﻿ 基于神经网络和粒子群算法的环肋圆柱壳优化设计
 舰船科学技术  2016, Vol. 38 Issue (3): 5-9 PDF

1. 上海交通大学 高新船舶与深海开发装备协同创新中心, 上海 200240;
2. 中国舰船研究设计中心, 湖北 武汉 430064

Optimization of ring-stiffened cylindrical shell based on neural network and particle swarm optimization algorithm
ZHANG Yu1, HUANG Xiao-ping1, YAN Xiao-shun2
1. State Key Lab of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China;
2. China Ship Development and Design Center, Wuhan 430064, China
Abstract: For the external pressure vessel such as submarine shell, it is important to meet stability requirement. This paper wrote an improved particle swarm optimization(PSO), in which the penalty function is employed to transform nonlinear constraint optimization to unconstrained optimization. Then based on Matlab and Ansys, BP neural network and particle swarm optimization were applied to optimize ring-stiffened cylindrical shell , with the stability as constraint, with the total mass of stiffened cylindrical as objective function. And the optimal variables are shell thickness, frame dimensions and frame spacing. In the process of optimization, latin hypercube sampling method are used to choose sample points, and the finite element analysis was carried out on the sample points. With the analysis result, BP neural network can be built. Then this paper discuss the sample’s influence on prediction accuracy of neural network. Finally, this paper optimize the neural network with improved particle swarm optimization method. Optimum results shows that the validity of the proposed approach is examined, and this method can be used to solve nonlinear constraints discrete structural optimization problems. Use BP-PSO optimization algorithm can get good optimization result and save lots of time.
Key words: BP neural network    particle swarm optimization(PSO)    ring-stiffened cylindrical shell    optimization    stability analysis
0 引 言

1 BP-PSO 算法的基本原理 1.1 BP 神经网络

BP神经网络是近年来应用最为广泛的一种近似代理模型，具有很强的非线性映射能力，可以根据一定数量的样本点建立起输入变量到输出变量间的一一映射关系。并且，可以通过改变样本点的个数、隐含层的神经元个数以及隐含层的层数来获得想要的映射精度[9]。因此，在结构优化领域，可以根据这一映射关系来获得结构响应，从而替代耗时的有限元分析。

1.2 改进粒子群算法基本原理

1) 速度和位置更新公式

 $x_i^{k + 1} = x_i^k + v_i^{k + 1},$ (1)

 $v_i^{k + 1} = wv_i^k + {c_1}{r_1}[p_i^k - x_i^k] + {c_2}{r_2}[p_g^k - x_i^k],$ (2)

 $x_i^{k + 1} = {\rm{round}}(x_i^k + v_i^{k + 1})。$ (3)

2) 自适应权重系数

 $w = \left\{ {\begin{array}{*{20}{l}} {{w_{\min }} - \frac{{({w_{\max }} - {w_{\min }}) \cdot (f - {f_{\min }})}}{{({f_{avg}} - {f_{\min }})}},f \le {f_{avg}},}\\ {{w_{\max }},\quad \quad \quad \quad \quad \quad \quad \quad f > {f_{avg}}{\rm{。}}} \end{array}} \right.$ (4)

3) 约束处理

 $F(x) = f(x) + \lambda \cdot \varphi (x),$ (5)

2 基于 BP-PSO 算法的环肋圆柱壳优化设计 2.1 优化策略以及流程

 图 1 BP-PSO算法优化流程 Fig. 1 Flow chart of BP-PSO
2.2 有限元模型

 图 2 环肋圆柱壳几何模型 Fig. 2 Geometric model of ring-stiffened cylindrical shell

 图 3 有限元模型 Fig. 3 Finite element model
2.3 优化的数学模型

 $\min f(x) = W(x)。$ (6)

 ${P_c}1.2P = 7.2{\mkern 1mu} {\rm{MPa}}。$ (7)

3 结果分析与讨论 3.1 神经网络预测精确度分析

 ${\rm{ARV}} = \frac{{\sum\limits_{i = 1}^N {{{[x(i) - \hat x(i)]}^2}} }}{{\sum\limits_{i = 1}^N {{{[x(i) - \mathop {{\rm{ }}x}\limits^ - (i)]}^2}} }}。$ (8)

