Efficient seismic fragility analysis method utilizing ground motion clustering and probabilistic machine learning

Machine learning (ML) techniques have been recently adopted in engineering practice to define the relationship between seismic intensity measure (IM) and structural damage measure (DM) based on a limited set of numerical simulations. However, they only offer deterministic prediction, which failing to reflect the aleatoric uncertainty related to input variables (e.g. seismic excitation and structural properties) and the epistemic uncertainty associated with modeling. This paper proposes a probabilistic ML method combined with ground motion clustering for seismic fragility analysis of structures. In the probabilistic ML method, by the natural gradient boosting (NGBoost), the conditional probability distribution can be evaluated for each structural response instead of producing point estimation. In addition, ground motion clustering is based on the time series K-means, which can capture the hidden features and select the representative subset of ground motions. The proposed framework was implemented for seismic fragility analysis of a typical 3-span, 6-storey reinforced concrete (RC) frame system. Analysis results indicated that the point estimation accuracy of the NGBoost was comparable to that based on excellent deterministic ML techniques, e.g. artificial neural network (ANN), random forest (RF), extreme gradient boosting (XGBoost). Moreover, the probabilistic prediction can efficiently provide the conditional probability of exceeding a damaged state in the structure given an IM level, eliminating the need for additional input of uncertainties from structural properties in traditional ML methods. Ultimately, the cluster-based ground motion selection reduced the model uncertainty and improves the prediction accuracy of the probabilistic ML model.