非线性主轴降维映射法在固体火箭发动机设计优化中的应用

为在二维或三维空间中表达固体火箭发动机高维设计空间,引入非线性主轴降维映射法对多维非线性设计优化问题进行降维处理。以某大型固体火箭发动机设计问题为例,将10变量4有效约束优化问题降维映射到二维空间进行研究,拟合的非线性主轴降维映射模型中,目标函数和约束函数的相对误差控制在1.5%以内。研究表明,非线性主轴降维映射法具有发现多变量非线性优化数学模型本征特性的特点,能对设计变量重要性排序;通过降维展示设计空间全景,为优化算法和优化初始点优选提供了直观、有力的工具;优化轨迹实时展示为优化算法性质研究及算法切换提供了依据;根据优化轨迹从优化结果在降维空间中的位置能够判断优化结果是否具有全局最优解特性。

Nonlinear principal axis mapping applied in design optimization for solid rocket motor

Nonlinear principal axis mapping(NPAM) method is proposed to express high-dimensional design space in two or three dimensional space.Taking a solid rocket motor as an example,a 10 variables and 4 constraints optimization problem is fitted by two variables in NPAM,and the errors of the objective and constraints are below 1.5%.It can be seen that NPAM discovers the intrinsic structure of the optimization model and ranks design variables according to their importance.NPAM shows panoramic picture of the design space to help designers choose optimization algorithms and design beginning points.Showing the tracks of optimization in real-time is much helpful to study the optimization algorithms character and switch them.It also helps to judge if the optimal solution is global optimal solution according to its position in the design space.