Seismic fragility analysis of structures based on Bayesian linear regression demand models

Bayesian linear regression (BLR) based demand prediction models are proposed for efficient seismic fragility analysis (SFA) of structures utilizing limited numbers of nonlinear time history analyses results. In doing so, two different BLR models i.e. one based on the classical Bayesian least squares regression and another based on the sparse Bayesian learning using Relevance Vector Machine are explored. The proposed models integrate both the record-to-record variation of seismic motions and uncertainties due to structural model parameters. The magnitude of uncertainty involved in the fragility estimate is represented by providing a confidence bound of the fragility curve. The effectiveness of the proposed BLR models are compared with the commonly used cloud method and the maximum likelihood estimates methods of SFA by considering a nonlinear single-degree-of-freedom system and a five-storey reinforced concrete building frame. It is observed that both the BLR models can estimate fragility with improved accuracy compared to those common analytical SFA approaches considering direct Monte Carlo simulation based fragility results as the benchmark.