基于样本映射与动态Kriging的飞行器离散连续优化方法  

Kriging⁃based mixed⁃integer optimization method using sample mapping mechanism for flight vehicle design

作　　者：李昊达 龙腾[1,2] 史人赫 叶年辉 LI Haoda;LONG Teng;SHI Renhe;YE Nianhui(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;Key Laboratory of Dynamics and Control of Flight Vehicle of Ministry of Education,Beijing Institute of Technology,Beijing 100081,China;Beijing Institute of Technology Chongqing Innovation Center,Chongqing 401121,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]北京理工大学飞行器动力学与控制教育部重点实验室,北京100081 [3]北京理工大学重庆创新中心,重庆401121

出　　处：《航空学报》2024年第3期143-159,共17页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(52272360,52005288);北京市自然科学基金(3222019);北京理工大学青年教师学术启动计划(XSQD-202101006);北京理工大学科技创新计划项目(2021CX01013);北京理工大学研究生科研水平和创新能力提升专项计划(2022YCXZ017)。

摘　　要：针对复杂飞行器系统离散连续混合优化计算成本高、全局收敛性差等问题,提出了一种基于样本映射与动态Kriging的离散连续优化方法(SMDK-DC)。该方法采用Kriging代理模型代替高耗时仿真模型以降低计算成本,并定制一种基于综合曼哈顿距离准则的样本点映射机制,在连续-离散空间内高效生成满足均布性要求的真实样本点。将期望改善度准则与重点采样空间方法相结合,辨识优质新增样本点,持续动态更新Kriging,引导离散连续优化过程快速收敛。标准数值算例测试结果表明,与SOMI、NOMAD等国际同类方法相比,SMDK-DC方法在全局收敛性与鲁棒性方面具有显著优势。使用该方法求解固体火箭发动机多学科设计优化问题,优化方案在满足燃烧室、内弹道等学科约束条件前提下,使得发动机总冲提升12.92%以上,且优化收益较SOMI方法提高1.71%,从而验证了本文工作的有效性与工程实用性。To deal with the problems of high computational cost and poor global convergence that often exist in discretecontinuous mixed optimization of complex flight vehicle systems,a Sample Mapping and Dynamic Kriging based Discrete-Continuous Mixed Optimization method(SMDK-DC)is proposed.In this method,time-consuming simulation model is replaced by Kriging surrogate model to reduce computational expenses.A sample point mapping mechanism based on generalized Manhattan distance criterion is also proposed to efficiently generate uniformly-distributed real sample points in continuousdiscrete domain.Expected improvement criteria is combined with significant sampling space to identify new sample points,update Kriging continuously and dynamically,and guide the rapid convergence of the discrete-continuous optimization process.Benchmark cases show that compared with international methods such as SOMI and NOMAD,SMDK-DC has significant advantages in global convergence and robustness.Finally,SMDK-DC is used for solving a multidisciplinary design optimization problem of solid rocket motor.The method,on the premise of satisfying all the constraints of the combustion chamber and internal ballistic discipline,leads to a total impulse increase of at least 12.92%,and the optimization yield is 1.71%higher than that of SOMI,which verifying the effectiveness and engineering practicability of SMDK-DC.

关 键 词：KRIGING 离散连续混合优化 近似优化 期望改善度 重点采样空间 

分 类 号：V221[航空宇航科学与技术—飞行器设计]