为在小样本、不确定环境下捕捉燃油消耗趋势，精细化描述燃油消耗状态的动态演化过程，研究基于灰色预测与PDE的舰船燃油动态建模与节能控制方法。依据舰船总阻力与主机输出功率，构建舰船燃油消耗模型，获取实际燃油消耗量；通过灰色预测模型分析实际燃油消耗量，捕捉其变化趋势，预测期望燃油消耗量；以实际舰船燃油消耗量为状态量，利用偏微分方程对舰船燃油消耗过程进行动态建模，精细化描述燃油消耗状态的动态演化过程；以最小化实际与期望燃油消耗量的跟踪误差为优化目标，以偏微分方程的动态建模结果为约束条件，建立燃油消耗优化控制模型，完成舰船燃油消耗动态建模及优化控制。实验证明，该方法可有效计算实际燃油消耗量，并精准预测期望燃油消耗量；该方法可有效优化控制舰船燃油消耗，在不同海况下，均可提升节油率。
To capture fuel consumption trends under small-sample and uncertain environments and finely describe the dynamic evolution process of fuel consumption states, this study investigates a ship fuel dynamic modeling and energy-saving control method based on grey prediction and partial differential equations (PDEs). Based on the ship's total resistance and main engine output power, a ship fuel consumption model is constructed to obtain the actual fuel consumption. The grey prediction model is employed to analyze the actual fuel consumption, capture its changing trends, and predict the expected fuel consumption. Taking the actual ship fuel consumption as state variables, the dynamic process of ship fuel consumption is modeled using PDEs to finely describe the dynamic evolution of fuel consumption states. With the objective of minimizing the tracking error between actual and expected fuel consumption and using the dynamic modeling results from PDEs as constraints, a fuel consumption optimization control model is established to achieve dynamic modeling and optimization control of ship fuel consumption. Experimental results demonstrate that this method can effectively calculate the actual fuel consumption and accurately predict the expected fuel consumption. Moreover, it can effectively optimize and control ship fuel consumption, improving fuel efficiency under various sea conditions, with a minimum fuel savings rate of approximately 65%.
2026,48(5): 75-79 收稿日期：2025-9-8
DOI：10.3404/j.issn.1672-7649.2026.05.012
分类号：U664.1
作者简介：陆雨(1993-),男,硕士,讲师,研究方向为微分方程建模
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