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.