针对船舶方案设计阶段难以评估随机环境条件下船舶倾覆风险的问题，本文提出一种基于马尔可夫过程的船舶主尺度优化设计方法。该方法充分考虑阻尼力矩与复原力矩的非线性特性以及风浪的随机性，建立随机风浪中船舶非线性横摇运动的伊藤随机微分方程模型；采用二阶随机龙格-库塔法求解方程，结合蒙特卡洛模拟计算船舶在随机环境条件下的倾覆概率；进而，将倾覆概率作为安全性指标融入优化过程，构建以主尺度为变量的优化模型。算例验证了方法的有效性，并进行了参数敏感性分析。研究表明，该方法计算高效、易于实施，能在方案设计阶段有效评估船舶倾覆风险，为船型方案优选提供关键决策依据。
To address the challenge of evaluating ship capsize risk under stochastic environmental conditions during the preliminary design phase, this paper proposes a Markov process-based method for optimal ship design focusing on principal dimensions. The approach comprehensively accounts for the nonlinear characteristics of damping and restoring moments and the stochastic nature of wind waves, establishing a model of It? stochastic differential equations for nonlinear ship rolling in random seas. The SRI-2 stochastic Runge-Kutta method is employed to solve the equations, combined with Monte Carlo simulations to compute ship capsize probability under stochastic environmental conditions. Subsequently, the capsize probability is incorporated as a safety metric into the optimization process, constructing an optimization model with principal dimensions as variables. Case studies validate the method's effectiveness and include parametric sensitivity analyses. Research demonstrates that this approach achieves high computational efficiency and ease of implementation, enabling effective capsize risk assessment during preliminary design while providing critical decision-making basis for hull form selection.
2026,48(7): 18-24 收稿日期：2025-7-29
DOI：10.3404/j.issn.1672-7649.2026.07.004
分类号：U662.2
基金项目：在职培养博士科研启动费（1012931704）
作者简介：董新硕(1987-),男,博士,讲师,研究方向为船舶现代设计理论、随机风浪中船舶非线性动力学
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