Efficient time-variant reliability analysis through approximating the most probable point trajectory

Time-variant reliability analysis (TRA) is widely utilized to assess the performance of engineering structures under various time-variant uncertainties. Recently, the time discretization-based TRA (TDTRA) methods have been developed, which can achieve satisfactory accuracy but need to excessively perform most probable point (MPP) searches at many equidistant time instants. To improve the efficiency of TDTRA, this paper proposes a TRA method based on approximating the MPP trajectory, referred to as AMPPT. First, this paper introduces a new concept of the MPP trajectory (MPPT), which is defined as the moving path of the MPP in the U-space when time changes. Then, a one-dimensional Kriging model is constructed to approximate the MPPT by the adaptive sampling method, which only performs MPP searches at several critical time instants. To further improve the computational efficiency, a warm-starting strategy is proposed to accelerate the MPP search. Then, the approximated MPPT is employed to transform the time-variant response into an equivalent Gaussian process. Finally, the spectral decomposition method and Monte Carlo simulation are used to compute the time-variant reliability. Comparative studies on four numerical examples and one practical engineering example of the solid rocket engine shell verify that the proposed AMPPT outperforms TDTRA in terms of both accuracy and efficiency. Test results also indicate that the efficiency gain of the proposed AMPPT comes from not only the reduction in the number of MPP searches but also the acceleration of the MPP search itself.