Research On High Dimensional Model Representation Based Metamodel

Constructing approximation models for complex physical systems with surrogate modeling is often used in engineering design in order to save computational cost and shorten design cycle.However,the problem “curse of dimensionality” still exists when the number of design variables is more than ten.High dimensional model representation(HDMR)is proposed to solve high dimensional computationally expensive black-box problems.In this paper,multiple direcitons of the HDMR technology are deeply studied,including the metamodel construction of HDMR,high dimensional adaptive sampling criterion,HDMR-based optimization method and the application of shape optimization for blended-wing–body underwater glider(BWBUG).The main research results and innovation are as follows:(1)In order to improve prediction accuracy and alleviate prediction uncertainty for different problems,a new HDMR by combining the separate stand-alone metamodels to form an ensemble based on cut-HDMR is proposed,which is named EOM-HDMR.It fuses the prediction information from three surrogate models PRS,RBF and Kriging,and obtains the weight factors of each stand-alone meta-models for various problems by using k-fold cross-validation.The predictions of unknown points in the design space can be calculated based on the weight factors and the three stand-alone meta-models.Ten representative mathematical examples and two engineering examples are used to illustrate the proposed EOM-HDMR.According to the results of performance criteria,EOM-HDMR can provide more accurate and robust results in prediction of different problems compared with single HDMRs,and it’s more efficient to tackle high dimensional computationally expensive black-box problems.(2)This thesis proposes a HDMR-based high dimensional adaptive sampling approache to further improve the accuracy of the surrogate models.First,a comprehensive comparison between three sequential sampling approaches and one-stage sampling approache on different HDMRs has been given,and CV-Voronoi is chosen as sampling approache for the EOM-HDMR instead of one-stage sampling approache or randomly sampling approache.Then an adaptive modeling framework is employed to construct and update the component terms of EOM-HDMR.In each cycle,GMSE values of all the constructed component functions are calculated and component function with the largest GMSE is updated via adding a new sample point by CV-Voronoi.Compared with current sampling approache of HDMR,the proposed sampling approache can reduce the number of function evaluations to the greatest extent and improve efficiency of the HDMR model,and this has more advantages on solving engineering problems.(3)Traditional single surrogate-based optimization method may be suitable for some problems but has a poor performance for others.By making full use of individual HDMR model’s advantages and avoiding error information,a new multi-surrogate-based optimization method with score-based infill criterion(MSIC)based on HDMR is developed,which is named MSIC-HDMR.For each component function,a score-based infill criterion is proposed to obtain new samples and a reduced space is used to accelerate the local convergence performance of the algorithm.Simultaneously,mean square errors(MSE)of the individual surrogate models for infill points are calculated to determine which surrogate is suitable for the component terms.Moreover,multiple numerical examples are used to verify the practicability of the proposed MSIC-HDMR optimization method,and the results show that the proposed algorithm has extensive applicability,strong stability,and remarkable performance for different kinds of problems compared with other HDMR-based optimization methods.(4)MSIC-HDMR is applied to the shape optimization for blended-wing-body underwater glider(BWBUG)in order to maximize the lift-to-drag ratio.Firstly,class-shape function transformation(CST)method is used for parameterization of the airfoils which are selected from the BWBUG.The parameterization model is controlled and an automated computational framework is designed to improve the calculation accuracy and efficiency of hydrodynamic parameters.It can be seen from the results that the lift-to-drag ratio of the BWBUG is improved with more high lift coefficient and same drag coefficient.This work can support the design and manufacturing of BWBUG.