基于核主成分分析的涡轮盘结构设计优化

Optimization of Turbine Disk Structure Design Based on Kernelized Principal Component Analysis

关键词:  涡轮盘  非均匀有理B样条  结构设计优化  核主成分分析  降维空间

Key words:  Turbine disk  Nonuniform rational B-spline  Structure design optimization  Kernelized principal component  Dimension reduction space

摘要:

为解决轮盘形状优化过程中变量多且高度非线性的问题，建立了基于核主成分分析（Kernelized Principal Component Analysis，KPCA）技术的航空发动机轮盘优化方法。利用控制点形式的非均匀有理B样条（NURBS）曲线构造涡轮盘截面形状，以控制点的坐标作为设计变量；利用实验设计（DOE）进行采样，从中选取60个较优样本，计算核矩阵K，应用核矩阵K的特征向量计算投影向量的系数矩阵，采用投影后的变量作为新的设计变量，重构设计空间；最后，在降维后的设计空间中优化涡轮盘。结果表明：优化后轮心当量应力降低4.21%，周向应力降低0.26%，轮背径向应力降低1.58%，子午截面平均周向应力降低2.57%，圆柱截面平均径向应力降低6.51%。

Abstract:

In order to solve the problem of many variables and high nonlinearity in wheel shape optimization， an aero-engine wheel optimization method based on Kernelized Principal Component（KPCA） was established. Firstly， the section shape of turbine disk is constructed by using Nonuniform rational B-spline（NURBS） curve in the form of control points， and the coordinates of control points are used as the design variables. Then the design of experiment （DOE） was used for sampling， from which 60 better samples were selected， the kernel matrix K was calculated， the eigenvector of the kernel matrix K was used to calculate the coefficient matrix of the projected vector， and the projected variable was used as a new design variable to reconstruct the design space. Finally， the turbine disk is optimized in the design space after dimensionality reduction. The results show that： After optimization， the equivalent stress of the wheel center is reduced by 4.21%， the circumferential stress of the wheel center is reduced by 0.26%， the radial stress of the wheel back is reduced by 1.58%， the mean circumferential stress of the meridian section is reduced by 2.57%， and the mean radial stress of the cylindrical section is reduced by 6.51%.