An improved adaptive Kriging method for the possibility-based design optimization and its application to aeroengine turbine disk

Possibility-based design optimization (PBDO) can provide theoretical basis for the structural optimal design of fuzzy uncertainty model in engineering, so as to obtain the optimal design variables. The genetic algorithm (GA) based on adaptive Kriging method for PBDO requires high precision in the whole design space, while the region far from the limit state surface (LSS) of the constraint function has little effect on PBDO, thus greatly affects the computational efficiency. In order to improve the efficiency of PBDO, an improved adaptive Kriging method combined with active possibility constraint (I-AK-AC) is proposed in this paper. In I-AK-AC, the enhanced expected improvement learning function is first put forward to promote the convergence efficiency of Kriging model by reducing the accuracy of the region far from the LSS of the constraint function. Whereafter, the active possibility constraint is identified, and only the boundaries of active possibility constraint need to be approximated precisely by Kriging model. By these ways, the convergence speed of Kriging model is further ameliorated without affecting the computational accuracy, and the efficiency of PBDO is significantly improved. Three test examples and an engineering application of aeroengine turbine disk illustrate the validity and accuracy of the proposed I-AK-AC.