PDEM-Based Perspective to Probabilistic Seismic Response Analysis and Design of Earthquake-Resistant Engineering Structures

Abstract

A perspective based on the probability density evolution method (PDEM) to the probabilistic seismic response analysis and design of earthquake-resistant engineering structures is provided in this paper. The development of characterization of randomness in seismic ground motions and nonlinear seismic dynamic response analysis of engineering structures are first reviewed and found to be almost independent, which hinders rapid adoption of refined methods for seismic design. The approaches for stochastic dynamics, which is expected to bridge the above gap, in earthquake engineering are revisited, which results in the statement that more physically based methodology is in urgent need for nonlinear stochastic dynamic response analysis of structures. This is the role that the PDEM will play, and thus the theoretical basis and some new advances of PDEM, including the ensemble evolution form of the generalized density evolution equation, ensemble evolution–based dimension reduction of Fokker-Planck-Kolmogorov (FPK) equation, and the improved point rearrangement strategy by reducing the generalized F-discrepancy (GF-discrepancy) for PDEM, are discussed. The stochastic response analysis and reliability evaluation of a 25-story floor-shear frame structure subjected to seismic ground motion is studied as an example, demonstrating the fair accuracy and effectiveness of the PDEM. Problems to further studies are outlined.