针对高非线性船舶横摇运动的精确建模问题,提出了一种基于Koopman算子的数据驱动建模方法.首先,根据随机海浪模型和船舶横摇动力学模型建立随机海浪下的船舶横摇动力学模型;其次,使用扩展动态模式分解(extended dynamic mode decomposition,EDMD)法对Koopman算子进行近似化处理,建立船舶横摇的高维线性模型;最后,在确定高维线性模型使用的基函数和系统提升的空间维数后,根据Matlab Simulink模块仿真得到的船舶横摇数据进行数据驱动建模.实验结果表明,所建立的Koopman线性模型在对船舶横摇角和横摇角速度的跟踪精度方面明显优于局部线性化、反馈线性化、无迹卡尔曼滤波3种模型,同时模型计算速度显著提高.该研究成果为高维线性控制拟合方法在船舶姿态稳定性控制的应用提供了一定技术支撑.
To address the precise modeling problem of highly nonlinear ship rolling motion, a data-driven modeling method based on Koopman operator was proposed. Firstly, based on the random wave model and the ship rolling dynamics model, the ship rolling dynamics model under random waves was established. Secondly, the extended dynamic mode decomposition (EDMD) method was used to approximate the Koopman operator, and a high-dimensional linear model of ship rolling was established. After determining the basis function used by the high-dimensional linear model and the spatial dimension of system lifting, data-driven modeling was carried out based on the ship rolling data obtained by Matlab Simulink simulation. The experimental results show that the established Koopman linear model is significantly better than the three models of local linearization, feedback linearization, and unscented Kalman filter in terms of tracking accuracy for ship roll angle and roll angular velocity, and the calculation speed of the model is significantly improved. The research results in this paper provide certain technical support for the application of the high-dimensional linear control fitting method in ship attitude stability control.
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