A partial decomposition cutting method with CF-discrepancy for points selection in stochastic seismic analysis of structures

The probability density evolution method is renowned for its effectiveness in conducting stochastic seismic response analyses of structures with uncertain parameters. Within this method, the points selection strategy, particularly in high-dimensional problems, is of paramount importance to achieving a balance between accuracy and efficiency. This paper proposes a novel point selection method designed to capture the probabilistic response of structural dynamic systems. The method starts by generating an initial uniform point set within a unit cube, using an improved number-theoretical method with a large number size. It then employs a partial decomposition cutting method to select a small number of samples from this initial uniform point set, which are subsequently scaled to the unit cube to serve as the representative points. These representative points are then transformed into the original random-variate space, and the corresponding assigned probabilities are computed accordingly. To enhance accuracy, a characteristic function-based discrepancy is proposed and applied to rearrange the representative points in the original random-variate space. The effectiveness of this method is demonstrated through two numerical examples, along with comparisons to results obtained using Monte Carlo Simulation and other comparable point sets.