A marginal fractional moments based strategy for points selection in seismic response analysis of nonlinear structures with uncertain parameters

The present paper proposes a new strategy for selecting representative points in the probability density evolution method (PDEM) to conduct stochastic seismic response analysis of nonlinear structures with uncertain parameters. In PDEM, the strategy for selecting representative points in random-variate space is of critical importance to the efficiency and accuracy. The proposed strategy is established based on the marginal fractional moments of input random variables, which can be evaluated both analytically and numerically without difficulty before performing stochastic analysis. In this strategy, an optimization problem is actually involved. First, the initial points are generated by a low discrepancy sequence and the corresponding assigned probabilities can be computed accordingly. Then, the initial points are rearranged to minimize the index, which is adopted as the maximum relative error between the estimated marginal moments and the exact ones. The rearranged points are accepted as the representative points in PDEM when the index reaches the prescribed tolerance. Numerical example is investigated, showing that the proposed strategy can achieve the good tradeoff of efficiency and accuracy in PDEM for seismic response analysis of structures with uncertain parameters.