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This paper proposes metamodel optimization methodology based on multi-level fuzzy-clustering space reduction strategy with Kriging interpolation. The proposed methodology is composed of three levels. In the 1st level, the initial samples need partitioning into several clusters due to design variables by fuzzy-clustering method. Sequentially, only some of the clusters are involved in building metamodels locally in the 2nd level. Finally, the best optimized result is collected from all metamodels in the 3rd level. The nonlinear problems with multi-humps as test functions are implemented for proving accuracy and efficiency of proposed method. The practical nonlinear engineering problems are optimized by suggested methodology and satisfied results are also obtained.

In this study, an adaptive space mapping technique based on response of objective was suggested for solving practical engineering problems. Response surface methodology was engaged in approximation of objective and constraint functions based on coarser model. The fine simulation model is not only used for correction of the coarser simulation model and validation of final solution but also for applied construction of space mapping expression. Finally, genetic algorithm (GA) was used to optimize updated metamodel according to coarse model. The proposed method combines the space mapping technology based on response of coarse model and modification of design of experiment. It guarantees that metamodel based coarser model is stepwise updated in the right searching direction. For demonstrating practicability of developed method, it was applied for optimization of geometric parameters of addendum surface, blank holder force and drawbead restraining force in sheet forming problems. It was confirmed that the corresponding problem can be optimized successfully in remarkably short computing time by proposed optimization method.

A metamodelling technique based on an adaptive intelligent sampling scheme and Kriging interpolation method are suggested in this study. The proposed method is applied for drawbead geometry parameters inverse problem. The suggested sampling scheme applies uniform Latin Hyper Sampling to generating initial samples. According to the different metamodelling strategies, the adaptive intelligent sampling scheme is implemented for updating new samples. To validate the suggested method, the non-linear function as benchmark is optimised via proposed strategy. Finally, the sheet forming optimisation problem indicates that suggested method is a high accuracy, efficiency and rapid convergence for design of mould in practice.