基于AR-EMD方法的扩展非平稳船舶运动极短期预报AR模型

准确的极短期预报技术能够提高对船舶摇荡运动敏感的海洋特种作业安全性和效率。自回归（auto-regressive，AR）预报模型由于其自适应性强、计算效率高而被广泛应用于船舶运动的极短期预报研究。但该模型基于平稳随机假设，因而在非平稳船舶运动的极短期预报中存在困难。针对非平稳船舶运动极短期预报，文章提出一种基于AR-EMD方法的扩展AR模型，称为EMD-AR预报模型。其中，AR-EMD方法是指在经验模态分解（empirical mode decomposition，EMD）的过程中，采用AR预报的方法处理端点效应问题。 EMD-AR预报模型将非平稳信号分解成若干平稳的固有模态函数分量及余项，然后对各个分量分别用AR模型预报，得到最终的预报结果，以此克服非平稳性对AR预报模型的影响。研究基于船舶试验数据将EMD-AR模型与线性AR模型、非线性支持向量机回归（support vector regression，SVR）预报模型进行对比分析，结果表明，AR-EMD方法能够有效处理船舶运动非平稳性对AR预报模型的影响，提高该模型的预报精度，且EMD-AR模型预报性能较线性AR模型和非线性SVR模型更优。

Extending the Scope of AR Model in Forecasting Non-stationary Ship Motion by Using AR-EMD Technique

Accurate short-term prediction of ship motions allows better improvements in safety and con-trol quality in ship motion sensitive maritime operations. Inspired by the high adaptive and effective nature of auto-regressive (AR) model, it was widely studied in substantial papers concerning short-term prediction of ship motion. However, it suffers theoretical difficulty when the ship motion becomes non-stationary. In this paper, an extended AR model designated as EMD-AR for non-stationary ship motion forecast is developed by using AR-EMD technique. Where, AR-EMD technique refers to empirical mode decomposition (EMD) applying AR prediction method in boundary extension. EMD-AR model overcomes the non-stationarity in ship motion by decomposing the complex ship motion data into a couple of simple intrinsic mode functions (IMFs) and residual. Each sub-compo-nent is predicted individually, and predictions are then aggregated to attain the final results. Com-parative study with linear AR model and nonlinear support vector regression (SVR) model employing model testing ship motion data was conducted. The results show that AR-EMD is effective in han-dling the negative effect on the prediction accuracy resulting from non-stationarity in ship motion and EMD-AR model produces better prediction compared to AR and SVR models.