﻿ 基于高斯过程回归的船舶动力学模型辨识
 舰船科学技术  2022, Vol. 44 Issue (19): 1-5    DOI: 10.3404/j.issn.1672-7649.2022.19.001 PDF

Identification of ship dynamics model based on Gaussian process regression
CHEN Gang, WANG Wei, HUO Cong
College of Naval Architecture and Ocean Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Ship dynamics model is crucial for intelligent navigation and design of the ship’s controller, nonparametric regression based on Gaussian process regression is used for ship dynamics model identification. it can capture the strong nonlinearity and motion cou-pling in ship motion, and deal with the presence of uncertainty and noise. The identified model can provide ship acceleration, speed and position information for a period of time in the future when the sensor signal is lost. The experimental data of KVLCC2 ship are used to verify the validity of the proposed method, the results show that Gaussian process regression can provide accurate predictions of ship’s state, the position prediction error of 1000 steps is 0.599 m.
Key words: gaussian processes regression     identification     ship dynamics
0 引　言

1 船舶动力学参数模型和非参数模型

 $M\dot{s}+C\left(s\right)s+D\left(s\right)s+g\left(\eta \right)+{g}_{0}=\tau +{\tau }_{wind}+{\tau }_{wave}。$ (1)

 图 1 地球和船舶固定坐标系 Fig. 1 Earth and ship-fixed coordinate systems

 $M\dot{s}+C\left(s\right)s+D\left(s\right)s=\tau。$ (2)

 $\dot{s}=f(s,\tau )。$ (3)

 ${\dot{u}}_{k}={f}_{u}\left({u}_{k},{v}_{k},{r}_{k},{T}_{k},{\delta }_{k}\right) ，$ (4)
 ${\dot{v}}_{k}={f}_{v}\left({u}_{k},{v}_{k},{r}_{k},{T}_{k},{\delta }_{k}\right)，$ (5)
 ${\dot{r}}_{k}={f}_{r}\left({u}_{k},{v}_{k},{r}_{k},{T}_{k},{\delta }_{k}\right) 。$ (6)
2 基于高斯过程回归的非参数建模 2.1 高斯过程回归

$\left\{({x}_{i},{y}_{i})|i=1,\cdots ,n\right\}$ 是回归的输入和输出，它们之间的关系可以表示为：

 ${y}_{i}=f\left({x}_{i}\right)+\varepsilon ,\varepsilon \sim N(0,{\mathrm{\sigma }}_{n}^{2})，$ (7)

 $\left[\begin{array}{c}y\\ {f(x}^{*})\end{array}\right] \sim N\left(0,\left[\begin{array}{cc}K\left(\mathrm{X},\mathrm{X}\right)+{{\mathrm{\sigma }}_{n}}^{2}I& K\left({x}^{*},\mathrm{X}\right)\\ K\left(\mathrm{X},{x}^{*}\right)& K\left({x}^{*},{x}^{*}\right)\end{array}\right]\right)，$ (8)

${f(x}^{*})$ 的预测值为：

 ${f(x}^{*})=k\left({x}^{*},X\right){\left(\mathrm{K}\right(\mathrm{X},\mathrm{X})+{{\mathrm{\sigma }}_{n}}^{2}{I}_{n})}^{-1}y ，$ (9)
 $\begin{split} Var\left[{f(x}^{*})\right]=&k\left({x}^{*},{x}^{*}\right)-\\ &k\left({x}^{*},X\right){\left(\mathrm{K}\right(\mathrm{X},\mathrm{X})+{{\mathrm{\sigma }}_{n}}^{2}{I}_{n})}^{-1}k\left(X,{x}^{*}\right) \end{split}，$ (10)

 $k\left({x}_{i},{x}_{j}\right)={f\left({x}_{i}\right)}^{{\rm{T}}}f\left({x}_{j}\right)={{\mathrm{\sigma }}_{f}}^{2}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{1}{2}({x}_{i}-{x}_{j})^{{\rm{T}}}\mathrm{\Lambda }({x}_{i}-{x}_{j})\right)。$ (11)

2.2 船舶运动状态多步预测模型

 图 2 多步预测模型的输入和输出 Fig. 2 The inputs and outputs of multi-step prediction model

3 KVCLL2船舶动力学辨识 3.1 实验船模型和数据集

3.2 基于高斯过程回归的船舶动力学辨识

 图 3 25°/5°Z形运动中的加速度3700步预测 Fig. 3 3700 steps prediction of acceleration in 25°/5° zigzag maneuver

 图 4 25°/5°Z形运动中的速度3700步预测 Fig. 4 3700 steps prediction of speed in 25°/5° zigzag maneuver

 图 5 25°/5°Z形运动中的轨迹3700步预测 Fig. 5 3700 steps prediction of position in 25°/5° zigzag maneuver

4 结　语

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