大型运载火箭加筋柱壳近似建模方法

为提高大型运载火箭中薄壁加筋柱壳结构的后屈曲分析、优化设计的计算效率，提出基于矩估计的增广径向基函数(ARBF)近似建模方法。首先，分析了形状参数对ARBF近似模型泛化能力的影响规律；然后，基于样本点局部密度给出了ARBF基准形状参数确定方法，并根据模型响应特点，引入缩放系数对形状参数进行自适应调整；进一步，基于矩估计方法将确定形状参数的复杂域优化问题转化为确定缩放系数的优化问题，并利用多起点并行优化算法求解该问题，显著降低了计算复杂度；最后，通过典型数值算例和工程应用，对比研究了本文方法与其他典型近似建模方法的优劣。数值和工程算例表明，相较其他典型近似建模方法，本文方法可通过训练较少的样本点达到较高的近似精度，对比结果验证了本文方法的有效性和高鲁棒性，表明其具有一定的工程应用价值。

Approximation Modeling Method for Cylindrical Stiffened Shells in Large Launch Vehicles

To improve the efficiency of post buckling analysis and optimization design of cylindrical stiffened shells in large launch vehicles, a novel modeling method for the augmented radial basis function (ARBF) approximation model is proposed based on moment estimate. Above all, the influence of the shape parameters on the generalization ability of the ARBF approximation model is analyzed. Then, an estimation procedure for the reference shape parameters is presented by incorporating the local density of sampling points. According to the characteristics of the response of the real model, the scale factor is introduced to control the shape parameters adaptively. Afterwards, the optimization problem of the shape parameters in complex domain is converted into an optimization problem of the scale factor based on the moment estimate method, and the parallel multi start algorithm is applied to solve the problem, which reduces the computational burden significantly. Ultimately, the method presented in this paper and other conventional approximation modeling methods are compared through the typical numerical functions and cylindrical stiffened shells. The comparison results with other conventional approximation modeling methods in numerical and engineering studies reveal that the proposed method can achieve higher approximate accuracy by training fewer sampling points. The proposed modeling method for ARBF approximation model is validated for the prospect of the engineering applications.