Time domain intrusive probabilistic seismic risk analysis of nonlinear shear frame structure

Uncertainty quantification in the calibration of numerical elements in nonlinear seismic analysis

“…Polynomial chaos expansions (PCEs) are a powerful metamodeling tool that has been introduced in earthquake engineering in recent years. [21][22][23][24] PCE can also be implemented as an efficient tool to conduct global sensitivity analysis. 25 In this paper, PCE metamodels are shown to be able to predict the output accurately with only hundreds of sets of training data.…”

“…PCEs are a powerful metamodeling tool that has been introduced in earthquake engineering in recent years. [21][22][23][24] In short, a PCE model can be defined as follows as a function of M input parameters: where Ψ 𝛼 are multivariate orthonormal polynomials corresponding to the distribution of X, 𝛼 is a multi-index that identifies the components of Ψ 𝛼 , and 𝑦 𝛼 are the coefficients that can be determined using training data.…”

“…PCEs are a powerful metamodeling tool that has been introduced in earthquake engineering in recent years 21–24 . In short, a PCE model can be defined as follows as a function of M input parameters: $$\begin{equation} \mathcal{M}\left( X \right)=\underset{\alpha \in {{\mathbb{N}}^{M}}}{\mathop \sum }\,{{y}_{\alpha }}{{\Psi }_{\alpha }}\left( X \right)\end{equation}$$where $${{{\Psi}}_\alpha }$$ are multivariate orthonormal polynomials corresponding to the distribution of X , α is a multi‐index that identifies the components of $${{{\Psi}}_\alpha }$$, and $${y_\alpha }$$ are the coefficients that can be determined using training data.…”

“…In order to overcome the extensive computational demand in the analysis, a metamodeling technique is introduced to predict the relation between calibration and global errors. Polynomial chaos expansions (PCEs) are a powerful metamodeling tool that has been introduced in earthquake engineering in recent years 21–24 . PCE can also be implemented as an efficient tool to conduct global sensitivity analysis 25 .…”

A modular methodology for time-domain stochastic seismic wave propagation

“…For engineering practices, time domain uncertain input motions can be simulated using the stochastic method (Boore 2003). For example, Wang et al (2020) proposed a methodology to simulate scenario-consistent time domain uncertain motions using stochastic Fourier amplitude spectra and Fourier phase derivative. It is also common practice to scale and select past-recorded seismic motions as the population of underlying uncertain seismic input by matching site-specific target spectrum.…”