针对船舶推进轴系在实际运行中的轴承位移变化情况，提出基于弯矩变化预测轴承位移的方法。使用传递矩阵法推导弯矩影响系数矩阵，通过给定弯矩计算出轴承实际位移值，以数值仿真方式研究不同测点布局下的预测结果，分析影响系数方法在病态矩阵和测量误差下的适用性和局限性。进一步提出采用粒子群优化改进的BP神经网络模型，通过PSO优化网络初始权重，提升网络收敛性与预测精度，以数据驱动的方式构建轴系弯矩与轴承位移间的映射关系。通过数值算例表明，在给定的仿真条件与测点组合下，神经网络较影响系数法在一定噪声扰动下表现出相对稳定的预测性能。
Aiming at the variation of bearing displacement in the ship propulsion shafting during actual operation, a method for predicting bearing displacement based on the change of bending moment is proposed. The bending moment influence coefficient matrix is derived by using the transfer matrix method. The actual displacement value of the bearing is calculated based on the given bending moment. The prediction results under different measurement point layouts are studied through numerical simulation, and the applicability and limitations of the influence coefficient method under the pathological matrix and measurement error are analyzed. Further, a BP neural network model improved by particle swarm optimization is proposed. The initial weights of the network are optimized through PSO to enhance the convergence and prediction accuracy of the network, and the mapping relationship between the bending moment of the shafting and the displacement of the bearing is constructed in a data-driven manner. Numerical examples show that under the given simulation conditions and measurement point combinations, the neural network exhibits relatively stable prediction performance compared to the influence coefficient method under certain noise disturbances.
2026,48(7): 1-7 收稿日期：2025-7-22
DOI：10.3404/j.issn.1672-7649.2026.07.001
分类号：U664.2
基金项目：辽宁省高等学校创新团队项目（LT2014002）
作者简介：冯梓豪(2000-),男,硕士研究生,研究方向为船舶推进轴系动态校中
参考文献：
[1] 贺威. 不同对中状态下的轴系动态负荷测量方法研究[D]. 上海: 上海交通大学, 2020.
[2] KYOKAI N K. Guidelines on shafting alignment[J]. ClassNK, 2006, 6.
[3] American Bureau of Shipping. Guidance notes on propulsion shafting alignment[S]. New York: American Bureau of Shipping, 2004.
[4] 张玉龙, 吴炜, 周建辉. 基于灰色系统理论的推进轴系负荷预测分析[J]. 中国舰船研究, 2022, 17(6): 141-147 ZHANG Y L, WU W, ZHOU J H. Prediction analysis on propulsion shafting load based on grey system theory[J]. Chinese Journal of Ship Research, 2022, 17(6): 141-147
[5] 耿厚才, 陈兵, 钟庆华, 等. 船体艉部变形计算及其在轴系坞内校中技术中的应用[J]. 中国造船, 2011, 52(4): 153-160 GENG H C, CHEN B, ZHONG Q H, et al. Calculations of stern hull deflection and its application in drydock shaft alignment[J]. Shipbuilding of China, 2011, 52(4): 153-160
[6] 陈昊, 周瑞平, 雷俊松, 等. 基于弯矩影响系数的轴系安装状态评估逆计算方法[J]. 中国舰船研究, 2019, 14(2): 137-143 CHEN H, ZHOU R P, LEI J S, et al. Inverse calculation method of shaft system installation status evaluation based on bending moment influence coefficient[J]. Chinese Journal of Ship Research, 2019, 14(2): 137-143
[7] 杨小钢, 邓义斌, 朱汉华, 等. 基于机器学习的船舶多支撑轴系智能装调方法[J]. 中国造船, 2021, 62(3): 184-191 YANG X G, DENG Y B, ZHU H H, et al. Intelligent assembly and adjustment method of ship multi support shafting based on machine learning[J]. Shipbuilding of China, 2021, 62(3): 184-191
[8] 郑瑞栋, 朱汉华, 赵修叁, 等. 基于机器学习的船舶轴系安装校调方法研究[J]. 舰船科学技术, 2025, 47(4): 59-65 ZHENG R D, ZHU H H, ZHAO X S, et al. Research on the installation and adjustment method of ship shafting based on machine learning[J]. Ship Science and Technology, 2025, 47(4): 59-65
[9] DENG Y, LI Y, ZHU H, et al. Displacement values calculation method for ship multi-support shafting based on transfer learning[J]. Journal of Marine Science and Engineering, 2023, 12(1): 36-52
[10] MAGALHÃES, DIEGO L, et al. Machine learning performance comparison for main propulsive shafting systems alignment[J]. Ocean Engineering, 2023, 280: 114556
[11] ISMAIL A, JENG D S, ZHANG L L. An optimised product-unit neural network with a novel PSO-BP hybrid training algorithm: Applications to load–deformation analysis of axially loaded piles[J]. Engineering Applications of Artificial Intelligence, 2013, 26(10): 2305–2314.
[12] MIRCHANDANI G, CAO W. On Hidden Nodes for Neural Nets[J]. IEEE Transactions on Circuits andSystems, 1989, 36(5): 661-664
[13] 柴聪聪, 易贤, 郭磊, 等. 基于BP神经网络的冰形特征参数预测[J]. 实验流体力学, 2021, 35(3): 16-21 CHAI C C, YI X, GUO L, et al. Prediction of ice shape characteristic parameters based on BP neural network[J]. Journal of Experiments in Fluid Mechanics, 2021, 35(3): 16-21
[14] XUE K, WANG J, CHEN Y, et al. Improved BP neural network algorithm for predicting structural parameters of mirrors[J]. Electronics, 2024, 13(14): 2789
[15] MULUMBA, DORCAS M, et al. Application of an optimized PSO-BP neural network to the assessment and prediction of underground coal mine safety risk factors[J]. Applied Sciences, 2023, 13(9): 5317
[16] 娄高中, 谭毅. 基于PSO-BP神经网络的导水裂隙带高度预测[J]. 煤田地质与勘探, 2021, 49(4): 198-204 LOU G Z, TAN Y. Prediction of the height of water flowing fractured zone based on PSO-BP neural network[J]. Coal Geology & Exploration, 2021, 49(4): 198-204
