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

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.