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摘要: 根据时域运动方程快速计算的需求, 采用4种基于辨识理论并适用于时延函数快速计算的方法, 建立替代卷积分项的状态空间模型, 同时满足时延函数性质与拟合质量; 以海洋石油286船为研究对象, 分别采用频域和时域辨识方法进行时延函数拟合结果的对比。计算结果表明: 当置信度为0.99时, 频域回归法和频域迭代法拟合结果与期望值整体趋势一致, 在频率为0.92~1.05rad·s-1时达到峰值, 然后逐渐衰减, 最后趋于0;在频率为0.05~0.50rad·s-1时, 频域回归法的拟合结果与期望值偏差约为20%, 准确度明显低于频域迭代法; 当置信度为0.99时, 脉冲响应曲线拟合法和实现理论法拟合结果与时延函数期望值趋势一致, 都是由初始峰值逐渐衰减到约3.5s达到最小值, 然后逐渐增大, 在约15s趋于0;在7~11s时, 脉冲响应曲线拟合法拟合精度低于实现理论法; 在考虑垂荡对纵摇方向影响时, 实现理论法在横荡、垂荡、纵摇方向拟合的状态空间模型阶数分别为4、3、3阶, 是4种方法中最小的; 在不考虑垂荡对纵摇方向影响时, 频域迭代法在横荡、垂荡、纵摇方向拟合的状态空间模型阶数分为3、2、2, 是4种方法中最小的; 采用脉冲响应曲线拟合法在考虑垂荡对纵摇方向影响去拟合状态空间模型时, 拟合纵摇所需的状态空间模型阶数是不考虑时的2倍, 而实现理论法阶数相同。Abstract: To meet the demand of fast computation of time-domain motion equations, four methods suitable for the fast computation of a retardation function were proposed based on the identification theory. Applying these methods, a state-space model was established by replacing the convolution term, to satisfy the property of the retardation function and fitting quality. Considering the HYSY286 vessel as the research object, the time-domain and frequency-domain identification methods were used to compare the fitting results of retardation function. Calculation result shows that when the confidence coefficient is 0.99, the fitting results of the frequency-domain regression method and the frequency-domain iteration method are consistent with the expected value. The fitting curve reaches to peak when the frequency value is 0.92-1.05 rad·s-1, then gradually decreases to 0. When the frequency is 0.05-0.50 rad·s-1, the deviation of the fitting result from the expected value is approximately 20%, and the accuracy is obviously lower than the frequency-domain iterative method. When the confidence coefficient is 0.99, the fitting results of the impulse response curve fitting method and the realization theory method are consistent with the expected value of retardation function. The fitting curves reach to peak initially and decrease to the minimum value at approximately 3.5 s, then increase again until they tend toward 0 at approximately 15 s. The fitting precision of the realization theory method is better than that of the impulse response curve fitting method during 7-11 s. Considering the effect of heaving direction on pitching direction, the realization theory method requires the least order of the state-space model, to be 4, 3, and 3 for swaying, heaving and pitching, respectively. Without such consideration, the frequency-domain iteration method requires the least order of the state-space model, to be 3, 2, and 2 for swaying, heaving and pitching, respectively. When the impulse response curve fitting method considers the influence of heaving direction on pitching direction to fit the state-space model, the order of the model required to fit pitching is twice as much as that without considering heaving direction, whereas the realization theory method requires the same order.
