Efficient probabilistic response analysis of large-scale engineering structures under stochastic excitation via the DR-PDEE incorporating an auxiliary diffusion process
Über dieses Buch
Probabilistic response analysis of engineering structures under stochastic excitation remains a critical and long-standing challenge. The main difficulties arise from the high dimensionality of structural systems, nonlinear material behavior, and uncertainties in both system parameters and external excitations. To address these challenges, an efficient framework is developed based on the dimension-reduced probability density evolution equation (DR-PDEE) incorporating an auxiliary diffusion process. The DR-PDEE is a low-dimensional partial differential equation (PDE) governing the instantaneous probability density function (PDF) of a path-continuous response of interest in a high-dimensional dynamical system. However, under non-white stochastic excitation, the intrinsic diffusion function of the response generally vanishes. This zero-diffusion issue complicates the numerical solution of the DR-PDEE. To overcome this difficulty, white noise statistically correlated with the original non-white excitation is constructed and applied to a simple stochastic system. The system output is then selected as the auxiliary diffusion process. Consequently, a two-dimensional DR-PDEE with nonzero diffusion is formulated for the joint process of the response of interest and the auxiliary variable. This formulation avoids the construction of an equivalent linear filter and provides high flexibility for complex non-white excitations. The proposed method is applied to a high-rise reinforced concrete (RC) frame-core tube structure subjected to stochastic near-field seismic excitation. Nonlinear constitutive behavior of both reinforcing steel and concrete is considered, together with uncertainties in the concrete material properties. The proposed method accurately captures the pronounced nonstationary and non-Gaussian features of the response PDFs. The results demonstrate its applicability and efficiency for probabilistic response analysis of large-scale nonlinear structures under complex non-white stochastic excitations.
