A multi-objective optimization method based on Gaussian process simultaneous modeling for quality control in sheet metal forming

  • Wei Xia
  • Huan YangEmail author
  • Xiao-ping Liao
  • Jian-min Zeng


A new modeling method, related to multiple inputs and multiple outputs (MIMO), simultaneously based on Gaussian process (GP), is proposed to optimize the combinations of process parameters and improve the quality control for multi-objective optimization problems in sheet metal forming. In the MIMO surrogate model, for the use of the system information in processing and the accuracy of the model, quantitative and categorical input variables are both taken into account in GP simultaneously. Firstly, a general method is proposed for constructing covariance functions for GP simultaneous MIMO surrogate model based on correlation matrices. These covariance functions must be able to incorporate the valid definitions of both the spatial correlation based on quantitative input variables and the cross-correlation based on categorical input variables. Secondly, the unrestrictive correlation matrices are constructed by the hypersphere decomposition parameterization, thus directly solving optimization problems with positive definite constraints is needless, and the computational complexity is simplified. Compared with independent modeling method, the proposed GP simultaneous MIMO model has higher accuracy and needs less number of estimated parameters. Moreover, the cross-correlation between the outputs (quality indexes) obtained by proposed model provides some reference to further develop quality intelligent control strategies. Finally, a drawing-forming process of auto rear axle housing is taken as an example to validate the proposed method. The results show that the proposed method can effectively decrease the crack and wrinkle in sheet metal forming.


Sheet metal forming Multi-objective optimization Gaussian process Correlation matrix Hypersphere decomposition 


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Authors and Affiliations

  • Wei Xia
    • 1
  • Huan Yang
    • 1
    Email author
  • Xiao-ping Liao
    • 2
  • Jian-min Zeng
    • 1
  1. 1.Ministry–Province Jointly Constructed Cultivation Base for State Key Laboratory of Processing for Non-ferrous Metal and Featured MaterialsNanningPeople’s Republic of China
  2. 2.College of Mechanical and EngineeringGuangxi UniversityNanningPeople’s Republic of China

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