Modeling and prediction method of ship maneuvering motion facing environmental uncertainty
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摘要: 为解决复杂环境因素影响下的船舶操纵运动预报精度问题，提出了一种面向环境不确定性的船舶操纵运动灰箱辨识建模与预报方法；参考分离型船舶操纵运动模型结构，考虑船舶操纵运动机理，建立了简化的灰箱模型；选取合适的试验对象，运用最小二乘支持向量机算法对建立的船舶操纵运动灰箱模型进行参数辨识，并通过旋回试验和Z形操纵试验测试了模型的泛化性；通过环境不确定性因素分析，构建了波浪作用力干扰模型、数据传输延时模型和感知设备误差模型，并以此为基础，生成了具有多种环境不确定性因素影响的船舶运动响应训练数据；通过仿真试验，验证了预报方法在环境不确定性因素干扰下的预报精度。研究结果表明：在引入环境不确定性因素影响的船舶操纵运动预报试验中，当感知设备误差由0逐渐提升至5%和10%时，除受较小的初始数量级因素影响的横摇速度外，其余船舶运动响应预报结果的均方根误差增幅均小于10%，预测模型的精度可以得到有效保证；而在感知设备误差达到20%的极端条件下，纵荡速度、横荡速度、艏摇速度预报误差相较于0时分别提升4.65%、15.97%、18.17%，误差增幅仍能有效控制在20%以下。可见，船舶操纵运动建模与预报方法可在一定程度上实现环境不确定性因素干扰下的高精度船舶操纵运动预报。Abstract: In response to the issue of prediction accuracy of ship maneuvering motion under complicated environmental factors, a grey box identification modeling and prediction method for ship maneuvering motion under environmental uncertainty was proposed. The separated ship maneuvering motion model structure was referenced, the ship maneuvering motion mechanism was considered, and a simplified grey box model was developed. Suitable test subjects were selected, and parameter identification was conducted on the established ship maneuvering motion grey box model using the least squares support vector machine algorithm. The generalization ability was examined by means of the turning cycle tests and zigzag maneuvering tests. By analyzing the environmental uncertainty factors, the wave force interference model, data transmission delay model, and sensing device error model were constructed. Based on these models, the ship motion response training data affected by multiple environmental uncertainties were generated. Through the simulated tests, the prediction accuracy of the proposed method under environmental uncertainties was validated. Research results reveal that in ship maneuvering motion prediction tests with environmental uncertainty factors, when the sensing device error gradually increases from 0 to 5% and 10%, except for the rolling speed affected by a small initial magnitude, the root mean square errors (RMSEs) of other ship motion response prediction results increase by less than 10%, so the accuracy of the prediction model can be effectively guaranteed. Under the extreme condition with a 20% sensing device error, the prediction errors of surge speed, sway speed, and yawing speed increase by 4.65%, 15.97%, and 18.17%, respectively compared to the 0 error level, so the error increase is effectively controlled below 20%. Thus, the ship maneuvering motion modeling and prediction method can achieve a high-precision prediction of ship maneuvering motion under the interference of environmental uncertainty factors to a certain extent.
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图 2 基于LS-SVM的灰箱辨识建模过程
Figure 2. Grey box identification modeling process based on LS-SVM
图 5 灰箱辨识模型与MMG模型20°旋回试验对比
Figure 5. Comparison of responses of 20° turning cycle test between grey box identification model and MMG model
图 6 灰箱辨识模型与MMG模型±20°Z形操纵试验对比
Figure 6. Comparison of responses of ±20° zigzag maneuvering test between grey box identification model and MMG model
图 10 面向环境不确定性的船舶操纵运动预报流程
Figure 10. Ship maneuvering motion prediction process facing environmental uncertainty
图 12 含有感知设备误差的船舶运动响应训练数据
Figure 12. Ship motion response training data with device perception error
图 13 环境不确定性影响下的船舶操纵运动预报结果
Figure 13. Prediction results of ship maneuvering motion under environmental uncertainty
表 1 船舶操纵运动各参数和符号
Table 1. Parameters and symbols of ship maneuvering motion
物理量 x轴方向 y轴方向 z轴方向 速度 纵荡速度u 横荡速度v 垂荡速度ω 角速度 横摇角速度p 纵摇角速度q 艏摇角速度r 力 纵向力X 横向力Y 垂向力Z 力矩 横摇力矩K 纵摇力矩M 艏摇力矩N 转动角 横摇角φ 纵摇角θ 艏摇角ψ 
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表 2 船舶主要参数
Table 2. Main parameters of ship
船舶部分 参数 数值 船体 船长/m 175 船宽/m 25.4 平均吃水/m 8.5 排水体积/m3 21 222 方形系数 0.559 菱形系数 0.58 浮心纵坐标/m 0.8 螺旋桨 螺距比 1.009 螺旋桨直径/m 6.533 船舵 舵面积/m2 33.037 6 舵叶高/m 7.758 3 舵展弦比 1.821 9
