A Multipeak Parallel Adaptive Infilling Strategy And Its Engineering Application

The cheap-to-run surrogate models are widely used in simulation-based engineering design to replace time-consuming simulations.The distribution of samples directly determines the quality and efficiency of surrogate models,which has a significant influence on follow-up work.Infilling strategy,also known as sequential sampling,which can extract the established model information to guide the sampling position so that new samples are added in turn to fill the sampling space that has not yet been detected or(and)the regions of interest that have larger prediction errors.The infilling strategies have the potential to build more accurate global surrogate models with fewer samples.This paper proposes a novel and robust expected improvement(EI)based parallel adaptive infilling strategy.This strategy,namely,the multipeak parallel adaptive infilling(MPEI)strategy,aims to explore the entire space and exploit subdomains of interest to select samples with uniform distribution in multiple uncorrelated candidate peak areas to efficiently establish a high-precision surrogate model.Seven benchmark cases and one engineering problem are used to validate the performance of the MPEI strategy.The results show that the MPEI strategy can efficiently obtain the desired prediction accuracy of surrogate models at a small price of a few samples and confirm the feasibility and robustness of the presented methodology.The primary contents are as follows:(1)EI strategy can balance global exploration and local exploitation.Because it has multipeak characteristics,selecting samples at peaks can not only improve the global optimization capability but also increase the accuracy of the model.Based on that,the MPEI strategy can be divided into two stages: the construction of candidate peak areas and the selection of appropriate candidates at the candidate peak areas.In the first stage,the candidates are divided into the corresponding subspaces in sequence by combining their EI values and the distribution characteristics of the candidates.In the second stage,the Gaussian function is used to extract the uncorrelated parent point and the corresponding offspring points in each candidate peak area.(2)The influences of different combinations of parameters and the initial sample sizes on the performance of the MPEI strategy are analyzed based on two benchmark cases.On this basis,the selection range of the hyperparameters that can give full play to the performance of MPEI strategy are summarized.The recommended hyperparameters and the initial samples are used to test the performance of the MPEI strategy through a one-dimensional numerical case.(3)The MPEI strategy is compared with other adaptive sampling strategies,i.e.,Expected improvement(EI),Inter-quartile range(IQR),Go-inspired hybrid infilling(GO-HI),Kriging Believer(KB),and Constant Liar(CL),by applying seven numerical cases and an engineering problem.Each test runs 10 times to eliminate the effect of the initial random sampling plan on the performance of the infilling strategies.The results indicate that the MPEI strategy can efficiently obtain the desired accuracy of surrogate models with a few samples.It can avoid the problem of being trapped in a local optimum and balance global exploration and local exploitation.The new samples selected by MPEI strategy are more concise and more representative of the model.With respect to the structural analysis of an 800 MN die-forging hydraulic press,compared to the EI,IQR,GO-HI,CL and KB strategies,the MPEI strategy can save 12.1%-37.0% of the computational costs and requires only 33.3%-88.9% of the number of iterations for the desired accuracy.These further proves that the MPEI strategy has excellent practicability,and also shows that the development of the MPEI strategy has a great influence on the application of surrogate model technology in engineering design.