A multi-fidelity Bayesian framework for robust seismic fragility assessment

Fragility analysis of structures via numerical methods involves a complex trade-off between the desired accuracy, the explicit consideration of uncertainties (both epistemic and aleatory) related to the numerical structural model and the available computational performance. This paper introduces a framework for deriving numerical fragility relationships based on multi-fidelity non-linear models of the structure under investigation and response-analysis types. The proposed framework aims to reduce the computational burden while achieving a desired accuracy of the fragility estimates without neglecting aleatory and epistemic uncertainties. The proposed approach is an extension of the well-known robust fragility (RF) analysis framework. Different model classes, each characterised by increasing refinement, are used to define multi-fidelity polynomial expansions of the fragility model parameters. Each analysis result is then considered as a ‘new observation’ in a Bayesian framework and used to update the coefficients of the polynomial expansions. An adaptive sampling algorithm is also proposed to futher improve the performance of the multi-fidelity framework. Specifically, such an adaptive sampling algorithm relies on partitioning the sample space and the Kullback–Leibler divergence to find the optimal sampling path. The sample space partitioning allows an analyst to specify different criteria and parameters of the algorithm for different regions, thus further improving the performance of the procedure. The proposed approach is illustrated for an archetype reinforced concrete (RC) frame for which two model classes are developed/analysed: the simple lateral mechanism analysis (SLaMA), coupled with the capacity spectrum method, and non-linear dynamic analysis. Both model classes involve a cloud-based approach employing unscaled real (i.e. recorded) ground motions. The fragility relationships derived with the proposed procedure are finally compared to those calculated by using only the most advanced/high-fidelity (HF) model class, thus quantifying the performance of the proposed approach and highlighting further research needs.