﻿ 舰载直升机通用矩阵式系留座优化设计方法研究
 舰船科学技术  2018, Vol. 40 Issue (8): 133-136, 140 PDF

Investigation on the optimization design for matrix lashing holes of shipboard helicopter
ZHU Feng, AN Qiang-lin, WEN Qi-mu
Systems Engineering Research Institute, Beijing 100094, China
Abstract: To improve the compatibility of the shipboard helicopters’ lashing, matrix lashing holes are used. An optimization model is established for the lashing hole design. In contrast to traditional optimization models, this model considers both two helicopter’s lashing strength, deals with the bi-objective optimization by fuzzy processing, and uses penalty function to restrict the rig’s length and load. The the particle swarm algorithm is utilized to solve the problem. The feasibility of the model and algorithm are verified by a simulation analysis.
Key words: shipboard helicopter     matrix lashing hole     particle swarm algorithm     bi-objective optimization
0 引　言

1 舰载直升机矩阵式系留座优化模型 1.1 目标函数

1）重力。作用在机体重心，竖直向下。

2）风力。作用在形心处，设定为正侧方来风，方向为水平。

3）惯性力。作用在机体重心，沿3个座标轴方向分别为 $M{a_x}$ $M{a_y}$ $M{a_z}$ $M$ 为直升机质量； ${a_x}$ ${a_y}$ ${a_z}$ 分别为舰船纵向，横向和垂向加速度。

 $\Delta T = EA\left(\frac{{\Delta L}}{{{L_0}}}\right)\text{，}$ (1)

 $\frac{{\partial (U - W)}}{{\partial u}} = \frac{{\partial (U - W)}}{{\partial v}} = \frac{{\partial (U - W)}}{{\partial {\theta _z}}} = 0\text{，}$ (2)

 $\left\{ {\begin{array}{*{20}{c}} {{f_1}({d_x},{d_y}) = \max ({T_{1i}}),i = 1,2,...{J_1}} \text{，} {{f_2}({d_x},{d_y}) = \max ({T_{2i}}),i = 1,2,...{J_2}} \text{。}\end{array}} \right.$ (3)

 $\left\{ {\begin{array}{*{20}{c}} {{f_1}({d_x}) = \max ({T_{1i}})}\text{，} {{f_2}({d_x}) = \max ({T_{2i}})} \text{。}\end{array}} \right.$ (4)
1.2 约束条件

 $\left\{\!\!\!\!\!\!\!\!\! {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{l_{1i}} - {L_{1\max }} \leqslant 0,i = 1,2,...,{J_1}}\text{，} \\ {\begin{array}{*{20}{c}} {{T_{1i}} - {T_{1\max }} \leqslant 0,i = 1,2,...,{J_1}}\text{，} \\ {{l_{2i}} - {L_{2\max }} \leqslant 0,i = 1,2,...,{J_2}}\text{，} \end{array}} \end{array}} \\ {{T_{2i}} - {T_{2\max }} \leqslant 0,i = 1,2,...,{J_2}} \text{。}\end{array}} \right.$ (5)

1.3 双目标模糊策略

1）以A型舰载直升机的所有索具的系留载荷极值 ${f_1}$ 为目标函数进行优化，得到A型机系留载荷极值的下限，记为 ${F_1}_m$ ，根据此时的设计变量求解 ${f_2}$ ，得到B型机系留座载荷极值的上限，记为 ${F_2}_M$

2）以B型舰载直升机所有索具的系留载荷极值 ${f_2}$ 为目标函数进行优化，得到B型机系留载荷极值的下限，记为 ${F_2}_m$ ，根据此时的设计变量求解 ${f_1}$ ，得到A型机系留载荷极值的上限，记为 ${F_1}_M$

3）进行双目标函数模糊化处理，建立单目标函数值到其隶属度函数的映射。假定隶属度函数按照线性规则确定，则隶属度函数为：

 $\eta ({f_i}) = \left\{ {\begin{array}{*{20}{c}} 1\text{，} {\displaystyle\frac{{{F_{iM}} - {f_i}}}{{{F_{iM}} - {F_{im}}}}}\text{，} 0\text{，} \end{array}} \right. \begin{array}{*{20}{c}} \!{{f_i} \leqslant {F_{im}}}\text{，}\qquad\qquad {{F_{im}} \leqslant {f_i} \leqslant {F_{iM}}}\text{，} \!{{f_i} \geqslant {F_{iM}}}\text{。}\qquad\qquad\end{array}$ (6)

4）综合2个目标函数隶属度：

 $F = \min (\eta ({f_1}),\eta ({f_2}))\text{。}$ (7)

2 粒子群优化算法

 $\begin{gathered} {V_i}^{k + 1} = w \times {V_i}^k + {c_1} \times {r_1} \times ({({p_{best}})_i}^k - {X_i}^k)+ \\ \qquad \quad {c_2} \times {r_2} \times ({({g_{best}})^k} - {X_i}^k)\text{，} \hfill \\ \end{gathered}$ (8)
 ${X_i}^{k + 1} = {X_i}^k + {V_i}^{k + 1}\text{，}$ (9)
 $\omega = 0.9 - (0.9 - 0.4) \times k/Nummax \text{。}$ (10)

3 算例分析 3.1 舰载直升机参数

 图 1 舰船飞行甲板舰载直升机停放示意图 Fig. 1 Shipboard helicopter parking on the flight deck

3.2 优化结果分析

 图 2 系留载荷粒子群优化流程图 Fig. 2 The PSO flow chart of the tie-down loads

${f_1}$ 为目标函数进行优化时，此时全局最优解对应的甲板系留座间距使得A型舰载直升机的系留载荷极值达到最小，即 ${F_{1m}}$ ，以间距为输入求得此时的B型舰载直升机的系留载荷极值，即 ${F_{2M}}$ ；以 ${f_2}$ 为目标函数进行优化时，可得 ${F_{2m}}$ ${F_{1M}}$ ；随后对双目标模糊化处理后的目标函数 $F$ 进行优化。

 图 3 目标函数 ${f_1}$ 收敛曲线 Fig. 3 The convergence curve of objective function f1

 图 4 目标函数 ${f_2}$ 收敛曲线 Fig. 4 The convergence curve of objective function f2

 图 5 双目标模糊函数 $F$ 收敛曲线 Fig. 5 The convergence curve of bi-objective function F

4 结　语

 [1] 王丹. 舰载直升机系留载荷分析及优化设计研究[D]. 哈尔滨: 哈尔滨工程大学, 2008. [2] 李书, 何忠恒, 徐丽娜. 舰载直升机系留座的布置优化[J]. 航空学报, 2005, 26(6): 715–719. http://mall.cnki.net/magazine/Article/HKXB200506011.htm [3] 吴靖, 胡国才. 基于蚁群算法的直升机舰面系留座优选[J]. 计算机仿真, 2015, 32(7): 357–360. [4] KENNEDY J, EBERHART R. Particle swarm optimization[C]// In Proceeding of IEEE International Conference on Neural Networks, Washington, 1995:1942–1948. [5] K.E. PARSOPOULOS, M.N. VRAHATIS. Paricale swarm optimization method in multiobjective problems[C]// In Proceeding of the 2002 ACM symposium on Applied computing, 2002: 603–607. [6] KENNEDY J. Small worlds and mega-minds: effect of neighborhood topology on particle swarm performance[C]// IEEE Congress on Evolutionary Computation, 1999:1931–1938. [7] 黄梅, 王一依, 张彩萍, 马伟强, 安动. 充换电储能系统模糊双目标优化调度方法. 北京交通大学学报. 2014, 38(5): 97–102.