随着舰船对高性能、轻量化、耐腐蚀复合材料需求的增长，为解决传统优化方法在舰船用复合材料复杂非线性关系处理中效率低、易陷局部最优的问题，提出了基于Lambert W函数的优化模型。本文首先明确纤维体积分数、铺层角度、基体交联度、纤维长度等优化变量，构建含最大化拉伸强度、最小化密度、最大化耐蚀寿命的多目标函数，通过Lambert W函数解析变量耦合关系；选用改进粒子群算法（IPSO），设定粒子群规模、迭代次数等参数，以加权和为适应度函数求解模型；最后对比IPSO与传统粒子群（PSO）、遗传算法（GA）的优化效果。结果显示，本文的研究结果为舰船复合材料设计提供高效优化方法与量化依据。
With the increasing demand for high-performance, lightweight and corrosion-resistant composite materials in ships, in order to solve the problems of low efficiency and easy to fall into local optimum in the processing of complex nonlinear relationships of composite materials for ships by traditional optimization methods, an optimization model based on Lambert W function is proposed. This paper first clarifies the optimization variables such as fiber volume fraction, layup Angle, matrix crosslinking degree, and fiber length, constructs a multi-objective function containing maximizing tensile strength, minimizing density, and maximizing corrosion resistance life, and analyzes the variable coupling relationship through the Lambert W function. The Improved Particle Swarm Optimization (IPSO) algorithm was selected. Parameters such as the particle swarm size and the number of iterations were set, and the weighted sum was used as the fitness function to solve the model. Finally, the optimization effects of IPSO were compared with those of traditional particle swarm optimization (PSO) and genetic algorithm (GA). The results show that the research findings of this paper provide an efficient optimization method and quantitative basis for the design of ship composite materials.
2025,47(18): 45-48 收稿日期：2025-3-15
DOI：10.3404/j.issn.1672-7649.2025.18.008
分类号：U668
作者简介：张娅妮（1987 – ），女，博士，讲师，研究方向为数学与应用数学
参考文献：
[1] 闫玉红. 基于复合材料的舰船上层建筑连接结构优化[J]. 船舶工程, 2024, 46(9): 179.
[2] 代丽华, 陈雷. 舰船建造工艺参数优化的数学模型构建[J]. 舰船科学技术, 2022, 44(4): 83-86.
DAI L H, CHEN L. Construction of mathematical model for optimization of shipbuilding process parameters[J]. Ship Science and Technology, 2022, 44(4): 83-86.
[3] 施兴华, 许文强, 袁海, 张婧. 舰船复合材料防护结构的选择与优化[J]. 舰船科学技术, 2020, 42(7): 36-40.
SHI X H, XU W Q, YUAN H, ZHANG J. Selection and optimization of ship composite protection structures[J]. Ship Science and Technology, 2020, 42(7): 36-40.
[4] CALASAN M. Iterative solution of the current-voltage relationship in a four-diode solar cell model using the Lambert W equation[J]. Solar Energy, 2025, 290: 113390.
[5] ABBASSI R, SAIDI S, JERBI H, et al. Accurate parameters extraction of photovoltaic models using Lambert W-function collaborated with AI-based Puma optimization method[J]. Results in Engineering, 2025, 25: 104268.
[6] CALASAN M, VUJOSEVIC S, MICEV M, et al. Triple-diode solar cell current optimization – An analytical solution based on the Lambert W function[J]. Alexandria Engineering Journal, 2024, 104: 95-114.
[7] CALASAN M, ABDEL ALEEM S H E, HASANIEN H M, et al. An innovative approach for mathematical modeling and parameter estimation of PEM fuel cells based on iterative Lambert W function[J]. Energy, 2023, 264: 126165.
[8] GUDE S, JANA K C. A multiagent system based cuckoo search optimization for parameter identification of photovoltaic cell using Lambert W-function[J]. Applied Soft Computing, 2022, 120: 108678.
