Vectorial surrogate modeling method for multi-objective reliability design

Abstract

To improve the computational cost and accuracy for the multi-objective reliability design of complex structures, a synchronous modeling concept is proposed by introducing matrix thought into the surrogate modeling methods, the purpose of which is to realize the transformation from single-objective reliability design to comprehensive (multiple objectives) reliability design. With respect to the synchronous modeling concept, vectorial surrogate modeling (VSM) method is developed to synchronously establish an overall model of complex structures with multiple objectives. Besides, the types of examples including a numerical example and four engineering cases are adopted to highlight the abilities of the developed VSM method in accuracy, computational efforts and capability. It is illustrated that (1) the developed VSM method is workable in the synchronous modeling and comprehensive reliability design of complex structures with many objectives; (2) the proposed VSM method has the superior performances in both computational efficiency and accuracy for high-dimensional nonlinear problems, by comparison of methods; (3) By comparing with the analytical approaches, the efficient results based on computational times and elevating the performance are provided using the proposed method for highly nonlinear problems; (4) the comprehensive reliability level of turbine blisk deformation, stress and strain is 0.9974 obtained by the VSM method, by considering the effect of fluid-thermal-structural interaction, when the allowable values are 4.3698 × 10−3 m, 1.0389 × 109 Pa and 6.4298 × 10−3 m/m (determined by 3-sigma level); (5) the modeling and simulation efficiencies of the VSM method are improved by 42.56% and 0.31% relative to the RSM. The VSM method are validated to hold high accuracy and high efficiency in modeling characteristics and simulation performance of high-dimensional structural reliability problems. The efforts of this study are to provide a promising synchronous modeling concept and methodology with the VSM method for the multi-objective reliability design of complex systems, which contributes to enrich mechanical reliability theory.