水下滑翔机外形的高维参数化及Jacobian-Free优化方法研究

Fine shape optimization design of underwater glider can greatly improve the hydrodynamic performance of underwater glider and play an important role in increasing the range of underwater glider. But how to realize the fine modeling of shape and reduce the amount of calculation which increases sharply with the increase of the number of optimization variables is a difficult problem to be solved urgently. For this reason, this project proposes to carry out the research of high-dimensional parameterization and Jacobian-Free optimization of underwater glider shape. To combine step-by-step shape parameterization with CFD mesh deformation, a high-dimensional parameterization method based on NURBS and FFD two-stage manipulation is proposed to achieve fine shape modeling. By using the augmented Lagrange multiplier method, a Jacobian-Free optimization algorithm based on the product of Jacobian matrix and vector is constructed, which avoids the complete Jacobian matrix calculation and greatly reduces the computational load caused by the increase of optimization variables. Fine shape optimization system is built to optimize the shape of the blended-wing-body underwater glider. The potential of high lift-drag ratio of the blended-wing-body configuration is fully tapped, and the experimental verification is completed. The research results will enrich and improve the optimization theory of underwater glider, and greatly improve the hydrodynamic performance and range of underwater glider, which has important theoretical and application value.

水下滑翔机外形的精细化优化设计可大幅提高水下滑翔机的水动力性能，对增加水下滑翔机的航程具有重要作用，但在优化过程中如何实现外形的精细化建模，并减少随优化变量个数增多而急剧增加的计算量是目前亟需解决的难题。为此，本项目提出开展水下滑翔机外形的高维参数化和Jacobian-Free优化方法研究。拟将分步进行的外形参数化和CFD网格变形合二为一，提出一种基于NURBS和FFD两级操控的高维参数化方法，实现外形的精细化建模；采用增广拉格朗日乘子法，构建一种基于雅可比矩阵向量积的Jacobian-Free优化算法，避免进行完整的雅可比矩阵计算，大幅减少优化变量增加带来的计算量；搭建外形精细化优化系统，进行翼身融合水下滑翔机外形的精细化优化设计，充分挖掘翼身融合构型的高升阻比潜力，并完成实验验证。研究成果将丰富和完善水下滑翔机优化理论，大幅提高水下滑翔机的水动力性能和航程，具有重要的理论和应用价值。

水下滑翔机外形的精细化优化设计可大幅提高水下滑翔机的水动力性能，对增加水下滑翔机的航程具有重要作用，但在优化过程中如何实现外形的精细化建模，并减少随优化变量个数增多而急剧增加的计算量是目前亟需解决的难题。本项目开展了水下滑翔机外形的高维参数化和高效优化设计方法研究，主要研究成果包括：（1）提出了一种水下滑翔机外形的精细参数化建模方法：采用最小二乘法对各个翼型剖面的型值点进行拟合，将各个翼型剖面的控制点作为参数化变量；利用偏移、比例、旋转、位置等参数化变量对各个翼型剖面的控制点进行操控，并使用NURBS曲面方程进行几何描述，实现水下滑翔机外形的精细参数化建模。（2）提出了一种基于FFD和轴变形的水下滑翔机外形参数化建模方法：基于B样条方法，建立翼身融合水下滑翔机外形的FFD参数化模型，实现滑翔机外形的自由变形；并在此基础上，针对FFD参数化方法优化变量多的缺点，提出一种翼身融合水下滑翔机外形的轴变形参数化方法，对FFD控制体进行间接变形操纵，减少优化变量的数目。（3）搭建了一种高效、灵活的水下滑翔机外形优化框架：基于水下滑翔机外形的精细参数化方法，推导了几何约束、梯度信息的解析表达式，搭建了一种基于Kriging模型的代理模型优化框架，并依据几何约束的梯度信息，采用梯度优化算法动态添加样本点，提高优化效率。（4）提出了一种水下滑翔机外形的多保真度高效优化设计方法：通过构建多保真度代理模型，减少了水下滑翔机外形优化过程中的高保真度CFD模型及几何约束计算次数，大幅提高优化效率。（5）利用上述方法实现了翼身融合水下滑翔机的精细化外形优化设计，充分挖掘了翼身融合构型的高升阻比潜力，并完成了实验验证。