Hierarchical Bayesian calibration of Bouc–Wen hysteretic models with applications to seismic isolators

Abstract

Harnessing the potential of base-isolation devices requires both experimental testing campaigns to observe their behavior as well as properly calibrated hysteretic models to predict their response for future hazards. However, calibrating a nonlinear hysteretic model based on a single experimental test might omit critical behaviors observed in other tests. This study performs hierarchical Bayesian calibrations for a series of bi-axial hysteretic models from the Bouc–Wen family that attempt to capture the restoring force behavior observed in two steel yielding damper pairs during a full-scale testing campaign at E-Defense. Critically, the hierarchical approaches incorporate data from numerous tests featuring different ground motions into calibration. Two different treatments of the prediction error variance are explored to cover both non-informative assumptions as well as probabilistic models for the error variance. The results demonstrate that the two different approaches yield fairly comparable measures of parametric uncertainty, e.g., posterior distributions, for a given device, but the different devices actually produce different degrees of uncertainty in the hysteretic shape parameters. Further, the impact of the two different approaches is minimal in terms of the prediction error variance for observed data, but the probabilistic model is much better suited to unobserved data. A joint calibration considering data from both devices also reveals that adding data from a second device does not necessarily result in a reduction in the overall uncertainty of model parameters or response predictions.

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