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表 1 船舶主尺度
Table 1. Ship principal dimensions
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[1] 张秀凤, 尹勇, 金一丞. 规则波中船舶运动六自由度数学模型[J]. 交通运输工程学报, 2007, 7 (3): 40-43. doi: 10.3321/j.issn:1671-1637.2007.03.009ZHANG Xiu-feng, YIN Yong, JIN Yi-cheng. Ship motion mathematic model with six degrees of freedom in regular wave[J]. Journal of Traffic and Transportation Engineering, 2007, 7 (3): 40-43. (in Chinese). doi: 10.3321/j.issn:1671-1637.2007.03.009 [2] 钱小斌, 尹勇, 张秀凤, 等. 海上不规则波浪扰动对船舶运动的影响[J]. 交通运输工程学报, 2016, 16 (3): 116-124. doi: 10.3969/j.issn.1671-1637.2016.03.014QIN Xiao-bin, YIN Yong, ZHANG Xiu-feng, et al. Influence of irregular disturbance of sea wave on ship motion[J]. Journal of Traffic and Transportation Engineering, 2016, 16 (3): 116-124. (in Chinese). doi: 10.3969/j.issn.1671-1637.2016.03.014 [3] 孙明, 刘培林, 孙丽萍, 等. 深海安装中多浮体作业的水动力分析[J]. 水动力学研究与进展, 2011, 26 (3): 351-358. https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201103013.htmSUN Ming, LIU Pei-lin, SUN Li-ping, et al. Hydrodynamic analyzing of multi-body operation in deepwater installation[J]. Chinese Journal of Hydrodynamics, 2011, 26 (3): 351-358. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201103013.htm [4] 何广华, 陈丽敏, 王佳东. 船舶在波浪中运动的强非线性时域模拟[J]. 哈尔滨工业大学学报, 2017, 49 (4): 142-148. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX201704023.htmHE Guang-hua, CHEN Li-min, WANG Jia-dong. Stronglynonlinear simulation of ship motions in head waves[J]. Journal of Harbin Institute of Technology, 2017, 49 (4): 142-148. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX201704023.htm [5] 陈京普, 朱德祥. 船舶在波浪中运动的非线性时域数值模拟[J]. 水动力学研究与进展, 2010, 25 (6): 830-836. doi: 10.3969/j.issn.1000-4874.2010.06.015CHEN Jing-pu, ZHU De-xiang. Numerical simulations of nonlinear ship motions in waves by a Rankine panel method[J]. Chinese Journal of Hydrodynamics, 2010, 25 (6): 830-836. (in Chinese). doi: 10.3969/j.issn.1000-4874.2010.06.015 [6] XU Xin, YANG Jian-min, LI Xin, et al. Time-domain simulation for coupled motions of three barges moored sideby-side in floatover operation[J]. China Ocean Engineering, 2015, 29 (2): 155-168. doi: 10.1007/s13344-015-0012-4 [7] HU Zhi-huan, LI Xin, ZHAO Wen-hua, et al. Nonlinear dynamics and impact load in float-over installation[J]. Applied Ocean Research, 2017, 65: 60-78. doi: 10.1016/j.apor.2017.03.013 [8] CUMMINS W E. The impulse response function and ship motions[R]. Hamburg: Universität Hamburg, 1962. [9] OGILVIE T F. Recent progress toward the understanding and prediction of ship motions[C]∥Boat Design. Proceedings of the 5th Symposium on Naval Hydrodynamics. Beaver Island: Boat Design, 1964: 3-80. [10] SEN D. Time-domain computation of large amplitude 3Dship motions with forward speed[J]. Ocean Engineering, 2002, 29 (8): 973-1002. doi: 10.1016/S0029-8018(01)00041-5 [11] RAJENDRAN S, FONSECA N, GUEDES SOARES C. Simplified body nonlinear time domain calculation of vertical ship motions and wave loads in large amplitude waves[J]. Ocean Engineering, 2015, 107: 157-177. doi: 10.1016/j.oceaneng.2015.07.050 [12] HIRDARIS S E, LEE Y, MORTOLA G, et al. The influence of nonlinearities on the symmetric hydrodynamic response of a10, 000TEU container ship[J]. Ocean Engineering, 2016, 111: 166-178. doi: 10.1016/j.oceaneng.2015.10.049 [13] CHEN Ming-sheng, TAYLOR R E, CHOO Y S. Time domain modeling of a dynamic impact oscillator under wave excitations[J]. Ocean Engineering, 2014, 76: 40-51. doi: 10.1016/j.oceaneng.2013.10.004 [14] WANG Ying-guang. Robust frequency-domain identification of parametric radiation force models for a floating wind turbine[J]. Ocean Engineering, 2015, 109: 580-594. doi: 10.1016/j.oceaneng.2015.09.049 [15] LIN Zi, SAYER P. An enhanced stiffness model for elastic lines and its application to the analysis of a moored floating offshore wind turbine[J]. Ocean Engineering, 2015, 109: 444-453. doi: 10.1016/j.oceaneng.2015.09.002 [16] YANG Shun-han, RINGSBERG J W, JOHNSON E, et al. A comparison of coupled and de-coupled simulation procedures for the fatigue analysis of wave energy converter mooring lines[J]. Ocean Engineering, 2016, 117: 332-345. doi: 10.1016/j.oceaneng.2016.03.018 [17] YE Yi-zhi, CHEN Wei-dong. Frequency and time-domain analysis of a multi-degree-of-freedom point absorber wave energy converter[J]. Advances in Mechanical Engineering, 2017, 9 (12): 1-10. [18] 霍聪, 董文才. 