A rapid response calculation method for symmetrical floating structures based on state-space model solving in hybrid time-Laplace domain
A rapid response calculation method for symmetrical floating structures based on state-space model solving in hybrid time-Laplace domain
复制标题
基于混合时拉普拉斯域状态空间模型求解的对称浮体结构快速响应计算方法
DOI：
10.1016/j.oceaneng.2020.107227
复制
发表时间：
2020
影响因子：
5
通讯作者：
Hou Falei
中科院分区：
文献类型：
--
作者：
Lu Hongchao;Fan Tianhui;Zhou Lin;Chen Chaohe;Yu Guangming;Li Xiaochen;Hou Falei
通过求解康明斯方程，基于传递函数辨识出的状态空间模型，提出了一种新的对称浮体时-拉混合域响应计算方法。与时域或频域方法不同，该方法从拉普拉斯域的传递函数估计浮式结构系统的状态空间模型，并将激振力作为状态空间模型的输入来计算响应。通过对迟滞函数进行复指数分解，将拉普拉斯域内的迟滞函数用一系列极点和相应的留数表示，避免了康明斯方程中卷积项的数值积分，大大提高了动力响应分析过程中的计算效率。通过三个算例验证了该方法的有效性。第一个是一个简单的单自由度的数学模型激发的不规则波。研究表明，该方法计算的响应与传统Newmark-β方法计算的响应吻合较好。同时，该方法对计算间隔时间不敏感，计算时间少，具有较高的精度和计算效率。最后两个例子是一个Spar型海上风力涡轮机和一个半潜式平台模型（SEMI）在SESAM，扩展所提出的方法来解决响应估计问题的海洋结构。对某Spar型浮体结构的计算结果表明，该方法与传统的时域法计算结果吻合较好。通过对SEMI响应计算的研究，可以得出以下结论：（1）估计的响应与传统的时域方法和SESAM的WASIM程序相匹配;（2）与Newmark-β方法相比，新方法的计算时间显著减少，特别是在较长的仿真时间下。
The article focuses on proposing a new hybrid time-Laplace domain response calculation method for symmetrical floating structures by solving Cummins equation, which is depending on the state–space model identified from transfer function. Different from a time or frequency domain method, the proposed approach estimates the state–space model of a floating structure system from the transfer function in the Laplace domain and calculates the response by considering the exciting forces as an input of the state–space model. Implementing complex exponential decomposition to the retardation functions, the retardation functions in the Laplace domain are expressed using a series of poles and the corresponding residues, which avoids the numerical integral of the convolution terms in the Cummins equation and greatly improves the computational efficiency during the process of a dynamic response analysis. Three examples are applied to investigate the validity of the proposed method. The first is a simple single degree of freedom mathematical model excited by an irregular wave. Studies have shown that the response calculated by the proposed method matches well with that of a traditional Newmark-β method. Meanwhile, this approach is insensitive to the interval time of the calculation and consumes less calculation time, which means that the proposed method has higher precision and computational efficiency. The last two examples are a spar-type offshore wind turbine and a semi-submersible platform model (SEMI) in SESAM, which extend the proposed method to solve the response estimation problem of marine structures. The results of the spar-type floating structure show that the estimated responses when using the proposed method are in good agreement with the results of the traditional time domain method. By studying the response calculation of SEMI, the following conclusions can be obtained:(1) the estimated responses match well with the traditional time domain method and WASIM code of SESAM, and (2) the calculation time of the new approach is reduced significantly compared with the Newmark-β method especially under a long simulation time.