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.