基于梯度增强 Kriging 方法的水下航行器结构优化设计

陈力铭，邱浩波*，高亮华中科技大学机械科学与工程学院，湖北武汉 430074

摘 要:［目的］船舶结构优化设计过程通常涉及对高精度数值仿真进行响应分析，其耗时特性决定了可调用的仿真次数十分有限，使得优化过程受到限制。为了探索基于梯度增强Kriging 代理模型的高效设计优化方法，缩短设计周期，节省设计成本，提出基于缩减型梯度增强Kriging的加点策略，仅在有实际改进的采样位置进行梯度计算，以减少仿真调用次数。［方法］首先，使用多起点局部优化算法搜索改进期望函数的若干局部最优解作为候选加点位置；然后，计算相应的近似驻点概率，并根据改进期望值和近似驻点概率值的一致程度来确定加点位置，从而提高优化效率；最后，针对某水下航行器结构进行优化设计，以提高其水下无约束自由振动时的第7阶固有频率为目标，对所提方法的可行性进行验证。［结果］结果表明，优化后的固有频率值与基准型相比提升了14.6%，方法的可行性得到验证。［结论］所提方法可以将基于梯度增强Kriging代理模型的优化方法泛化至梯度信息只能通过有限差分法获取的场景。

关键词：船舶结构优化；基于代理模型的优化；梯度增强Kriging

中图分类号: U662.2文献标志码:A DOI：10.19693/j.issn.1673-3185.02066

Structural design optimization of underwater vehicle via Gradient-enhanced Kriging

School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract: ［Objectives］The structural optimization of ships usually involves the use of high-fidelity numerical simulations which are time-consuming and thus difficult to evaluated frequently, and this intrinsic property hinders the optimization process. To promote efficient design optimization, this paper explores the use of Gradient-enhanced Kriging (GEK) surrogate mode in order to shorten the design loop and save design cost. A reduced GEK-based infill criterion is proposed to decrease the number of simulations by calculating the gradients only for sample locations where improvement occurs.［Methods ］ A multi-start local optimization algorithm is employed to search the local optima of the "expected improvement" function and locate candidate infill points. The associated "approximate probability of stationary point (APSP)" values are also evaluated, and infill decisions are made according to the extent of consistency between these two quantities, thereby improving optimization efficiency. The proposed method is then applied to the structural optimization of an underwater vehicle to increase the seventh-order natural frequency under unconstrained free vibration in an underwater environment, and the validity is verifed.［Results ］ The result shows that， compared with the baseline，the optimized design achieves a 14.6% improvement.［Conclusions］The proposed GEK-based optimization method can be generalized to cases when gradients can only be evaluated by finite difference.

Key words: ship structural optimization；surrogate-based optimization；Gradient-enhanced Kriging

收稿日期: 2020–08–11 修回日期: 2020–10–28 网络首发时间: 2021–06–09 13:54

基金项目: 国家自然科学基金资助项目（51675198）；国防基础科研计划资助项目（41423010205）；华中科技大学学术前

沿青年团队资助项目（2017QYTD04）

作者简介: 陈力铭，男，1995 年生，博士生。研究方向：基于代理模型的设计优化。E-mail：liming_chen@hust.edu.cn邱浩波，男，1975年生，博士，教授，博士生导师。研究方向：基于代理模型的设计优化，可靠性设计优化，工

艺智能优化方法，设备健康管理和系统可靠性建模。E-mail：hobbyqiu@hust.edu.cn高亮，男，1974年生，博士，教授，博士生导师。研究方向：智能优化方法及其在设计制造中的应用。

E-mail：gaoliang@mail.hust.edu.cn

*通信作者:邱浩波

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