面向多级加筋壳的高效变保真度代理模型

李增聪; 田阔; 赵海心

doi:10.7527/S1000-6893.2019.23435

航空学报 >

2020 , Vol. 41 >Issue 7: 623435 - 623435

DOI: https://doi.org/10.7527/S1000-6893.2019.23435

先进制造技术与装备专栏

面向多级加筋壳的高效变保真度代理模型

李增聪 ,
田阔 ,
赵海心

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1. 大连理工大学工业装备结构分析国家重点实验室工程力学系, 大连 116024;
2. 大连理工大学机械工程学院, 大连 116024

收稿日期: 2019-09-02

修回日期: 2019-10-03

网络出版日期: 2019-11-14

基金资助

国家自然科学基金（11902065，11825202）；中国博士后科学基金面上项目（2019M651107）；兴辽英才计划（XLYC1802020）；国家"973"计划（2014CB049000）；中央高校基本科研业务费专项资金（DUT2019TD37）

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Efficient variable-fidelity models for hierarchical stiffened shells

LI Zengcong ,
TIAN Kuo ,
ZHAO Haixin

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1. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;
2. School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China

Received date: 2019-09-02

Revised date: 2019-10-03

Online published: 2019-11-14

Supported by

National Natural Science Foundation of China (11902065, 11825202); China Postdoctoral Science Foundation (2019M651107); Liaoning Revitalization Talents Program (XLYC1802020); National Basic Research Program of China (2014CB049000); The Fundamental Research Funds for the Central Universities (DUT2019TD37)

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摘要

多级加筋壳结构作为一种新颖的航空航天薄壁结构，具有轻质、高承载的优势。由于其加筋结构复杂，导致基于高保真度模型的多级加筋壳后屈曲分析耗时较长，提高其后屈曲分析及优化效率对于多级加筋壳快速设计具有重要的意义。变保真度模型在复杂工程问题的设计与优化过程中得到了广泛的应用，其通过桥函数连接高保真度模型和低保真度模型，具有预测精度高和计算成本低的优点。首先建立了多级加筋壳结构的高保真度模型和低保真度模型，并基于高斯过程回归构建了多级加筋壳结构的变保真度模型，然后基于变保真度模型的最大均方根误差方法开展自适应加点。结果表明，在达到同样的较高预测精度水平时，基于提出方法构建的变保真度模型比直接采用高保真度模型构建的代理模型节约了60%的计算成本，表现出优异的效率优势。同时，还探讨了不同类型低保真度模型对于多级加筋壳结构变保真度模型预测精度的影响。分析结果表明，对于多级加筋壳承载力评估这类典型的后屈曲问题，建立可捕捉后屈曲特性的低保真度模型能有效提升变保真度模型的精度。

关键词： 变保真度模型; 多级加筋壳; 屈曲分析; 自适应加点方法; 渐近均匀化法

本文引用格式

李增聪 , 田阔 , 赵海心 . 面向多级加筋壳的高效变保真度代理模型[J]. 航空学报, 2020 , 41(7) : 623435 -623435 . DOI: 10.7527/S1000-6893.2019.23435

Abstract

The hierarchical stiffened shell is one kind of innovative aerospace thin-walled structures, and it has the advantages of lightweight and high load-carrying capacity. Since the stiffener configurations of hierarchical stiffened shells are complex, they would result in longer computational time of post-buckling analysis. In this case, it is meaningful to improve the efficiency of post-buckling analysis and optimization for the rapid design of hierarchical stiffened shells. Variable-Fidelity Model (VFM) has been widely used in the design and optimization of complex engineering structures. High-Fidelity Model (HFM) and Low-Fidelity Model (LFM) linked by the bridge function can indicate high prediction accuracy and low computational cost. In this paper, the establishment methods of HFM and LFM are proposed for hierarchical stiffened shells. Then, the Gaussian process regression method is employed to establish VFM, where an adaptive updating method is proposed according to the root mean square error of VFM. Results indicate that, when achieving the similar prediction accuracy, the computational cost of the VFM based on the proposed method is lower by about 60% than that of the surrogate model based on the direct sampling of HFM, indicating the significant advantage of the proposed method in prediction accuracy. In addition, the effects of various types of LFMs on the prediction accuracy of VFM are discussed. Results reveal that, with regard to the post-buckling problems for the load-carrying capacity prediction of hierarchical stiffened shells, the prediction accuracy of VFM can be improved if the post-buckling analysis ability is retained in the establishment of LFM.

Key words： variable-fidelity model; hierarchical stiffened shells; buckling analysis; adaptive updating method; asymptotic homogenization method

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