Optimization Methods Based On Kriging Surrogate Model And Their Application In Injection Molding

The developments of communication and consumer electronic products require higher for the qualities of high precise injection molded parts,especially as the components continue to move toward being lighter,thinner,shorter,and smaller.Shrinkage,warpage and residual stress are important defects for the thin-wall components(1～2mm thick),and among them the warpage affects greatly the quality of the components.Injection molding is a highly non-linear process with interactions of parameters,thus qualities of components are related with all parameters through the total process.With the developments of some commercial analysis software for injection molding,the application of optimization based on computer aided engineering(CAE) technologies greatly improves the qualities of the components and efficiency of molding.However,it is still a challenge problem to implement effective optimization based on the computational time-consumed analysis software.First,theory of kriging surrogate model is expatiated,which is a kind of special interpolated technology based on statistics with no specific formula assumed.Through an engineering problem,a compare between sequential linear programming and kriging-based optimization method is done,and it shows kriging-based optimization method has a lot of merits.With the merits of the kriging-based optimization method,the kriging surrogate model is introduced in injection molding field.At the same time,a modified rectangular grid sampling developed.Then the sequential approximation optimization procedure,with minimizing response surface and maximizing expected improvement,is proposed to find the optimal process parameters and good result is obtained.Furthermore,an analysis about the effects of process parameters on warpage is performed at the optimal process setting.A sequential approximation optimization method,considering simultaneously the predictor and its uncertainty,is represented.This sequential method updates the kriging surrogate model by adding current optimal point for the accuracy of the interest region and the points with larger predicted uncertainty for the accuracy of the global approximation. Using this optimization method,more than one new point is selected to improve the surrogate, so it is called "multi-point addition" criterion.Through two mathematic functions,an investigation is done for the proposed optimization method,and a compare is implemented between the expected improvement sampling criterion and the multi-point addition criterion. The compare results show the proposed optimization method here effectively improves the optimum.Subsequently,the multi-point addition criterion is used for the robust optimization under uncertainty.It makes adaptive iteration come true through the consideration of predictor and its uncertainty and reduce the function evaluation.In addition,the use of the second-layer kriging model saves computational complexity and improves the computational efficiency.The mechanism of warpage is rather complicated,and it has high nonlinear relationship with part geometry and process parameters.For the reduction of warpage,the optimization model is proposed with the process parameters and part geometry as variables.The sequential optimization is performed through multi-point addition criterion and the warpage is reduced effectively.Meanwhile,the effects of process and material properties(viscosity and PVT relationship) on warpage are analyzed,and the results provide some advice for improvement of the part quality.In addition,considering the instability of some process parameters,the robust optimization model with variables process parameters and part geometry is constructed and the optimal robust design is obtained by the sequential robust optimization method based on kriging surrogate model.The optimization result shows the proposed sequential approximation optimization method is effective.The authors gratefully acknowledge financial support for this work from the Major program(No.10590354) of the National Natural Science Foundation of China.