Nonstationary spatial coherence modeling via wavelet packet transform and deep recurrent neural networks

For large-scale extended infrastructure like long-span bridges, the non-uniform ground motion excitation of multiple supports significantly affects structural responses. Traditional empirical models typically assume stationarity and neglect the temporal evolution of spatial coherence, which artificially smooths out transient intervals of high synchronization and compromises seismic safety assessments. To address this, a novel data-driven framework is proposed for modeling nonstationary coherence using the Wavelet Packet Transform (WPT) and deep sequence learning. WPT first extracts high-resolution time-frequency coherence features from 288 sequences in the SMART-1 dense array. To resolve the computational inconsistency caused by variable earthquake durations, the framework maps the temporal evolution into a normalized intensity domain using the analytic signal envelope ( En ). A Deep Ensembles Long Short-Term Memory (LSTM) architecture is then trained to autonomously learn the non-linear mapping between coherence and its governing parameters. A sequence-level Permutation Feature Importance analysis verifies the model's physical interpretability, revealing that En dynamically modulates coherence (contributing ∼10.2%). Evaluated on a completely unseen earthquake event, the deep ensemble demonstrates robust site-specific generalization (Pearson correlation of 0.78), successfully quantifying epistemic uncertainty and outperforming traditional point-based networks and analytical empirical models. Finally, a 30-run Monte Carlo simulation of a long-span suspension bridge confirms that the proposed framework captures more physically realistic structural demands. By correctly restoring synchronized motion during peak shaking phases, the nonstationary model simultaneously mitigates the exaggerated pseudo-static tearing demands and prevents the underestimation of synchronous inertial forces inherent to stationary assumptions. Note that the specific neural network parameters in the proposed model inherently reflect the localized soft alluvial conditions of the SMART-1 array.