快速交叉验证改进的运载火箭近似建模方法

doi:10.7527/S1000-6893.2021.25967

固体力学与飞行器总体设计

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快速交叉验证改进的运载火箭近似建模方法

文谦, 杨家伟, 武泽平, 杨希祥, 赵海龙, 王志祥

国防科技大学空天科学学院,长沙 410073

收稿日期:2021-06-16 修回日期:2021-07-06 出版日期:2022-09-15 发布日期:2021-08-17
通讯作者: 武泽平,E-mail:zeping123@nudt.edu.cn E-mail:zeping123@nudt.edu.cn
基金资助:
国家自然科学基金(52005502)；湖南省科技创新计划(2020RC2035)；国防科技大学科研计划(ZK19-11)

An approximation modeling method of launch vehicles improved by fast cross-validation

WEN Qian, YANG Jiawei, WU Zeping, YANG Xixiang, ZHAO Hailong, WANG Zhixiang

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

Received:2021-06-16 Revised:2021-07-06 Online:2022-09-15 Published:2021-08-17
Supported by:
National Natural Science Foundation of China (52005502); Science and Technology Innovation Program of Hunan Province (2020RC2035); Research Project of National University of Defense Technology (ZK19-11)

摘要/Abstract

摘要： 针对运载火箭智能化设计对近似模型计算效率及精度提出的更高要求,提出快速交叉验证改进的径向基函数(RBF)近似建模方法。RBF是非线性多峰耗时模型近似建模的重要方法之一,其基函数形状参数的合理确定可大幅提升RBF近似模型预测精度。针对现有RBF形状参数确定中待求变量多和计算复杂等问题,提出基于样本局部密度的形状参数表征方法。将多个形状参数的复杂域优化问题转化为缩放系数确定的单变量优化问题,实现形状参数优化与训练样本数量解耦。提出通用快速K-折交叉验证算法合理确定缩放系数,推导出通用交叉验证误差求解过程中高阶矩阵快速求逆和交叉验证误差快速求解公式,将径向基函数形状参数确定的计算复杂度从n³降低为(n/k)³,提升了径向基函数近似建模效率和精度。采用数值算例和工程算例进行校验,结果表明本文方法具有较好的预测精度和通用性,在飞行器设计领域有一定的工程应用价值。

关键词: 运载火箭, 智能化设计, 近似模型, 交叉验证, 径向基函数, 局部密度

Abstract: The intelligent design of launch vehicles requires the high calculation efficiency and accuracy of the approximation model, hence a fast cross-validation improved RBF approximation modeling method is proposed. Radial Basis Function (RBF) is one of the most widely-used approximation metamodeling methods for nonlinear multi-peak time-consuming models. Reasonable determination of the shape parameters could greatly improve the prediction accuracy of the RBF approximation model. To solve the problems that many variables are to be determined for RBF with multiple shape parameters and the calculations are complex, a shape parameters characterization method based on the local density of sampling points is proposed. With the proposed method, the determination of multiple RBF shape parameters is transformed into the determination of a single scale factor based on the local density of sampling points. Therefore, the shape parameters optimization problem in RBF is decoupled from the number of training samples. Furthermore, a general fast K-fold cross-validation algorithm is proposed to determine the scale factor of RBF. The fast higher-order inverse matrices formula and fast solution of cross-validation errors formula are derived, which further reduces the computational complexity of shape parameters determination of RBF from n³ to (n/k)³, and improves the efficiency and accuracy of the RBF approximation model. Different numerical examples and engineering examples are used to verify that the proposed method not only has competitive prediction accuracy and versatility but also has application value in the field of flight vehicle design.

Key words: launch vehicles, intelligent design, approximation model, cross-validation, radial basis function, local density

中图分类号:

文谦, 杨家伟, 武泽平, 杨希祥, 赵海龙, 王志祥. 快速交叉验证改进的运载火箭近似建模方法[J]. 航空学报, 2022, 43(9): 225967-225967.

WEN Qian, YANG Jiawei, WU Zeping, YANG Xixiang, ZHAO Hailong, WANG Zhixiang. An approximation modeling method of launch vehicles improved by fast cross-validation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 225967-225967.

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E-mail：hkxb@buaa.edu.cn

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快速交叉验证改进的运载火箭近似建模方法

An approximation modeling method of launch vehicles improved by fast cross-validation

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