Considering structural modelling uncertainties using Bayesian cloud analysis

Quantifying the impact of modelling uncertainty on the seismic performance assessment is a crucial issue for existing buildings, considering the partial information available related to material properties, construction details and the uncertainty in the capacity models. The effect of structural modelling uncertainties on the seismic performance of existing buildings can be -under certain circumstances- comparable to that of uncertainty in ground motion representation. In this work, a modified version of Cloud analysis considering the (eventual) cases of global dynamic instability and adopting the critical demand to capacity ratio as the damage measure/decision variable, based on coupling the simple regression in the logarithmic space of structural response versus seismic intensity for a suite of registered records with logistic regression, has been implemented to consider the record-to-record variability, structural modelling uncertainties and the uncertainties in the parameters of the adopted fragility model. For each of the registered records within the suite of ground motion records, a different realization of the structural model has been generated through a standard Monte Carlo Simulation procedure. A Bayesian version of the Cloud method is employed, in which the uncertainty in the structural fragility model parameters is considered. This leads to a robust fragility estimate-reflecting both record-to-record variability and structural modeling uncertainties-- and a desired confidence interval defined around it -reflecting the uncertainty in the fragility model parameters. The longitudinal frame of an existing building in Van Nuys, CA, modeled in OpenSees considering the flexural-shear-axial interaction, has been employed in order to demonstrate this procedure. The critical demand to capacity ratio adopted as the damage measure/decision variable, corresponding to the component or mechanism that leads the structure closest to the onset of limit state (e.g., near collapse), is adopted as the structural response parameter. This structural response parameter can encompass both ductile and fragile failure mechanisms. Moreover, it can register a possible shift in the governing failure mechanism with increasing intensity. The selection of the suite of ground motion records has been based on a set of criteria that ensure the statistical significance of the linear regression in predicting the structural response as a function of the intensity measure.