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表 3 辨识参数a1~a7结果对比
Table 3. Results comparison of identification parameters a1-a7
参数 实际值 SVM LS-SVM(多项式核) LS-SVM(线性核) 辨识值 误差/% 辨识值 误差/% 辨识值 误差/% a1 -0.000 000 29 -0.000 000 29 0.00 -0.000 000 29 0.00 -0.000 000 29 0.00 a2 -0.000 073 09 -0.000 071 10 2.72 -0.000 072 39 0.96 -0.000 072 18 1.25 a3 -0.001 457 04 -0.001 434 13 1.57 -0.001 399 43 3.95 -0.001 438 53 1.27 a4 0.907 771 59 0.903 933 34 0.42 0.910 438 28 0.29 0.911 635 92 0.43 a5 8.884 944 44 8.806 729 29 0.88 8.770 213 97 1.29 8.900 255 72 0.17 a6 0.022 659 59 0.023 012 62 1.56 0.022 345 10 1.39 0.022 665 56 0.03 a7 0.000 000 02 0.000 000 02 0.00 0.000 000 02 0.00 0.000 000 02 0.00
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表 4 辨识参数b1~b7结果对比
Table 4. Results comparison of identification parameters b1-b7
参数 实际值 SVM LS-SVM(多项式核) LS-SVM(线性核) 辨识值 误差/% 辨识值 误差/% 辨识值 误差/% b1 -0.049 617 18 -0.049 163 92 0.91 -0.049 223 49 0.79 -0.050 105 66 0.98 b2 2.351 321 57 2.305 617 39 1.94 2.297 371 16 2.29 2.363 733 14 0.53 b3 -0.719 577 94 -0.721 057 47 0.21 -0.715 657 80 0.54 -0.712 723 42 0.95 b4 -0.016 349 38 -0.016 667 46 1.92 -0.016 434 06 0.52 -0.016 191 90 0.96 b5 0.700 191 47 0.694 044 18 0.88 0.682 917 40 2.47 0.691 264 30 1.27 b6 -16.624 404 30 -16.389 888 80 1.41 -16.480 080 10 0.87 -16.723 567 60 0.60 b7 0.000 000 03 0.000 000 03 0.00 0.000 000 03 0.00 0.000 000 03 0.00
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表 5 辨识参数c1~c8结果对比
Table 5. Results comparison of identification parameters c1-c8
参数 实际值 SVM LS-SVM(多项式核) LS-SVM(线性核) 辨识值 误差/% 辨识值 误差/% 辨识值 误差/% c1 -0.000 153 60 -0.000 153 87 0.18 -0.000 148 71 3.18 -0.000 151 47 1.39 c2 -0.154 792 83 -0.157 176 09 1.54 -0.154 363 12 0.28 -0.154 855 89 0.04 c3 0.003 359 45 0.003 400 62 1.23 0.003 472 35 3.36 0.003 338 40 0.63 c4 -0.160 294 87 -0.155 069 42 3.26 -0.156 557 90 2.33 -0.157 363 69 1.83 c5 0.001 070 22 0.001 099 11 2.70 0.001 091 84 2.02 0.001 089 65 1.82 c6 -0.042 358 33 -0.043 156 25 1.88 -0.042 662 44 0.72 -0.042 332 88 0.06 c7 1.890 381 41 1.907 600 78 0.91 1.899 991 69 0.51 1.908 146 97 0.94 c8 -0.000 000 02 -0.000 000 02 0.00 -0.000 000 02 0.00 -0.000 000 02 0.00
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表 6 辨识参数d1~d9结果对比
Table 6. Results comparison of identification parameters d1-d9
参数 实际值 SVM LS-SVM(多项式核) LS-SVM(线性核) 辨识值 误差/% 辨识值 误差/% 辨识值 误差/% d1 -0.001 684 95 -0.001 681 57 0.20 -0.001 738 22 3.16 -0.001 699 62 0.87 d2 -0.139 527 25 -0.137 589 79 1.39 -0.140 386 58 0.62 -0.139 302 33 0.16 d3 -0.114 888 94 -0.117 081 82 1.91 -0.115 708 05 0.71 -0.115 976 92 0.95 d4 -1.950 281 07 -2.007 297 55 2.92 -1.925 972 44 1.25 -1.965 205 09 0.77 d5 -0.933 494 72 -0.919 446 13 1.50 -0.916 512 48 1.82 -0.923 135 09 1.11 d6 -0.001 636 63 -0.001 663 34 1.63 -0.001 646 35 0.59 -0.001 643 57 0.42 d7 -0.002 635 53 -0.002 601 33 1.30 -0.002 626 50 0.34 -0.002 626 79 0.33 d8 0.419 498 29 0.416 518 18 0.71 0.421 785 57 0.55 0.421 283 48 0.43 d9 -0.000 000 01 -0.000 000 01 0.00 -0.000 000 01 0.00 -0.000 000 01 0.00
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表 7 辨识时间消耗对比
Table 7. Comparison of identification time
s 辨识算法 SVM LS-SVM(多项式核) LS-SVM(线性核) 辩识时间 0.45 0.56 0.19
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表 8 灰箱辨识模型的RMSE
Table 8. RMSEs of grey box identification model
辨识算法 RMSE 纵荡速度/(m·s-1) 纵荡速度/(m·s-1) 横摇角速度/[(°)·s-1] 艏摇角速度/[(°)·s-1] SVM 0.177 0.271 0.451 0.168 LS-SVM(多项式核) 0.156 0.296 0.584 0.189 LS-SVM(线性核) 0.134 0.129 0.153 0.053
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表 9 波浪参数设置
Table 9. Setting of wave parameters
参数 波高/m 波浪周期/s 波长/m 波浪方向/(°) 数值 1.5 5.5 50 45
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表 10 船舶运动响应RMSE
Table 10. RMSEs of ship motion response
感知设备误差/% RMSE 纵荡速度/(m·s-1) 横荡速度/(m·s-1) 横摇角速度/[(°)·s-1] 艏摇角速度/[(°)·s-1] 0 0.129 0.169 0.020 0.073 5 0.131 0.171 0.020 0.074 10 0.131 0.184 0.036 0.081 20 0.135 0.196 0.103 0.087
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