中文摘要：

为提高船舶横摇运动预报的精度以及实时性，提出一种利用混沌理论和最小二乘支持向量机（Least Squares Sup—port Vector Machine，LSSVM）在线训练算法的实时在线预报方法。针对预报模型的固定核参数不能适应横摇运动的动态变化而进行自动调节这一问题，设计一种基于ESSVM的变参数在线建模方法。利用三个LSSVM并行建模，将整个预报过程分为初始阶段和若干个预报阶段，并在每个阶段末选出下一个预报阶段的预报LSSVM，同时根据启发式规则为另两个LSSVM设定核参数，它们作为下一阶段的比较LSSVM。对某船横摇运动时间序列进行预报，仿真结果表明，所提变参数I_SSVM在线预报方法平均相对均方误差为6．85％，相比于固定参数预报方法具有更好的适应性。

英文摘要：

In order to improve the accuracy and real-time nature of prediction model of ship rolling motion, an online real-time prediction method is presented, which combines chaos theory and least squares support vector machine（LSSVM）. Aiming at the problem that the fixed parameter of forecast- ing model can not be adaptively adjusted with dynamic change of ship rolling motion, a varying pa- rameter online modeling method is proposed based on LSSVM. Three LSSVMs are used to model par- allelly and the whole prediction processes are divided into an initial stage and several prediction stages. The next predicting LSSVM is selected at the end of each stage, at the same time, the kernel parameters of the other two LSSVMs are reset according to heuristic rules, which are used as compar- ative LSSVMs for the following predicting stages. The experiments of ship roiling time series predic- tion are made. The simulation results indicate that real-time prediction root-mean-square error of the proposed method is about 6.85%, which has better adaptability compared to fixed parameter predic- tion method.