﻿ 实船运动与包络的极短期预报分析
 舰船科学技术  2019, Vol. 41 Issue (6): 43-47 PDF

1. 中国船舶及海洋工程设计研究院，上海 200000;
2. 上海中船船舶设计技术国家工程研究中心有限公司，上海 200000

Research on extremely short-term prediction of real ship motion and envelope
YAN Chuan-xu1,2, SUN Hui2, ZHANG Shuai2
1. Marine Design and Research Institute of China, Shanghai 200000, China;
2. Shanghai Zhongchuan Nerc-Std Co., Ltd., Shanghai 200000, China
Abstract: The real-time prediction of ship motion and envelope can provide auxiliary decision-making guidance for some engineering operations. In this paper, the heave, pitch and roll data of a real ship was applied to build the second order Volterra adaptive prediction model. The kernel of Volterra series model was estimated by RLS algorithm. The accuracy of motion prediction was counted in different working condition. Analysis results showed that the Volterra adaptive model can describe the ship motion system. The prediction of pitch and heave was good. The motion and envelope prediction can be combined to give guidance to some engineering operations.
Key words: volterra series model     real ship motion     extremely short-term prediction     RLS algorithm
0 引　言

1 实船运动与包络极短期预报的应用设计

 图 1 运动与包络极短期预报的应用设计 Fig. 1 Application design for extremely short-term prediction of ship motion and envelope
2 实船运动与包络极短期预报方法

2.1 数据预处理

 $x(t) = {x_0}(t) - {\bar x_0} {\text{。}}$ (1)

2.2 二阶自适应Volterra级数模型

 $\begin{split} \hat x(t + 1) =& {h_0} + \displaystyle\sum\limits_{{m_1} = 0}^{m - 1} {{h_{{m_1}}}} (t)x(t - m) + \\ & \displaystyle\sum\limits_{{m_1} = 0}^{m - 1} {\displaystyle\sum\limits_{{m_2} = 0}^{m - 1} {{h_{{m_1},{m_2}}}} } (t)x(t - {m_1})x(t - {m_2}) {\text{。}} \end{split}$ (2)

 $\begin{split} U(t) =& [1,x(t),x(t - 1), \cdots ,x(t - m + 1), \\ &{x^2}(t),x(t)x(t - 1), \cdots ,{x^2}(t - m + 1)]^{\rm T} {\text{。}} \end{split}$ (3)

 $\begin{split} H(t) =& [{h_0},{h_0}(t),{h_1}(t), \cdots , \\ &{h_{0,0}}(t),{h_{0,1}}(t), \cdots ,{h_{m - 1,m - 1}}(t){]^{\rm T}} {\text{。}} \end{split}$ (4)

 $\hat x(t + 1) = {H^{\rm T}}(t)U(t){\text{。}}$
2.3 基于RLS算法的Volterra级数滤波器的核估计

 $\begin{gathered} \hat H(t + 1) = \hat H(t) + K(t + 1)[x(t + 1) - {U^{\rm T}}(t + 1)\hat H(t)] \end{gathered} {\text{，}}$ (5)
 $K(t + 1) = \frac{{{\varPhi _t}U(t + 1)}}{{1 + {U^{\rm T}}(t + 1){\varPhi _t}U(t + 1)}}{\text{，}}$ (6)
 ${\varPhi _{t + 1}} = {\varPhi _t} -{ K}(t + 1){U^{\rm T}}(t + 1){\varPhi _t}{\text{。}}$ (7)

 $\left\{ {\begin{array}{*{20}{c}} {{\varPhi _m} = I \times {{10}^4}}{\text{，}} \\ {\hat H(m) = 0} {\text{。}} \end{array}} \right.$
2.4 Volterra级数模型多步预测

$l = 1$

 $\begin{split} \hat x(t + l) =& {{\hat h}_0} + \sum\limits_{{m_1} = 0}^{m - 1} {{{\hat h}_{{m_1}}}} (t)x(t - m)+ \\ & \sum\limits_{{m_1} = 0}^{m - 1} {\sum\limits_{{m_2} = 0}^{m - 1} {{{\hat h}_{{m_1},{m_2}}}} } (t)x(t - {m_1})x(t - {m_2}) {\text{；}} \end{split}$ (8)

$1< l \leqslant m$ 时，令

 $\begin{split} {U_1}(t) =& [1,\hat x(t + l - 1),\hat x(t + l - 2), \cdots ,\hat x(t + 1), \\ &x(t), \cdots ,x(t + l - m){]^{\rm T}}, \end{split}$

 $\hat x(t + l) = {\hat H^T}(t){U_1}(t){\text{；}}$ (9)

$l > m$ 时，令

 ${U_2}(t) = {[1,\hat x(t + l - 1),\hat x(t + l - 2), \cdots ,\hat x(t + l - m)]^{\rm T}}{\text{，}}$

 $\hat x(t + l) = {\hat H^{\rm T}}(t){U_2}(t){\text{。}}$ (10)
3 实船运动和包络预报实例分析

 图 2 运动与包络预报模型参数向量的范数 Fig. 2 The norm for the parameter of ship motion and envelope prediction model