 图 4 结构重量预测输出 Fig. 4 Structure weight prediction output

 图 5 失稳临界压力预测输出 Fig. 5 Buckling pressure prediction output
3.2 优化结果分析

 图 6 BP-PSO 算法优化过程 Fig. 6 Optimization process of BP-PSO

4 结 语

 [1] 陈美霞, 金宝燕, 陈乐佳. 基于APDL语言的加筋圆柱壳的静 动态性能优化设计[J]. 舰船科学技术, 2008, 30(3): 64-68.CHEN Mei-xia, JIN Bao-yan, CHEN Le-jia. Optimization design of static and dynamic characteristics of stiffened cylindrical shells based on APDL[J]. Ship Science and Technology, 2008, 30(3): 64-68. [2] 龙连春, 赵斌, 陈兴华. 薄壁加筋圆柱壳稳定性分析及优化[J]. 北京工业大学学报, 2012, 38(7): 997-1003.LONG Lian-chun, ZHAO Bin, CHEN Xing-hua. Buckling analysis and optimization of thin-walled stiffened cylindrical shell[J]. Journal of Beijing University of Technology, 2012, 38(7): 997-1003. [3] 王存福, 赵敏, 葛彤. 考虑失稳模式的环肋圆柱壳结构优化设计[J]. 上海交通大学学报, 2014, 48(1): 56-63.WANG Cun-fu, ZHAO Min, GE Tong. Optimal design of ring-stiffened cylindrical shell considering instability mode[J]. Journal of Shanghai Jiaotong University, 2014, 48(1): 56-63. [4] PEREZ R E, BEHDINAN K. Particle swarm approach for structural design optimization[J]. Computers & Structures, 2007, 85(19/20): 1579-1588. [5] LUH G C, Lin C Y. Optimal design of truss-structures using particle swarm optimization[J]. Computers & Structures, 2011, 89(23/24): 2221-2232. [6] 何小二, 王德禹, 夏利娟. 基于粒子群算法的多用途船结构优化[J]. 上海交通大学学报, 2013, 47(6): 928-931.HE Xiao-er, WANG De-yu, XIA Li-juan. Optimization of multipurpose ship structures based on particle swarm approach[J]. Journal of Shanghai Jiaotong University, 2013, 47(6): 928-931. [7] 郭海丁, 路志峰. 基于BP神经网络和遗传算法的结构优化设计[J]. 航空动力学报, 2003, 18(2): 216-220.GUO Hai-ding, LU Zhi-feng. Structure design optimization based on BP-neural networks and genetic algorithms[J]. Journal of Aerospace Power, 2003, 180(2): 216-220. [8] 王建, 庞永杰, 程妍雪, 等. 近似模型在非均匀环肋圆柱耐压壳优化中的应用研究[J]. 船舶力学, 2014, 18(11): 1331-1338.WANG Jian, PANG Yong-jie, CHENG Yan-xue, et al. Application of approximation models to optimize the design of the non-uniform ring-frames pressure shell[J]. Journal of Ship Mechanics, 2014, 18(11): 1331-1338. [9] 王吉权. BP神经网络的理论及其在农业机械化中的应用研究[D]. 沈阳: 沈阳农业大学, 2011. [10] 敖永才, 师奕兵, 张伟, 等. 自适应惯性权重的改进粒子群算法[J]. 电子科技大学学报, 2014, 43(6): 874-880.AO Yong-cai, SHI Yi-bing, ZHANG Wei, et al. Improved particle swarm optimization with adaptive inertia weight[J]. Journal of University of Electronic Science and Technology of China, 2014, 43(6): 874-880. [11] 陈果. 神经网络模型的预测精度影响因素分析及其优化[J]. 模式识别与人工智能, 2005, 18(5): 528-534.CHEN Guo. Analysis of influence factors for forecasting precision of artificial neural network model and its optimizing[J]. Pattern Recognition and Artificial Intelligence, 2005, 18(5): 528-534.