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Abstract This study introduces an approach for probabilistic seismic performance estimation, which focuses on the probability of intensity measures exceeding a specified value based on engineering demand parameters. Conventional methods face challenges owing to the increase in computational costs associated with the uncertainties in earthquake scenarios. To address this, we use high‐fidelity (HF) and low‐fidelity (LF) model data to develop a multilevel hierarchy of surrogate models, which improves the simulation‐based probabilistic estimation. However, designing a reliable LF model and ensuring the accuracy of the surrogate model hierarchy remains challenging. Herein, we present a multi‐fidelity Monte Carlo (MFMC) predictor combined with a conventional surrogate model to improve probabilistic seismic performance estimation, thereby leveraging LF model efficiency and HF data accuracy for unbiased results. We addressed the challenge of constructing a suitable LF model by using a surrogate model trained from limited HF data. The MFMC predictor improves the accuracy of probabilistic analysis than the surrogate models trained from limited HF data. Further, the automatic relevance determination method is introduced to select the most appropriate inputs for the surrogate model. A case study featuring a special moment‐resistant frame, subject to uncertainties from both ground motion and structural properties, illustrates the efficiency of the method. A LF model is developed using the Kriging method, followed by the construction of the MFMC predictor for probabilistic analysis, thereby leveraging both limited HF and numerous LF data. Comparing the exceedance probability curves obtained from the MFMC predictor with those from direct Monte Carlo simulations and conventional Kriging showed that our proposed method offers a promising tool for probabilistic seismic performance estimation under uncertainty.

Complex dynamic behavior of nonlinear structures makes it challenging for uncertainty analysis through Monte Carlo simulations (MCS). Surrogate modeling presents an efficient and accurate computational alternative for a large number of MCS. The previous study has demonstrated that the multi-input multi-output nonlinear autoregressive with exogenous input (MIMO-NARX) model provides good discrete-time representations of deterministic nonlinear multi-degree-of-freedom (MDOF) structural dynamic systems. Model order reduction (MOR) is executed to eliminate insignificant modes to reduce the computational burden due to too many degrees of freedom. In this study, the MIMO-NARX strategy is integrated with different meta-modeling techniques for uncertainty analysis. Different meta-models including Kriging, polynomial chaos expansion (PCE), and arbitrary polynomial chaos (APC) are used to surrogate the NARX coefficients for system uncertainties. A nine-DOF structure is used as an MDOF dynamic system to evaluate different meta-models for the MIMO-NARX. Good fitness of statistical responses is observed between the MCS results of the original system and all surrogated MIMO-NARX predictions. It is demonstrated that the APC-NARX model with the advantage of being data-driven is the most efficient and accurate tool for uncertainty quantification of nonlinear structural dynamics.