Time-variant reliability analysis via advanced most probable point trajectory tracking

• An adaptive virtual model-assisted most probable point trajectory-based approach for time-variant reliability analysis is proposed. • A two-stage adaptive sampling strategy enhances efficiency in capturing the most probable point. • The most probable point trajectory enables continuous reliability prediction over time. • The applicability and computational efficiency of the method are validated. Structural reliability evolves due to environmental conditions and varying loads, leading to gradual structural deterioration. Accurately capturing this time-variant behavior is essential for assessing failure probability over a specified time horizon. This study proposes an adaptive virtual model-assisted most probable point trajectory-based (AdaVM-MPPT) approach for time-variant reliability analysis under stochastic loadings, focusing on the trajectory tracking of the most probable point (MPP). A stochastic process discretization technique is adopted to decompose the time-variant limit state function in the time domain. To enhance computational efficiency and accuracy, the Extended Support Vector Regression (X-SVR) is utilized for virtual model construction. The virtual model approximates the relationship between the structural uncertainty inputs, including geometries, material properties, degradation processes, applied loading conditions, and the limit state hyperplane. Therefore, a two-stage adaptive sampling strategy is developed to effectively establish the virtual model and capture the MPP at all discretized time instants. The identified MPPs are then used to approximate the most probable point trajectory (MPPT), enabling continuous prediction at any time point within the specified period. The proposed framework consistently generates MPPs over the specified time period based on the MPPT, allowing for efficient computation of time-variant reliability using the multivariate normal distribution. The proposed AdaVM-MPPT method for time-variant reliability analysis offers several advantages. The X-SVR algorithm and two-stage adaptive sampling strategy improve the MPP capturing efficiency significantly. Furthermore, the computational cost of time-variant reliability analysis associated with the stochastic process discretization size can be significantly reduced based on the availability of MPPT. These two advancements significantly improve the efficiency of traditional time-variant reliability analysis methods. Finally, the applicability and computational efficiency of the proposed method are fully demonstrated through a test function and practice-stimulated engineering problems.