 图 3 20kn顶浪升沉运动与包络预报 Fig. 3 Heave motion and envelope prediction in head waves

 图 4 20kn顶浪纵摇运动与包络预报 Fig. 4 Pitch motion and envelope prediction in head waves

 图 5 20kn首斜浪横摇运动与包络预报 Fig. 5 Roll motion and envelope prediction in oblique waves

 $\eta = \frac{{\sum\limits_{t = N + 1}^{N + l} {\left\{ {\left[ {\hat x(t) - \bar {\hat x}(t)} \right]\left[ {x(t) - \bar x(t)} \right]} \right\}} }}{{(n - 1){\sigma _{\hat x}}{\sigma _x}}}{\text{。}}$ (11)

4 结　语

1）二阶自适应Volterra级数模型可以用来辨识船舶运动系统，RLS算法可以有效估计Volterra级数模型的核，收敛速度快；

2）包络预报可以预判未来2～3个周期的运动范围，可以将运动与包络的预报相结合，共同为舰船工程作业提供辅助意见；

3）升沉与纵摇的预报效果较好，横摇预报效果有待提高。对于该船，15 kn与20 kn航速下的运动预报效果并没有明显的变化；

4）针对文中实船数据，采用二阶自适应Volterra级数模型，升沉与纵摇的有效预报时长5～7 s，横摇有效预报约4 s。如果需要预报更长时间，可以考虑提高测量精度，滤掉运动信号中的杂波信号，或采用首前波法将波浪作为前馈添加至模型中。

 [1] 段文洋, 王瑞锋, 赵良明, 等. 基于AR预报的船舶减摇模拟分析[J]. 武汉理工大学学报, 2014, 36(3): 59-63. DUAN Wen-yang, WANG Rui-feng, ZHAO Liang-ming, et al. Simulation of ship stabilizing fin control based on AR forecasting[J]. Journal of Wuhan University of Technology, 2014, 36(3): 59-63. [2] 蔡韡, 任元洲, 严传续, 等. 基于神经网络的四自由度船舶操纵运动预报[J]. 中国造船, 2013, 54(4): 155-162. CAI Wei, REN Yuan-zhou, YAN Chuan-xu, et a1. Prediction of ship maneuvering motion in 4 degrees of freedom based on neural network[J]. Ship Building of China, 2013, 54(4): 155-162. DOI:10.3969/j.issn.1000-4882.2013.04.018 [3] RICHTER M, SCHNEIDER K, WALSER D, et al. Real time heave motion estimation using adaptive filtering techniques[C]//The International Federation of Automatic Control. Cape Town, South Africa,2014: 10119–10125. [4] YUMORI, ISAO Roy. Real time prediction of ship response to ocean waves using time series analysis [C]//In: Oceans 81 Conference Record. Piscataway, NJ: IEEE, 1981.1082–1089. [5] BROOME, D. R. HALL. M. S. Application of ship motion prediction[C]. Trans IEEE, Vol.110. [6] 刘长德. 基于时间序列的船舶运动建模预报方法研究[D]. 哈尔滨: 哈尔滨工程大学, 2009. LIU Chang-de. Research on ship motion modeling and prediction based on time series[D]. Harbin: Harbin Engineering University, 2009. [7] 彭秀艳, 王茂, 刘长德. AR模型参数自适应估计方法研究及应用[J]. 哈尔滨工业大学学报, 2009, 41(9): 12-16. PENG Xiu-yan, WANG Mao, LIU Chang-de. Adaptive estimation method of AR model parameters[J]. Journal of Harbin Institute of Technology, 2009, 41(9): 12-16. DOI:10.3321/j.issn:0367-6234.2009.09.003 [8] 黄礼敏, 段文洋, 韩阳, 等. 船舶运动极短期预报方法综述(英文)[J]. 船舶力学, 2014, 18(12): 1534-1542. HUANG Li-min, DUAN Wen-yang, HAN Yang, et al. A review of short-term prediction techniques for ship motions in seaway[J]. Journal of Ship Mechanics, 2014, 18(12): 1534-1542. DOI:10.3969/j.issn.1007-7294.2014.12.013 [9] 彭秀艳, 门志国, 王冠, 等. 变步长LMS算法相空间重构的AR模型预报仿真[J]. 计算机仿真, 2013, 30(01): 28-31. PENG Xiu-yan, MEN Zhi-guo, WANG Guan, et al. Phase space reconstruction AR model Predicted Simulator Based on VSS-LMS Algorithm[J]. Computer Simulation, 2013, 30(01): 28-31. DOI:10.3969/j.issn.1006-9348.2013.01.007 [10] 程超, 穆荣军, 蔡玲, 等. 基于遭遇波的艏前波法的航母姿态预报[J]. 中国惯性技术学报, 2015, 23(3): 409-414. CHENG Chao, MU Rong-jun, CAI Ling, et al. Doppler interpolation method based on extrapolation and CIC filter[J]. Journal of Chinese Inertial Technology, 2015, 23(3): 409-414.