﻿ 基于Kriging模型和NSGA-II的航空发动机管路卡箍布局优化
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 智能系统学报  2019, Vol. 14 Issue (2): 281-287  DOI: 10.11992/tis.201709044 0

### 引用本文

LIU Qiang, JIAO Guoshuai. Layout optimization of aero-engine pipe clamps based on Kriging model and NSGA-II[J]. CAAI Transactions on Intelligent Systems, 2019, 14(2): 281-287. DOI: 10.11992/tis.201709044.

### 文章历史

Layout optimization of aero-engine pipe clamps based on Kriging model and NSGA-II
LIU Qiang , JIAO Guoshuai
School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, China
Abstract: Considering the low efficiency and difficulty in solving multi-objective optimization problems of the traditional clamp layout planning methods, a multi-objective layout optimization method of aero-engine pipe clamps based on Kriging model and NSGA-II is presented. Firstly, the Kriging surrogate model is constructed to reflect the relationship between the clamp position and the vibration performance of the pipe, and the modeling accuracy is improved by using the Latin hypercube design method and particle swarm optimization (PSO). Secondly, the first natural frequency and second order natural frequency of pipe are selected as the optimization objectives, and then the NSGA-II algorithm is applied to solve the layout planning of the pipe clamp for avoiding resonance In the process of optimization, the Kriging models are used instead of the CAE analysis program to evaluate the fitness function, which significantly reduces the computational complexity. Numerical computations of engine pipe clamp layout show that the proposed method can obtain a set of non-dominated solutions meeting engineering requirements while improving the reliability of piping system and computational efficiency of algorithm, which demonstrates the effectiveness and efficiency of proposed method.
Key words: engine pipe    Kriging model    multi-objective optimization    clamp location    pipe vibration

1 总体设计

1) 建立UG模型，采用拉丁超立方抽样产生管路卡箍位置的试验样本。

2) 应用UG高级仿真模块的有限元分析计算方法，对样本点进行模态分析，得到样本响应值。

3) 根据样本及样本响应值分别建立Kriging近似模型并进行模型精度检验。

4) 基于Kriging代理模型和NSGA-II算法对管路卡箍位置进行多目标优化，最后进行验证、输出计算结果。

2 试验设计及Kriging代理模型 2.1 试验设计

1) 进行网格划分。选用十节点四面体单元，单元大小为1.5 mm，整个管路使用了35 470个节点, 19 976个单元，结果如图3(b)所示。

2) 添加约束。在管路两端添加固定约束，在卡箍位置处添加圆柱形约束(暂不考虑卡箍的刚度)，固定其径向和轴向增长，如图3(d)所示。

3) 进行求解，记录数据。使用UG软件高级仿真的NX NASTRAN求解器，解算方案类型为SOL 103 Real Eigenvalues。求解完成后，记录管路的一阶固有频率和二阶固有频率,求解结果如图3(c)所示。

2.2 Kriging模型的基本原理

 $y(x) = F(\beta ,x) + Z(x)$ (1)

3 基于Kriging模型和NSGA-II的管路卡箍布局优化 3.1 NSGA-II简介

NSGA-II是Deb等[18]在2002年对其算法NSGA的改进算法，它是目前多目标优化领域应用最广泛的算法之一。相对于NSGA而言，NSGA-II的主要特点包括：1) 使用一种新的快速非支配解排序方法，有效降低了计算的复杂度。2) 应用拥挤度的概念，克服了NSGA中需要人为指定共享参数的缺陷，从而使得个体能够扩展到整个Pareto前沿面并尽可能的均匀分布。3) 采用精英保留机制，不但扩大了采样空间，而且可以保证优良个体在进化过程中不会丢失，有效提高了种群的进化效率。

3.2 优化目标及编码设计 3.2.1 优化目标

 $\min \left\{ \begin{array}{l} {f_1}(x) = - |\Delta {w_1}| = - |{w_1} - {w_e}|\\ {f_2}(x) = - |\Delta {w_2}| = - |{w_2} - {w_e}| \end{array} \right.$ (2)

3.2.2 编码方式

 ${l_1} = \int_{{\varGamma _1}} {{\rm d}s}$ (3)
 ${l_2} = \int_{{\varGamma _2}} {{\rm d}s}$ (4)

 $\left[ \begin{array}{l} {l_{11}}\,\,\,\,{l_{12}}\,\,\,\, \cdots \,\,\,\,{l_{1n}}\\ \qquad\;\;\;\vdots \\ {l_{i1}}\,\,\,\,{l_{i2}}\,\,\,\, \cdots \,\,\,\,{l_{in}}\\ \qquad\;\;\;\vdots \\ {l_{M1}}\,\,\,\,{l_{M2}}\,\,\,\, \cdots \,\,\,\,{l_{Mn}} \end{array} \right]$

 Download: 图 4 卡箍布置点距离管路右端点的曲线长度 Fig. 4 The curve length of clamp placement distance line right endpoint
3.3 算法流程

4 仿真实验及结果分析

4.1 卡箍布局仿真

 Download: 图 6 发动机管路卡箍布局的Pareto解集前沿面 Fig. 6 Pareto set front surface of engine pipe clamp layout
 Download: 图 7 ${l_1}$ 和 ${l_2}$ 分布图 Fig. 7 The distribution map of ${l_1}$ and ${l_2}$

4.2 结果讨论

5 结束语

1) 本文提出了一种基于Kriging模型和NSGA-II算法的航空发动机管路卡箍多目标布局优化方法，以管路一阶固有频率和二阶固有频率为优化目标，应用NSGA-II对管路卡箍位置进行布局规划以避免共振，提高管路系统的稳定性。

2) 通过建立Kriging代理模型，避免了在优化过程中反复使用CAE分析程序对适应值函数进行评价，因此显著提高了优化效率。

3) 与传统的管路卡箍布局方法相比，本文所提方法可以得到一组非支配解集，设计人员可以根据工程经验选择适当的管路卡箍布局方案。

4) 所提方法具有很好的通用性，既适用于发动机管路卡箍布局，也适用于其他域的管路支撑部件布局问题，所用CAE软件可以根据行业特点选择Ansys、Cosmos、Pro/ENGINEER等。

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