The adaptive Kriging modeling (AKM) method based on entropy weight technique for order preference by similarity to an ideal solution (EWTOPSIS) is proposed in this chapter to deal with the problems in structural optimization based on current Kriging methods. The algorithm uses the comprehensive contribution analysis strategy based on EWTOPSIS to eliminate structural variables with low total contribution, significantly reducing the number of calls to objective functions when constructing the Kriging model. At the same time, this chapter proposes a surrogate model update strategy that objectively considers targets with different weights and applies it to the Kriging model’s update. The crucial design data points are obtained by optimal Latin hypercube design. Then calculate the boundary coefficients and construct the first-generation Kriging model with small samples. Afterward, to build the multilayer evolutionary Kriging model (MEKM), go through a series of processing, mainly including model grade division, selective processing of data points, and updates of surrogate models. Finally, a sequential quadratic programming algorithm is used to obtain the combination of the optimal structure size and the target performance. Compared with the traditional optimization method based on the standard Kriging model, the conventional way requires many calls to the actual function. The method proposed in this chapter can reduce the variable dimensions and adaptively select sample points of the Kriging model through the algorithm, which can design a three-dimensional structure that satisfies the constraints more efficiently. The engineering case shows that the proposed method is effective and suitable for the practical engineering optimization problem.

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An Adaptive Kriging Modeling Method Based on Entropy Weight TOPSIS for Structural Optimization

  • Chunhuan Jin,
  • Linsen Zhu,
  • Ji Lin,
  • Quanliang Liu

摘要

The adaptive Kriging modeling (AKM) method based on entropy weight technique for order preference by similarity to an ideal solution (EWTOPSIS) is proposed in this chapter to deal with the problems in structural optimization based on current Kriging methods. The algorithm uses the comprehensive contribution analysis strategy based on EWTOPSIS to eliminate structural variables with low total contribution, significantly reducing the number of calls to objective functions when constructing the Kriging model. At the same time, this chapter proposes a surrogate model update strategy that objectively considers targets with different weights and applies it to the Kriging model’s update. The crucial design data points are obtained by optimal Latin hypercube design. Then calculate the boundary coefficients and construct the first-generation Kriging model with small samples. Afterward, to build the multilayer evolutionary Kriging model (MEKM), go through a series of processing, mainly including model grade division, selective processing of data points, and updates of surrogate models. Finally, a sequential quadratic programming algorithm is used to obtain the combination of the optimal structure size and the target performance. Compared with the traditional optimization method based on the standard Kriging model, the conventional way requires many calls to the actual function. The method proposed in this chapter can reduce the variable dimensions and adaptively select sample points of the Kriging model through the algorithm, which can design a three-dimensional structure that satisfies the constraints more efficiently. The engineering case shows that the proposed method is effective and suitable for the practical engineering optimization problem.