Sequential Kriging Surrogate Model Based Optimization Methods And Their Applications In Engineering Design

In the optimization design process of underwater structure based on numerical simulations,it requires to evaluate a lot of design alternatives when exploring the design space for an optimum,which leads to its inability to meet the requirements of fast and efficient underwater structure design.Under this background,the surrogate model has been developed.It can effectively reduce the design cost by replacing the numerical simulation model approximately.Among the surrogate model,the sequential optimization methods using the surrogate model can effectively balance the relationship between convergence efficiency and accuracy by fully utilizing the data information obtained in the optimization process to guide the optimization process,and have shown great potential in ship structure optimization design.According to the different features of the problems,the optimization design of the ship structure can be divided into(1)The objective function is computationally expensive while the constraint function is computationally cheap;(2)The constraint function is computationally expensive while the objective function is computationally cheap;(3)Both of the objective and constraint functions are computationally expensive.Based on these three kinds of optimization problems,this paper has carried out research on optimization design methods based on the sequential Kriging surrogate model.The specific research contents include:(1)The objective function is computationally expensive while the constraint function is computationally cheap :For single-fidelity data sources,a sequential updating approach based on the lower confidence boundary and entropy weight(EW-LCB)method is proposed.In EW-LCB method,the information entropy method is used to adaptively calculate the objective weight coefficients between the predicted value and variance of the Kriging surrogate model,so as to avoid the disadvantage of possible aggregation of sample points in the original LCB method and improve the sequential optimization efficiency.For multi-fidelity data sources,a multi-fidelity sequential updating approach based on the lower confidence boundary and entropy weight(MF-EW-LCB)method is proposed.In the MF-EW-LCB method,the information entropy is used to adaptively balance the computational cost of high/low fidelity model samples,the degree of contribution to model accuracy,and the degree of influence on the optimal value,so as to maximize the utilization of computing resources.The effectiveness of EW-LCB and MF-EW-LCB methods are demonstrated by comparing several linear and nonlinear numerical functions with existing methods.(2)The constraint function is computationally expensive while the objective function is computationally inexpensive:For single-fidelity-data sources,a generalized sequential constraints updating approach based on the confidence intervals from Kriging surrogate model(SCU-CI)is proposed.In the proposed SCU-CI approach,the objective switching and distance measurement criteria are introduced to determine the sequential update sample points based on whether the feasibility status of the design alternatives would be changed or not because of the interpolation uncertainty from the Kriging surrogate model.For multi-fidelity data sources,a generalized multi-fidelity sequential constraints updating approach based on the confidence intervals from the Co-Kriging surrogate model(MF-SCU-CI)is proposed.In the proposed MF-SCU-CI approach,the cost coefficient and high/low fidelity model correlation function are introduced to establish the Co-H evaluation function.The Co-H function is used to measure the improvement degree of the prediction accuracy level at the constraint boundary due to the high/low fidelity sample points.The effectiveness of SCU-CI and MF-SCU-CI methods are demonstrated by comparing several linear and nonlinear numerical functions with existing methods.(3)Both of the objective and constraint functions are computationally expensive:For single-fidelity data sources,a sequential updating approach based on the entropy weight and constraint penalty(EW-PF)method is proposed.In the proposed EW-PF approach,the relationship between the feasibility of the design solution and the optimal objective is effectively balanced by finding the optimal objective solution in the feasible region,and an unified expression of the surrogate model for objective and the constraint functions is realized.For multi-fidelity data sources,a multi-fidelity sequential updating approach based on feasible region analysis(MF-FA)is proposed.In the proposed MF-FA approach,a two-stage multi-fidelity sequential surrogate model optimization strategy is proposed.In the first stage,sample points are added to the constraint boundary to find the feasible solution quickly.In the second stage,the quality of the feasible optimization solution is gradually improved in the feasible region until it converges to the global optimal solution.The effectiveness of EW-PF and MF-FA methods is demonstrated by comparing several linear and nonlinear numerical functions with existing methods.(4)The proposed methods above are applied to the optimization design of the impedance characteristics of the ship base structure,the optimization design of the vibration characteristics of the longitudinal and transverse stiffened conical shells of underwater structures,the optimization design of the structural stability performance of the stiffened cylindrical shells with variable stiffness,and the optimization design of a certain type of vibration isolator used by the underwater structure,respectively.The applied research covers the three kinds of computationally expensive optimization problems in the field of ship structure.At the same time,the influences of different constraints on engineering optimization problems are discussed.The results illustrate that the proposed sequential Kriging surrogate model based optimization methods in this work exhibits great capability and promising for practical simulation-based engineering design and optimization problems.