In this paper, a novel MRGP-SS method is proposed to deal with the reliability analysis problems under multiple failure modes. First, a random moving quadrilateral grid sampling (RMQGS) method is proposed to improve the randomness and uniformity of initial samples. Second, an adaptive procedure, which combines the multiple response Gaussian process (MRGP) model and the novel active learning functions, is proposed to efficiently and accurately produce surrogate models for failure surfaces. In this regard, two novel learning functions are introduced to adapt to different iterative cycles, one is employed to correct the quality of samples, and the other is used to search for the samples closest to the limit state surface. Third, the subset simulation (SS) is integrated into the adaptive MRGP model to estimate the failure probability under multiple failure modes with fewer function calls and time consumption. Numerical and engineering case studies are finally provided to demonstrate the effectiveness of the proposed method.

In this study, material and dynamic stress experiments are combined with finite element (FE) simulations to reveal the fracture mechanism of the wheelset lifting apparatus, and a structural design optimization scheme based on the double-layer Kriging surrogate model is proposed. The fracture mechanism of the wheelset lifting apparatus is first clarified through the material analysis of macro/micro and dynamic stress tests. Static strength and modal analyses are then performed to perfect the mechanism analysis in terms of structural performance. An efficient, robust, fatigue design optimization method based on the double-layer Kriging surrogate model and improved non-dominated sorting genetic algorithm II (NSGA-II) is finally proposed to improve the original design scheme. For the wheelset lifting mechanism’s fracture, the crack source is found on the transition fillet surface of the lifting lug and lifting ring, where the fracture has the characteristics of two-way, multisource, high-cycle, low-stress fatigue. It is further revealed that the vibration fatigue occurring at the point of maximum stress is the main cause of the fracture. The effectiveness of the proposed design optimization method is validated via comparative analysis.