Dimension-Reduction Modeling of Stochastic Mainshock-Aftershock Ground Motions via Weighted Multi-Objective Optimization and Vine-Copula Methods

The impact of mainshock-aftershock effects on civil structures has become a critical topic in earthquake engineering, and its accurate simulation is the premise and foundation for rational seismic design in engineering. However, current studies on mainshock-aftershock simulation face significant challenges. Most fail to capture the time-frequency nonstationary characteristics of ground motions, which are crucial for reflecting their dynamic properties. Additionally, the complex nonlinear correlations between mainshock and aftershock parameters, as well as within the parameters themselves, are often overlooked, reducing the physical consistency of models. Single-objective optimization methods struggle to simultaneously address time-domain, frequency-domain, and response spectrum features. Moreover, the computational complexity of high-dimensional random variables limits the efficiency and practical applicability of ground motion simulations. To address these challenges, this study proposes a new approach combining weighted multi-objective optimization, the Vine-Copula method, and dimension-reduction simulation. Multi-objective optimization ensures a balanced representation of time-domain, frequency-domain, and response spectrum features, while the Vine-Copula method captures the nonlinear dependencies between ground motion parameters. The dimension-reduction technique reduces computational complexity and improves simulation efficiency. Validation against recorded seismic data shows that the proposed method effectively captures the time-frequency nonstationary characteristics and parameter correlations of mainshock-aftershock ground motions. This method provides a robust and efficient tool for structural response analysis and reliability assessment based on the first-passage probability.