Chinese Journal of Ship Research
A SR-UKF-based method to identify submarine hydrodynamic coefficients
吕帮俊*，黄斌，彭利坤海军工程大学动力工程学院，湖北武汉 430033
网络首发地址：https://kns.cnki.net/kcms/detail/42.1755.TJ.20210422.1423.002.html 期刊网址：www.ship-research.com
引用格式：吕帮俊,黄斌, 彭利坤.基于 SR-UKF的潜艇水动力系数辨识方法[J]. 中国舰船研究, 2021, 16(3): 44–49. LYU B J, HUANG B, PENG L K. A SR-UKF-based method to identify submarine hydrodynamic coefficients[J]. Chinese Journal of Ship Research, 2021, 16(3): 44–49.
摘 要:［目的］针对潜艇运动模型中水动力系数难以准确获取的问题，采用平方根无迹卡尔曼滤波（SR-UKF）算法进行系统辨识。［方法］首先，以潜艇垂直面运动非线性数学模型为基础，结合SR-UKF 算法，建立潜艇垂直面水动力系数辨识模型；然后，利用自动操舵控制潜艇在垂直面进行类正弦机动，将运动仿真生成的数据作为 SR-UKF参数辨识的输入，并加入测量误差的影响；最后，通过数值仿真计算对潜艇垂直面机动的6个黏性无因次水动力系数进行辨识。［结果］仿真结果表明，全部待识别水动力系数在3 000 s内均收敛至固定值，通过合适的初值选取，辨识结果与水动力试验所测定标准值的最大误差仅1.5%。［结论］SR-UKF 能有效应用于潜艇水动力系数辨识，并可进一步拓展用于实艇的水动力系数辨识。关键词：潜艇；水动力系数；平方根无迹卡尔曼滤波；系统辨识；参数估计中图分类号: U661.1文献标志码:A DOI：10.19693/j.issn.1673-3185.01893 A SR-UKF-based method to identify submarine hydrodynamic coefficients LYU Bangjun*, HUANG Bin, PENG Likun
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: ［Objectives］The square root unscented Kalman filter (SR-UKF) algorithm was developed for the identification of hydrodynamic coefficients, which are difficult to obtain accurately in submarine motion models.［Methods］Firstly, the hydrodynamic coefficients identification model was established based on the nonlinear mathematical model of submarine motion in the vertical plane, combined with the SR-UKF algorithm. Then, a sinusoidal maneuvering in the vertical plane was carried out by the automatic steering method and the generated data in addition to the measurement errors were chosen as the input for SR-UKF parameter identification. Finally, six viscous hydrodynamic coefficients in the vertical motion plane were identified through a numerical simulation.［Results］The simulation results show that, all identified hydrodynamic coefficients converge to fixed values within 3 000 seconds, and through the selection of appropriate initial values, the maximum error between the identification results and the standard values measured by a hydrodynamic test is only 1.5%. ［Conlusions ］ SR-UKF can be effectively applied to identify submarine hydrodynamic coefficients, and can be further extended to real ship coefficients identification. Key words: submarine； hydrodynamic coefficients； square-root unscented Kalman filter (SR-UKF)；system identification；parameter estimation
0 引 言
潜艇（或水下航行器）的高精度数学模型对其设计和性能预报起着至关重要的作用。目前，进行潜艇运动性能计算、运动规律预报或是自动操艇控制器设计，大都依赖于 Gertler 等[1] 或是 Feldman
等 基于潜艇水动力泰勒展开推导得到的六自由度空间运动模型，以及由此简化得到的潜艇平面（水平面或垂直面）运动模型。而要精确获取上述模型方程中的各项水动力系数是建模的关键因素，但也是方程中最难以确定的，故系数精确与否将显著影响潜艇的性能计算和运动预报精度。
收稿日期: 2020–03–05 修回日期: 2020–05–04 网络首发时间: 2021–04–23 10:48基金项目: 重点实验室基金项目资助（6142217180201）作者简介: 吕帮俊，男，1981 年生，博士，讲师。研究方向：潜艇操纵，潜艇水动力。E-mail：71199512@qq.com *通信作者:吕帮俊