为了实时准确地反映船舶纵摇运动的非线性、随机性和非平稳性特点，提出了一种基于滑动数据窗口和利普希茨商值法的自适应预测模型。首先，利用滑动数据窗口作为系统局部观测器，将船舶纵摇运动姿态序列进行实时分割；同时采用利普希茨商对当前滑动数据窗口内表示的子系统进行自适应定阶；通过滑动数据窗口和利普希茨商实时为前馈神经网络模型提供在线小批量训练样本，克服单个样本和大批量数据样本对神经网络模型性能的影响。然后，针对基于确定性学习算法的前馈神经网络易陷入局部最优的问题，提出了一种基于改进蝴蝶优化算法训练器的前馈神经网络模型以提高船舶运动姿态的预测精度。在改进蝴蝶优化算法中，引入平衡因子指引的变异算子和最优个体引导机制的信息重组策略，提升算法避免陷入局部最优的能力。最后，通过利用基准测试函数和“育鲲”轮纵摇运动姿态数据集分别验证了改进蝴蝶优化算法和自适应预测模型的有效性和可行性。实验结果表明，改进蝴蝶优化算法比蝴蝶优化算法、粒子群优化算法及飞蛾扑火优化算法具有更好的收敛速度和收敛精度；所提出的自适应预测模型的泛化能力更强，预测精度更高，而且每步平均运行时间均在0.2s以内小于系统采样时间1s。所提出的自适应预测模型不仅能满足实时性要求，而且提高了船舶纵摇运动姿态预报的精度，可为复杂系统在线建模提供一种潜在的解决方案。

In order to accurately reflect the nonlinear, stochastic, and non-stationary characteristics of ship pitch motion in real-time, an adaptive prediction model is proposed based on sliding data window and Lipschitz quotients method. Firstly, the sliding data window is employed as a local observer to segment the ship's pitch motion status data in real-time, and the Lipschitz quotients method is used to adaptively determine the order of the subsystems represented within the current sliding data window. Online small batch training samples are provided for the feed-forward neural network model by using sliding data window and Lipschitz quotients method, which can overcome the impact of single sample and big batch data samples on the performance of the neural network model. Then, to address the problem that feed-forward neural networks based on deterministic learning algorithms are prone to fall into local optimums, a feed-forward neural network model based on the improved butterfly optimization algorithm trainer is proposed to improve the prediction accuracy of the ship's pitch motion status. In the improved butterfly optimization algorithm, a mutation operator guided by the balancing factor and an information reorganization strategy with an optimal individual guidance mechanism are employed to enhance the algorithm's ability to avoid falling into a local optimum. Finally, the effectiveness and feasibility of the improved butterfly optimization algorithm and the adaptive prediction model are verified by using the benchmark test functions and the measured pitch motion status data from M.V. “YuKun”, respectively. The experimental results show that the improved butterfly optimization algorithm in respect of convergence speed and accuracy outranks the butterfly optimization algorithm, particle swarm optimization algorithm, and moth-flame optimization algorithm; The proposed adaptive prediction model has stronger generalization ability and higher prediction accuracy, and the average running time of each step is within 0.2s, which is less than the system sampling time of 1s. The proposed adaptive prediction model not only meets real-time requirements but also improves the accuracy of ship's pitch motion status prediction, which can provide a potential solution for online modeling of complex systems.