Hierarchical Kriging Surrogate of the Seismic Response of a Steel Piping Network Based on Multi-Fidelity Hybrid and Computational Simulators
Giuseppe Abbiati1, Imad Abdallah2, Stefano Marelli2, Bruno Sudret2, Bozidar Stojadinovic1
1 Chair of Earthquake Engineering and Structural Dynamics, Institute of Structural Engineering (IBK), Department of Civil, Environmental and Geomatic Engineering (D-BAUG)
ETH Zürich, Switzerland
abbiati@ibk.baug.ethz.ch
stojadinovic@ibk.baug.ethz.ch
2 Chair of Risk, Safety and Uncertainty Quantification, Institute of Structural Engineering (IBK), Department of Civil, Environmental and Geomatic Engineering (D-BAUG)
ETH Zürich, Switzerland
abdallah@ibk.baug.ethz.ch
marelli@ibk.baug.ethz.ch
sudret@ibk.baug.ethz.ch
Abstract. When part of a structural system lacks of predictive numerical model, hybrid simulators can be conveniently used to emulate its seismic response history by replacing unknown subparts with laboratory experiments. Hybrid simulators suffer the same limitations of expensive-to-evaluate computational simulators and, in the current practice, solve deterministic structural systems. However, surrogate modeling, which is widely used in computer experiments, can be used to enable parametric/probabilistic studies. A pilot research conducted by the authors showed that few tens of hybrid simulations are sufficient to enable uncertainty propagation, global sensitivity and reliability analysis of time history response peaks of few-degrees-of-freedom hybrid systems with 2÷3 parameters and subjected to a unique seismic excitation signal. However, few tens of experiments are often not affordable when full-scale are tested. In order to circumvent such limitation, hierarchical Kriging is proposed to fuse computational and hybrid simulator outcomes into a unique multi-fidelity surrogate. In detail, a Kriging surrogate of a low-discrepancy computational simulator of the emulated system is used as trend of a hierarchical Kriging surrogate of the hybrid simulator response. A benchmark of the proposed method is conceived on a virtual piping network, which shows hysteretic behavior for the selected seismic loading. Results prove that hierarchical Kriging surrogates statistically outperform ordinary Kriging surrogates built on the sole hybrid simulator response.
Keywords: Hybrid simulator, computational simulator, multi-fidelity modeling, hierarchical Kriging, piping network.
