基于梯度增强Kriging方法的水下航行器结构优化设计

Structural design optimization of underwater vehicle via Gradient-enhanced Kriging

[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。

[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.