第14卷第2期 智能系统学报 Vol.14 No.2 2019年3月 CAAI Transactions on Intelligent Systems Mar.2019 D0:10.11992/tis.201709044 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.tp.20180416.131l.004.html 基于Kriging模型和NSGA-Ⅱ的 航空发动机管路卡箍布局优化 柳强，焦国帅 (辽宁石油化工大学信息与控制工程学院，辽宁抚顺113001) 摘要：针对传统卡箍布局规划存在效率低且难以解决多目标优化问题等难点，提出一种基于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。提出并建立反映卡箍位置与管路振动性能关系的 Kriging代理模型，同时结合拉丁超立方实验设计方法以及粒子群优化技术提高建模精度。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。在优化计算过程中 应用所建近似模型代替CAE分析程序对适应值函数进行评价，大大减小了计算量。发动机管路卡箍布局算例 表明：所提方法可一次性获得多个满足要求的非支配解方案，不仅提升了管路系统的可靠性，而且计算效率亦 得到了很大提高。最后仿真结果证明了所提方法的有效性。 关键词：发动机管路；Kriging模型：多目标优化：卡箍位置；管路振动 中图分类号：TP18文献标志码：A文章编号：1673-4785(2019)02-0281-07 中文引用格式：柳强，焦国帅.基于Kriging模型和NSGA-Ⅱ的航空发动机管路卡箍布局优化J川.智能系统学报，2019， 14(2):281-287. 英文引用格式：LIU Qiang,.JIAO Guoshuai.Layout optimization of aero-.engine pipe clamps based on Kriging model and NSGA- I[JI.CAAI transactions on intelligent systems,2019,14(2):281-287. 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 tradi- tional 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 relation- ship 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 Kri- ging 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. Keywords:engine pipe;Kriging model;multi-objective optimization;clamp location,pipe vibration 收稿日期：2017-09-22.网络出版日期：2018-04-17 管路系统作为能量传递和介质传输的重要通 基金项目：国家自然科学基金资助项目(51305192)：辽宁省自 道在各种复杂装备中起着重要的作用，对机械装 然料学基金计划重点项目(20170540589). 通信作者：焦国帅.E-mail:jiaoguoshuai123@163.com 备的安全性、可靠性及成本有重要影响。在机械DOI: 10.11992/tis.201709044 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.tp.20180416.1311.004.html 基于 Kriging 模型和 NSGA-II 的 航空发动机管路卡箍布局优化 柳强，焦国帅 （辽宁石油化工大学 信息与控制工程学院，辽宁 抚顺 113001） 摘 要：针对传统卡箍布局规划存在效率低且难以解决多目标优化问题等难点，提出一种基于 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。提出并建立反映卡箍位置与管路振动性能关系的 Kriging 代理模型，同时结合拉丁超立方实验设计方法以及粒子群优化技术提高建模精度。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。在优化计算过程中， 应用所建近似模型代替 CAE 分析程序对适应值函数进行评价，大大减小了计算量。发动机管路卡箍布局算例 表明：所提方法可一次性获得多个满足要求的非支配解方案，不仅提升了管路系统的可靠性，而且计算效率亦 得到了很大提高。最后仿真结果证明了所提方法的有效性。 关键词：发动机管路；Kriging 模型；多目标优化；卡箍位置；管路振动 中图分类号：TP18 文献标志码：A 文章编号：1673−4785(2019)02−0281−07 中文引用格式：柳强, 焦国帅. 基于 Kriging 模型和 NSGA-II 的航空发动机管路卡箍布局优化 [J]. 智能系统学报, 2019, 14(2): 281–287. 英文引用格式：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. 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 tradi￾tional 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 relation￾ship 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 Kri￾ging 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. Keywords: engine pipe; Kriging model; multi-objective optimization; clamp location; pipe vibration 管路系统作为能量传递和介质传输的重要通 道在各种复杂装备中起着重要的作用，对机械装 备的安全性、可靠性及成本有重要影响。在机械 收稿日期：2017−09−22. 网络出版日期：2018−04−17. 基金项目：国家自然科学基金资助项目 (51305192)；辽宁省自 然科学基金计划重点项目 (20170540589). 通信作者：焦国帅. E-mail：jiaoguoshuai123@163.com. 第 14 卷第 2 期 智 能 系 统 学 报 Vol.14 No.2 2019 年 3 月 CAAI Transactions on Intelligent Systems Mar. 2019