number of false modes. In this article, we propose an improved method of modal parameter estimation by reconstructing a new signal only with interested frequencies. The approach consists of three steps: 1) isolation and reconstruction of interested frequencies using FFT filtering, 2) smoothness of reconstructed signals, and 3) extraction of interested modal parameters in time domain. The theoretical improvement is that the frequency response function (FRF) of filtered signals is smoothed based on singular value decomposition technique. The elimination of false modes is realized by reconstructing a block data matrix of the eigensystem realization algorithm (ERA) using the filtered and smoothed signals. The advantage is that the efficiency of the identification process of modal parameters will be improved greatly without introducing any false modes. A five-DOF mass-spring system is chosen to illustrate the procedure and demonstrate the performance of the proposed scheme. Numerical results indicate that interested frequencies can be isolated successfully using FFT filtering, and unexpected peaks in auto spectral density can be removed effectively. In addition, interested modal parameters, such as frequencies and damping ratios, can be identified properly by reconstructing the Hankel matrix with a small dimension of ERA, even the original signal has measurement noises.

PERIODIC DAMAGE EVALUATION OF AGING OFFSHORE JACKETS BASED ON CONTINUOUS DYNAMIC TESTS

This study proposes a new method for evaluating the damage of aging offshore platforms, based on dynamic tests. The proposed method involves a new damage indicator for reducing the effects of occurred damages accumulated before the first measurement. One theoretical improvement is that the requirement of using the stiffness matrix of the finite element model to replace that of the measured model can be ignored in calculating the modal strain energy of the measured model. The other development is that the proposed approach can be used for providing reasonable evaluations of damages that occurred between two adjacent dynamic tests. This improvement is crucial for evaluating aging platforms because such platforms have seldom been tested for damage detection during their previous service life. For demonstrating the applicability of the proposed method, numerical studies were conducted for a 3D offshore platform based on data generated from finite element models. The results indicated that the proposed method can be used to identify accurately the damages that occurred between the two measurements and to provide an accurate estimation of damage severity.