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

Abstract

Modeling uncertainty in structural models can greatly affect the reliability of nonlinear time history results, which are central to performance‐based earthquake engineering. A crucial source of modeling uncertainty is the uncertainty in the parameters of constitutive models, which simulate the hysteretic behavior of key structural components. In current research and engineering practice, it is assumed that the accuracy of a nonlinear structural model is achieved by component calibration, which is conducted by trying to best match the response of a numerical model of a component to test results under a standardized quasi‐static loading regime. However, previous research has shown that even a very well‐fitted component‐level calibration might result in considerable errors in the system‐level structural dynamic response. This study is an initial attempt to investigate calibration relevance incorporating a rigorous uncertainty quantification framework. In the proposed framework, parameters of a constitutive model are considered as random inputs. Calibration error at the component level and global error at the system level are quantified based on the discrepancies between the simulation models with probabilistic inputs and reference models. Polynomial chaos expansions (PCEs) metamodels are implemented to conduct sensitivity analysis and investigate calibration relevance. Three buckling restrained braced frames (BRBFs) with different heights are investigated using the proposed framework. Four calibration methods’ relevance with global errors based on three engineering demand parameters (EDPs) are studied. The results allow for the identification of optimum hyperparameters to achieve peak calibration relevance and to evaluate different calibration methods for several EDPs for the three BRBFs.

Hybrid‐simulation‐based model calibration method for nonlinear seismic analysis

“…1 Zsarnóczay and Baker 1 proposed a framework of virtual experiments to investigate calibration relevance in order to evaluate different calibration methods. Zhang et al 16 further incorporated a rigorous uncertainty quantification framework to study calibration relevance. This framework utilized the method of LHS to propagate uncertainties of hysteretic parameters and a metamodel technique for estimating calibration relevance and conducting global sensitivity analysis.…”

“…This framework utilized the method of LHS to propagate uncertainties of hysteretic parameters and a metamodel technique for estimating calibration relevance and conducting global sensitivity analysis. 16 However, these two initial attempts that formulize the problem of calibration relevance are still F I G U R E 1 Four testing methods with different levels of complexity. concentrated on calibrations in method IV.…”

“…Zsarnóczay and Baker 1 proposed a framework of virtual experiments to investigate calibration relevance in order to evaluate different calibration methods. Zhang et al 16 . further incorporated a rigorous uncertainty quantification framework to study calibration relevance.…”

“…further incorporated a rigorous uncertainty quantification framework to study calibration relevance. This framework utilized the method of LHS to propagate uncertainties of hysteretic parameters and a metamodel technique for estimating calibration relevance and conducting global sensitivity analysis 16 . However, these two initial attempts that formulize the problem of calibration relevance are still concentrated on calibrations in method IV.…”