A Method of Multi-objective Topology Optimization of UUV Non-pressure-bearing Structure
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摘要: 鉴于非耐压承载结构对于UUV(Unmanned underwater vehicle)的重要意义,提出一种基于折衷规划法建立综合目标函数,以灰色-层次分析确定子目标权重系数的多目标优化方法。以某型UUV的非耐压承载结构为例,首先采用灰色-层次分析法,得到各子目标(典型工况的柔度和前3阶固有频率的平均值)的权重系数;然后,采用折衷规划法进行多目标拓扑优化设计。优化结果表明:该方法适用于UUV非耐压承载结构的初始设计,可行且有效。同时,对比层次分析法和灰色关联分析法,该方法计算效率更高,优化结果更加合理。Abstract: Considering the importance of a non-pressure-bearing structure to UUV, its multi-objective topology is optimized by using the compromise programming method so as to establish a comprehensive objective function. The grey-analytic hierarchy process is used to determine the weight factors of sub-objectives. Taking the non-pressure-bearing structure of UUV for example, firstly, the weight factors of sub-objectives (flexibility of typical operating conditions and average values of natural frequency of the first three orders) were obtained with the grey-analytic hierarchy process according to optimization results. Then, the multi-objective topology optimization was designed with the compromise programming method. The optimization results show that the method presented in this paper is feasible and effective for the initial design of the UUV non-pressure-bearing structure. At the same time, the grey-analytic hierarchy process is more efficient and more reasonable than analytic hierarchy process and grey relational analysis.
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表 1 目标间的重要性参考定义因素水平表
目标fi对目标fj相对重要度 αij 说明 极端重要 9 两指标的判断差异达到可能范围内的最大限度 强烈重要 7 两指标的判断差异强烈 明显重要 5 两指标的判断差异明显 稍重要 3 两指标的判断差异轻微 同等重要 1 两指标无判断差异 稍不重要 1/3 两指标的判断差异轻微 明显不重要 1/5 两指标的判断差异明显 强烈不重要 1/7 两指标的判断差异强烈 极端不重要 1/9 两指标的判断差异达到可能范围内的最大限度 注:若fi和fj的差异程度介于上述某两个相邻等级之间, 则αij相应为2, 4, 6, 8, 2, 1/2, 1/4, 1/6, 1/8 表 2 随机一致性指标RI参考值
矩阵阶数n 1 2 3 4 5 6 7 8 9 随机一致性指标RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 表 3 非耐压承载结构工况统计表
工况序号 工况名称 工况描述 优化目标 1 起吊工况 主要承受所搭载设备的重力 柔度最小 2 主要运行工况 主要承受使用过程中的反作用力 柔度最小 3 动态频率 满足系统的动态频率要求 固有频率最大 表 4 灰色-层次分析综合权重统计表
工况序号 工况名称 柔度/(N·mm) 前3阶固有频率平均值/Hz 1 起吊工况 45 352.1 36 751.4 16.92 2 主要运行工况 283 517.1 1 753.5 16.43 3 动态频率 83 262.3 9 653.9 25.75 被关联序列 45 352.1 1 753.5 25.75 综合权重值 0.528 2 0.774 5 0.589 6 表 5 权重系数设定方案
方案序号 权重系数确定方法 起吊工况 主要运行工况 前3阶固有频率平均值 1 层次分析法 0.256 5 0.846 8 0.466 2 灰色关联分析法 0.638 2 0.643 3 0.626 3 3 灰色-层次分析法 0.528 2 0.774 5 0.589 6 表 6 目标优化值与迭代次数统计表
方案序号 权重系数确定方法 柔度/(N·mm) 前3阶固有频率平均值/Hz 迭代次数 起吊工况 主要运行工况 1 层次分析法 54 482.4 2 819.7 24.13 113 2 灰色关联分析法 54 091.6 2 973.7 24.43 99 3 灰色-层次分析法 54 237.1 2 835.2 24.48 98 -
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