High-dimensional points selection strategy for PDEM-based stochastic dynamic analysis of structures

Abstract

The Probability Density Evolution Method (PDEM) is effective for stochastic dynamic analysis of structures. Within PDEM, the selection of representative point sets and the computation of their assigned probabilities are critical for balancing accuracy and efficiency, particularly in high-dimensional scenarios. This paper presents a novel strategy for point selection tailored to these requirements. The strategy integrates a deterministic low-discrepancy point set with a Bayesian-based Assigned Probability (BAP) calculation procedure within the PDEM framework. Initially, a New Generating Vector-based Number-Theoretical Method (NGV-NTM) is developed to produce a high-dimensional low-discrepancy point set. This set is then transformed into the original random-variate space to form the representative point set. Subsequently, the BAP procedure calculates the assigned probabilities for the representative point set by employing a Gaussian model for the prior distribution and likelihood function, and estimating the posterior probabilities through solving a maximum a posteriori estimation problem. Once the assigned probabilities are obtained, the representative point set is rearranged to better align with the input distributions. This refined set is then used for the final PDEM-based analysis. The effectiveness of the proposed method is validated through two numerical examples, with results compared to those obtained using Monte Carlo simulations and Sobol sequences.