基于拓展Kalman滤波的船舶自由横摇参数辨识[J]. 武汉理工大学学报: 交通科学与工程版, 2016, 40 (2): 214-218, 226. https://www.cnki.com.cn/Article/CJFDTOTAL-JTKJ201602004.htmHUO Cong, DONG Wen-cai. Identification of ship roll parameters from free-roll decay based on extended Kalman filtering[J]. Journal of Wuhan University of Technology: Transportation Science and Engineering, 2016, 40 (2): 214-218, 226. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JTKJ201602004.htm [19] 马雪泉, 季盛, 文逸彦, 等. 船舶横摇运动模式辨识仿真[J]. 上海船舶运输科学研究所学报, 2016, 39 (2): 1-4. https://www.cnki.com.cn/Article/CJFDTOTAL-JTYS201602001.htmMA Xue-quan, JI Sheng, WEN Yi-yan, et al. The system identification and simulation of ship roll motion[J]. Journal of Shanghai Ship and Shipping Research Institute, 2016, 39 (2): 1-4. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JTYS201602001.htm [20] 常永全, 范菊, 朱仁传, 等. 迎浪船舶的参数横摇分析[J]. 水动力学研究与进展, 2008, 23 (2): 204-211. https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ200802014.htmCHANG Yong-quan, FAN Ju, ZHU Ren-chuan, et al. Analysis of ship parametric rolling in head sea[J]. Chinese Journal of Hydrodynamics, 2008, 23 (2): 204-211. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ200802014.htm [21] 唐恺, 朱仁传, 缪国平, 等. 时域分析波浪中浮体运动的时延函数计算[J]. 上海交通大学学报, 2013, 47 (2): 300-306. https://www.cnki.com.cn/Article/CJFDTOTAL-SHJT201302025.htmTANG Kai, ZHU Ren-chuan, MIAO Guo-ping, et al. Calculation of retard function for time-domain analyzing floating body in waves[J]. Journal of Shanghai Jiaotong University, 2013, 47 (2): 300-306. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SHJT201302025.htm [22] TANG Kai, ZHU Ren-chuan, MIAO Guo-ping, et al. Retard function and ship motions with forward speed in timedomain[J]. Journal of Hydrodynamics, 2014, 26 (5): 689-696. doi: 10.1016/S1001-6058(14)60077-9 [23] 秦余钢, 马勇, 张亮, 等. 基于改进最小二乘算法的船舶操纵性参数辨识[J]. 吉林大学学报: 工学版, 2016, 46 (3): 897-903. https://www.cnki.com.cn/Article/CJFDTOTAL-JLGY201603033.htmQIN Yu-gang, MA Yong, ZHANG Liang, et al. Parameter identification of ship's maneuvering motion based on improved least square method[J]. Journal of Jilin University: Engineering and Technology Edition, 2016, 46 (3): 897-903. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JLGY201603033.htm [24] 谢朔, 初秀民, 柳晨光, 等. 基于多新息最小二乘法的船舶操纵响应模型参数辨识[J]. 中国航海, 2017, 40 (1): 73-78. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGHH201701016.htmXIE Shuo, CHU Xiu-min, LIU Chen-guang, et al. Parameter identification of ship maneuvering response model based on multi-innovation least squares algorithm[J]. Navigation of China, 2017, 40 (1): 73-78. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGHH201701016.htm [25] 孙功武, 谢基榕, 王俊轩. 基于动态遗忘因子递推最小二乘算法的船舶航向模型辨识[J]. 计算机应用, 2018, 38 (3): 900-904. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJY201803051.htmSUN Gong-wu, XIE Ji-rong, WANG Jun-xuan. Ship course identification model based on recursive least squares algorithm with dynamic forgetting factor[J]. Journal of Computer Applications, 2018, 38 (3): 900-904. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJY201803051.htm [26] ZHI Y, FALNES J. State-space modelling of dynamic systems in ocean engineering[J]. Journal of Hydrodynamics, 1998 (1): 1-17. [27] TAGHIPOUR R, PEREZ T, MOAN T. Hybrid frequencytime domain models for dynamic response analysis of marine structures[J]. Ocean Engineering, 2008, 35 (7): 685-705. [28] KRISTIANSEN E, HJULSTAD Ǻ, EGELAND O. Statespace representation of radiation forces in time-domain vessel models[J]. Modeling, Identification and Control, 2006, 27 (1): 23-41. [29] KRISTIANSEN E, EGELAND O. Frequency-dependent added mass in models for controller design for wave motion damping[J]. IFAC Proceedings Volumes, 2003, 36 (21): 67-72. [30] LIN P L, WU Y C. Reduction of transfer functions from the stability-equation method and complex curve fitting[J]. Journal of the Franklin Institute, 1982, 314 (2): 109-121. [31] PEREZ T, FOSSEN T L. Practical aspects of frequencydomain identification of dynamic models of marine structures from hydrodynamic data[J]. Ocean Engineering, 2011, 38 (2/3): 426-435.