船舶操纵运动仿真中改进变步长龙格库塔算法

Improved variable stepsize Runge-Kutta algorithm in the ship manoeuvring motion simulation

针对船舶四自由度操纵运动仿真对运算速度和精度的要求,提出了一种改进的变步长龙格库塔算法以求解船舶动力学和运动学方程.该算法每一次迭代求解过程中在局部将各运动姿态与步长转化为线性关系,根据各姿态实际相对误差与给定相对误差允许值之间的比值来调整步长,使得步长能够根据微分方程梯度变化情况进行自动调整.以某大型货船四自由度模型为对象,对比分析了本文变步长算法、定步长龙格库塔算法和常规变步长龙格库塔算法的仿真性能,结果表明变步长算法具有更快的运算速度和响应速度,非常适用于船舶操纵运动的一般仿真研究.

According to the arithmetic speed and computational accuracy of the ship manoeuvring mo tion simulation in four degrees of freedom, an improved variable stepsize Runge-Kutta algorithm to solve the ship kinetic equations and kinematical equations was proposed. During the iterative solving process, the improved algorithm linearizes the nonlinear function of motion states in local region, and adjusts the stepsize according to the ratio of real motion relative error to the given relative error toler ance. It makes the stepsize change adaptively according to the gradient of differential equation. Final- ly, this paper established a model of a container ship in four degrees of freedom, and analyzed the sim- ulation results calculated based on the improved variable stepsize Runge-Kutta algorithm, fixed step- size Runge-Kutta algorithm and conventional variable stepsize Runge-Kutta algorithm respectively. The results show that the variable stepsize algorithm with faster computing speed and response speed. It is very suitable for the simulation of ship maneuvering motion.