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针对舰船磁场混合模型建模中存在的建模精度不高和稳定性差的问题, 提出一种高精度稳定模型建立方法, 结合混合模型中磁偶极子参数与舰船结构的相关性, 以建模精度和模型稳定性为目标构造了多目标函数, 通过对多目标函数优化获得合理的磁偶极子参数, 间接地将建模求解问题转化为多目标函数优化问题.利用多目标粒子群优化算法进行求解, 得到了建模问题求解结果的可选集, 以建模精度为基准设计了从可选集中选取最佳结果的选择规则. 三种类型的舰船船模实测数据建模结果表明: 本文方法所建模型相对误差小于3%, 换算误差小于6%, 能够有效对舰船磁场进行建模; 当存在测量数据误差时, 本文方法建模求解结果稳定, 验证了文本方法建模具有较好的稳定性. 海上的某型舰船实测数据建模结果表明, 本文方法建模具有较高的建模精度和换算精度, 能够有效地在相关的工程中应用.
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关键词:
- 舰船磁场建模/
- 多目标函数/
- 多目标粒子群优化算法/
- 选择规则
Ship magnetic field modeling is not only beneficial to understanding the characteristics of ship magnetic field, but also can predict the space distribution of ship magnetic field, which has an important application in ship protection and underwater weapons. Aiming at the problems of low modeling accuracy and poor stability in establishing the ship magnetic field hybrid model, a method of establishing a high precision stablity model is proposed in this paper. A hybrid model of magnetic field of a ship is established by using a uniformly magnetized rotating ellipsoid and a magnetic dipole array. Since the number and positions of magnetic dipoles in the hybrid model have an important effect on the modeling accuracy and stability, the fitting error function representing the modeling accuracy and the coefficient matrix condition number function representing the stability of the model are constructed by taking the magnetic dipole parameters as unknown variables. The multi-objective function is constructed by combining the fitting error function with the coefficient matrix conditional number function, which indirectly transforms the modeling problem into a multi-objective optimization problem. The multi-objective function is solved by using the multi-objective particle swarm optimization algorithm, and an optional set of modeling solution results is obtained. In order to select the best results from the optional set, the corresponding selection rules are designed based on the modeling accuracy. The proposed method is validated by the measured data of three kinds of ship models, the modeling results show that the relative error of the model is less than 3%, and the conversion error is less than 6%, which verifies that the proposed method can effectively model the ship magnetic field. Though the measurement data error exists, the modeling solution results from the proposed method have the best stability, which verifies that the modeling method proposed in this work has good stability. Compared with the two existing modeling methods, the proposed method has very good modeling accuracy and stability. Finally, the actual data of a ship on the sea are used for modeling, and the modeling results further verify that the proposed method has high modeling accuracy and conversion accuracy, and can be effectively applied to the relevant projects.-
Keywords:
- ship magnetic field modeling/
- multi-objective function/
- multi-objective particle swarm optimizatialgorithm/
- selection rule
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目标 尺度参数/m 测量深度/m 航迹1/m 航迹2/m 航迹3/m L W ${Z_0}$ ${Z_1}$ 小型船模 57.2 8.6 8.6 17 X= –80:2:80,
Y= –4.2X= – 80:2:80,
Y= 0X= – 80:2:80,
Y= 4.2中型船模 76.5 8.5 12.75 20.5 X= –100:2.5:100,
Y=–15X= –100:2.5:100,
Y= 0X= –100:2.5:100,
Y= 15大型船模 153 17.3 17.2 28.8 X= –128:3.2:128,
Y= –8.64X= –128:3.2:128,
Y= 0X= –128:3.2:128,
Y= 8.64目标 小型舰船 中型舰船 大型舰船 磁偶极子数 10 8 14 系数矩阵条件数 85.13 76.5 128.95 建模相对误差 0.0295 0.0290 0.0256 目标 建模深度/m 换算深度/m 相对误差 小型舰船 8.6 8.6 0.0295 17 0.0402 17 8.6 0.0479 17 0.0256 中型舰船 12.75 12.75 0.0290 20.5 0.0323 20.5 12.75 0.0387 20.5 0.0201 大型舰船 17.2 17.2 0.0256 28.8 0.0301 28.8 17.2 0.0547 28.8 0.0152 目标 文献[1] 文献[25] 本文方法 小型舰船 磁偶极子数 10 10 10 系数矩阵条件数 1.28 × 103 34.65 85.13 建模相对误差 17 m 0.0464 0.1071 0.0295 8.6 m 0.0450 0.0458 0.0256 换算相对误差 8.6 m→17 m 0.0609 0.0913 0.0402 17 m→8.6 m 0.1208 0.1523 0.0497 中型舰船 磁偶极子数 8 8 8 系数矩阵条件数 709.8 28.02 76.5 建模相对误差 20.5 m 0.0568 0.0619 0.0290 12.75 m 0.0655 0.0872 0.0201 换算相对误差 12.75 m→20.5 m 0.077 0.1726 0.0323 20.5 m→12.75 m 0.129 0.1317 0.0387 大型舰船 磁偶极子数 14 14 14 系数矩阵条件数 2.36 × 103 78.29 128.95 建模相对误差 28.8 m 0.0991 0.1302 0.0256 17.2 m 0.0525 0.0602 0.0152 换算相对误差 17.2 m→28.8 m 0.0984 0.1033 0.0301 28.8 m→17.2 m 0.1769 0.1782 0.0547 航向 建模相对误差 换算误差 东航向 0.0243 0.0543 西航向 0.0257 0.0621 南航向 0.0236 0.0325 北航向 0.0276 0.0421 -
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