Optimization of Variable Blank Holder Force Based on a Sharing Niching RBF Neural Network and an Improved NSGA-II Algorithm

  • Yanmin XieEmail author
  • Wei Tang
  • Fei Zhang
  • BeiBei Pan
  • Yaopeng Yue
  • Meiqiang Feng
Regular Paper


Variable blank holder force (VBHF) is an important process parameter in sheet metal forming. The purpose of this study is to propose a sharing niching radial basis function (SNRBF) neural network for VBHF optimization. Two methods are put forward to improve the prediction accuracy of a RBF neural network. (1) A RBF neural network is trained by a sharing niching technique to achieve global optimal nodes. (2) In Latin hypercube design, Spearman correlation analysis is employed to decrease sample correlation. In addition, in order to improve the performance of the non-dominated sorting genetic algorithm (NSGA-II), excellent individuals in each class of non-dominated individuals are selected by employing immune operators. Based on the Spearman correlation analysis and the Latin hypercube method, training samples are generated and numerical simulations are performed for a double C part. The surrogate models between VBHF and forming quality are constructed by a SNRBF neural network. The Pareto frontier solutions are achieved by employing the improved NSGA-II algorithm. Grey relational analysis is applied to determine the optimal VBHF loading trajectory. The results show decreased wrinkles in the optimized forming part and greater uniformity in the plastic deformation by employing the optimized VBHF, thereby leading to improvement in the forming quality of the double C.


Variable blank holder force Sharing niching technique RBF neural network Spearman correlation analysis NSGA-II algorithm Grey relational analysis 

List of Symbols

\(x_{i} ,x_{j} ,x_{k} ,x_{m} ,x_{n}\)

The ith, jth, kth, mth, and nth individual

\(d_{ij} ,d_{mn}\)

Euclidean distance

\(sh\left( {d_{ij} } \right),sh\left( {d_{mn} } \right)\)

Shared function


Shared degree


Shared fitness of the ith individual


Initial fitness of the ith individual


Niche radius


Weight between the implicit layer and the input layer


The sth node data of hidden layer


Sum of Euclidean distances

\(\rho_{i}^{\prime }\)

Antibody density


Survival expectation of the antibody


A constant to adjust the shared function

L, q

The number of individuals


The width of hidden layer nodes



The research was supported by the National Natural Science Foundation of China (NSFC51005193) and National Training Program of Innovation and Entrepreneurship for Undergraduates (201710613033).


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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSouthwest Jiaotong UniversityChengduChina

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