基于置信区间的约束多精度序贯代理模型优化方法及应用

引用格式：钱家昌,程远胜, 张锦岚.基于置信区间的约束多精度序贯代理模型优化方法及应用[J]. 中国舰船研究, 2021, 16(4): 37–43.

QIAN J C, CHENG Y S, ZHANG J L. Multi-fidelity sequential constraint updating optimization approach based on confidence intervals and its application[J]. Chinese Journal of Ship Research, 2021, 16(4): 37–43.

钱家昌1,2，程远胜1，张锦岚*2

1华中科技大学船舶与海洋工程学院，湖北武汉 430074 2武汉第二船舶设计研究所，湖北武汉 430205

摘 要:［目的］水下结构物优化设计领域面临着仿真耗时优化的难题。针对目标不耗时、约束耗时这类优

化问题，开展多精度数据来源情况下的约束序贯代理模型优化方法研究。［方法］提出一种基于置信区间的约束多精度序贯 Co-Kriging 代理模型优化方法（ MF-SCU-CI ），建立能综合评估代理模型不确定性水平、高/低精度模型相关程度以及成本系数的Co-H函数，用于指导序贯优化过程。然后，通过3个典型的数值测试函数和纵横加筋圆锥壳结构振动优化工程案例进行应用研究。［结果］结果表明，所提出的MF-SCUCI方法较基于置信区间的约束单精度序贯代理模型优化方法（ SCU-CI）具有更优的可行性比率，且优化求解

效率更高，能够进一步减少耗时的仿真次数。［结论］该方法适用性好，具有良好的工程应用前景。关键词：代理模型；Co-Kriging；多精度；置信区间；序贯约束更新优化

中图分类号: U662.2文献标志码:A DOI：10.19693/j.issn.1673-3185.02025

Multi-fidelity sequential constraint updating optimization approach based on confidence intervals and its application

1 School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

2 Wuhan Second Ship Design and Research Institute, Wuhan 430205, China

Abstract: ［Objectives ］ This study addresses the problem of time-consuming simulation in the optimization design of underwater structures. Focusing on time-consuming and non-time-consuming targets and constraints, it proposes an optimization method for constrained sequential surrogate models in the case of multi-fidelity data sources.［Methods］ A multi-fidelity sequential constraint updating optimization approach based on confidence intervals and the Co-Kriging surrogate model (MF-SCU-CI) is proposed. The Co-H function is established to take into consideration the uncertainty of the surrogate model and the correlation degree and time consumption ratio of the high/low fidelity model. Three typical numerical test functions and an engineering example of longitudinal and transverse stiffened conical shell structure for vibration optimization are then tested.［Results ］ The results demonstrate that the feasibility ratio and effectiveness of the MF-SCU-CI method are better than those of the existing SCU-CI method. In addition, the MF-SCU-CI method can further reduce the number of simulation runs.［Conclusions］The proposed MF-SCU-CI method shows great potential for practical simulation-based engineering design optimization.

Key words: surrogate model；Co-Kriging；multi-fidelity；confidence interval；sequential constraint updating optimization

收稿日期: 2020–07–04 修回日期: 2020–09–23 网络首发时间: 2021–06–11 13:29

基金项目:国防科技工业海洋防务技术创新中心创新基金资助项目（YT19201701）

作者简介: 钱家昌，男，1983年生，博士，高级工程师

程远胜，男，1962年生，博士，教授，博士生导师。研究方向：结构分析与轻量化设计，结构冲击动力学与防

护设计，基于代理模型的优化方法。E-mail：yscheng@hust.edu.cn

张锦岚，男，1963年生，硕士，研究员，博士生导师

*通信作者:张锦岚